### Pages

- 10 times table – Explanation & Examples
- 11 times table – Explanation & Examples
- 12 Times Table - Explanation & Examples
- 13 Times Table - Explanation & Examples
- 14 Times Table - Explanation & Examples
- 15 Times Table - Explanation & Examples
- 16 times table - Explanation & Examples
- 16TH CENTURY MATHEMATICS
- 17 Times Table - Explanation & Example
- 17TH CENTURY MATHEMATICS
- 18 Times Table - Explanation & Examples
- 18TH CENTURY MATHEMATICS
- 19 Times Table - Explanation & Examples
- 19TH CENTURY MATHEMATICS
- 2 Times Table - Explanation & Examples
- 20 Times Table - Explanation & Examples
- 20TH CENTURY MATHEMATICS
- 21 Times Table - Explanation & Examples
- 22 Times Table - Explanation & Examples
- 23 Times Table - Explanation & Examples
- 24 Times Table - Explanation & Examples
- 3 4 5 Right Triangles – Explanation & Examples
- 3 Times Table - Explanation & Examples
- 30°-60°-90° Triangle – Explanation & Examples
- 360 Degree Angle
- 3d Coordinate System - Definition, Graphing Techniques, and Examples
- 3d vector - Explanation and Examples
- 4 Times Table - Explanation & Examples
- 45°-45°-90° Triangle – Explanation & Examples
- 5 Times Table - Explanation & Examples
- 6 Times Table - Explanation & Examples
- 7 Times Table - Explanation & Examples
- 8 times table – Explanation & Examples
- 9 times table – Explanation & Examples
- About Us
- Abraham De Moivre: History, Biography, and Accomplishments
- Absolute Convergence - Definition, Condition, and Examples
- Absolute maximum - Definition, Conditions, and Examples
- Absolute minimum - Definition, Conditions, and Examples
- Absolute Value – Properties & Examples
- Absolute Value Inequalities – Explanation & Examples
- Acute Angle
- Adding and Subtracting Decimals – Explanation & Examples
- Adding and Subtracting Expressions – Methods & Examples
- Adding and Subtracting in Scientific Notation – Methods & Examples
- Adding and Subtracting Integers – Methods & Examples
- Adding and Subtracting Polynomials – Explanation & Examples
- Adding and Subtracting Rational Expressions – Techniques & Examples
- Adding complex numbers - Techniques, Explanation, and Examples
- Adding Exponents – Techniques & Examples
- Adding Fractions – Methods & Examples
- Adding Mixed Numbers – Methods & Examples
- Addition – Explanation & Examples
- Addition Property of Equality - Definition and Examples
- Al-Khwarizmi - The Father of Algebra
- Alan Turing: Cracking the 'Enigma' Code
- Algebra
- Algebraic Expression – Explanation & Examples
- All About Yang Hui - A Nobel Chinese Mathematician
- Alternate Exterior Angles – Explanation & Examples
- Alternate Interior Angles – Explanation & Examples
- Alternate Segment Theorem – Explanation & Examples
- Alternating series - Definition, Convergence, and Sum
- Alternating series test - Definition, Conditions, and Examples
- Andre Weil: Founding Member of the Mathematical Bourbaki Group
- Angle between the two Vectors - Explanation and Examples
- Angle of Depression – Detailed Explanation and Examples
- Angle of Elevation — Detailed Explanation and Examples
- Angles – Explanation & Examples
- Angles in a Circle – Explanation & Examples
- Angles in Polygons – Explanation & Examples
- Angles of a Triangle – Explanation & Examples
- Anova Test - Explanation & Examples
- Antiderivative - Definition, Techniques, and Examples
- Applications of Trigonometry - Explanation & Examples
- Approximating Integrals - Midpoint, Trapezoidal, and Simpson's Rule
- Arc of a Circle – Explanation & Examples
- ARCHIMEDES OF SYRACUSE - Eureka & The Principle
- Area Between Two Curves - Definition, Process, and Examples
- Area of a Parallelogram – Explanation & Examples
- Area of an Ellipse – Explanation & Examples
- Area of Circle – Explanation & Examples
- Area of Polygons – Explanation & Examples
- Area of Rectangles – Explanation & Examples
- Area of Rhombus – Explanation & Examples
- Area of Sector – Explanation & Examples
- Area of Shaded Region
- Area of Squares – Explanation & Examples
- Area of Trapezoid – Explanation & Examples
- Area of Triangle – Explanation & Examples
- Area Under the Curve - Definition, Types, and Examples
- Arithmetic
- Arithmetic Mean
- Arithmetic Operations on Functions – Explanation & Examples
- Arithmetic sequence - Pattern, Formula, and Explanation
- Arithmetic Series - Definition, Formula, and Examples
- Associative Property – Explanation with Examples
- Asymptote - Three Different Types, Properties, and Examples
- Bar graph – Explanation & Examples
- Basic Algebra – Explanation & Examples
- Bayes Theorem - Explanation & Examples
- Bernhard Riemann - The Notorius German Mathematician
- Bernoulli Brothers -The Math Family
- Bernoulli Distribution - Explanation & Examples
- Bertrand Russell & Alfred North Whitehead - Principia Mathematica 1+1=2
- Bhaskara II - History, Biography, and Accomplishments
- Binomial Series - Definition, General Form, and Examples
- Binomial Theorem – Explanation & Examples
- Blaise Pascal Math
- Blog
- BOLYAI AND LOBACHEVSKY & HYPERBOLIC GEOMETRY
- Box and whisker plot
- Brahmagupta: Mathematician and Astronomer
- Buy Generic Ambien Online
- Calculus
- Car Depreciation Calculator + Online Solver With Free Steps
- Carl Friedrich Gauss: The Prince of Mathematics
- Carroll diagram
- Categorical Data
- Center of Mass - Definition, Formula, and Examples
- Central Limit Theorem - Explanation & Examples
- Chain rule - Step-by-Step Process, Explanation, and Example
- Change of base - Formula, Explanation, and Example
- Change of Variables in Multiple Integrals - Technique, Steps, and Examples
- Characteristic Equations - Definition, General Form, and Examples
- Chebyshev's Theorem - Explanation & Examples
- Chi square - Explanation & Examples
- Chinese Mathematics
- Chords of a Circle – Explanation & Examples
- Circles – Explanation & Examples
- Circumference of a Circle – Explanation & Examples
- Class width
- Cofunction identities
- Coin flip probability – Explanation & Examples
- Coinciding lines - Explanation and Examples
- Column vector - Explanation & Examples
- Combinations - Explanation & Examples
- Combine Like Terms – Methods & Examples
- Common and Natural Logarithms – Explanation & Examples
- Common difference - Formula, Explanation, and Examples
- Commutative Property
- Compare & Order Numbers – Techniques & Examples
- Comparing Fractions – According to the Denominators
- Complement of a set - Definition and Examples
- Complementary Events
- Completing the Square – Explanation & Examples
- Complex Fractions – Explanation & Examples
- Complex Numbers - Properties, Graph, and Examples
- Complex rational expressions - Definition, Methods, and Examples
- Complimentary Angles – Explanation & Examples
- Composite Functions – Explanation & Examples
- Compound Inequalities – Explanation & Examples
- Compound Interest – Explanation & Examples
- Concavity calculus - Concave Up, Concave Down, and Points of Inflection
- Condensing logarithms - Properties, Explanation, and Examples
- Conditional Convergence - Definition, Condition, and Examples
- Conditional probability - Explanation & Examples
- Conditional Statement
- Congruent Triangles – Explanation & Examples
- Conic Sections - Types, Properties, and Examples
- Conjugate math - Explanation and Examples
- Constant of Proportionality – Explanation & Examples
- Construct A 60 Degree Angle - Explanation & Examples
- Construct a Line Segment – Explanation & Examples
- Construct a Parallelogram
- Construct a Perpendicular Line
- Construct a Rectangle
- Construct a Square
- Construct a Triangle - Explanation & Examples
- Construct an Angle Bisector - Explanation & Examples
- Construct Parallel Lines - Explanation & Examples
- Constructing Perpendicular Bisector – Explanation & Examples
- Construction of A 30 Degree Angle - Explanation & Examples
- Construction of a 45 Degree Angle - Explanation & Examples
- Contact
- Continuous function - Conditions, Discontinuities, and Examples
- Convergent series - Definition, Tests, and Examples
- Converse Statement
- Converting Fractions – to Different Decimal Forms
- Converting to Scientific Notation – Technique & Examples
- Cookie Policy
- Coordinate Geometry – Explanation & Examples
- Coordinate Plane – Explanation & Examples
- Coplanar Lines - Explanations & Examples
- Correlation Coefficient
- Corresponding Angles – Explanation & Examples
- Cos Graph - Detailed Examples and Explanation
- Cosine – Explanation & Examples
- Coterminal Angles – Detailed Explanation & Examples
- Counterexample
- Cramer's rule - Explanation & Examples
- Critical numbers - Definition, Process, and Examples
- Cross Multiplication – Techniques & Examples
- Cross product - Explanation & Examples
- Cumulative Frequency – Explanation & Examples
- Curl Vector Field - Definition, Formula, and Examples
- Curve sketching - Properties, Steps, and Examples
- Cylindrical Coordinates - Definition, Graph, and Examples
- David Hilbert - The Foundations of Geometry
- De Moivre's theorem - Formulas, Explanation, and Examples
- Decimal Place Value – Explanation & Examples
- Degree and Radians – Explanation & Examples
- Demorgan's law - Explanation and Examples
- Dependent events - Explanation & Examples
- Derivative calculus - Definition, Formula, and Examples
- Derivative of arctan - Derivation, Explanation, and Example
- Derivative of cotx - Derivation, Explanation, and Example
- Derivative of csc - Derivation, Explanation, and Example
- Derivative of ln - Derivation, Explanation, and Example
- Derivative of secx - Derivation, Explanation, and Example
- Derivative rules - Common Rules, Explanations, and Examples
- Derivative test - Types, Explanation, and Examples
- Derivatives of Vectors - Definition, Properties, and Examples
- Describing Sets – Explanation & Examples
- Determinant of a 2x2 matrix
- Determinant of a 3x3 matrix - Explanation & Examples
- Determinant of a matrix - Explanation & Examples
- Diagonal matrix - Explanation & Examples
- Dice probability - Explanation & Examples
- Difference of Squares – Explanation & Examples
- Difference Quotient - Definition, Formula, and Examples
- Difference rule - Derivation, Explanation, and Example
- Differential Equations - Definition, Types, and Solutions
- Dilation in Geometry - Explanation and Examples
- Dimension of a matrix - Explanation & Examples
- Diophantus of Alexandria
- Dirac Delta Function - Definition, Form, and Applications
- Direction of a vector - Explanation and Examples
- Directional Derivative - Definition, Properties, and Examples
- Directly Proportional – Explanation & Examples
- Discrete Data
- Disjoint sets - Explanation and Examples
- Disk Method - Definition, Formula, and Volume of Solids
- Distance between polar coordinates - Derivation, Process, and Examples
- Distance Formula – Explanation & Examples
- Distributive Property – Definition & Examples
- Distributive Property of Equality – Explanation and Examples
- Divergence of a Vector Field - Definition, Formula, and Examples
- Divergent series math- Definition, Divergence Test, and Examples
- Dividing complex numbers - Techniques, Explanation, and Examples
- Dividing Decimals – Explanation & Examples
- Dividing Expressions – Methods & Examples
- Dividing Fractions – Methods & Examples
- Dividing Mixed Numbers – Methods & Examples
- Dividing Numbers in Scientific Notation – Technique & Examples
- Dividing Polynomials – Explanation & Examples
- Dividing Rational Expressions – Techniques & Examples
- Division – Explanation & Examples
- Division Property of Equality – Explanation and Examples
- Domain and Range of a Function – Explanation & Examples
- Dot Plot
- Double Angle Formula: Examples and Explanation
- Double Integrals - Definition, Formula, and Examples
- Double Integrals in Polar Coordinates - Definition, Formula, and Examples
- Egyptian Mathematics - Numbers & Numerals
- Ellipse - Properties, Components, and Graph
- Empty Set – Explanation & Examples
- Equal Vectors – Explanation & Examples
- Equation of a Line – Explanation & Examples
- Equation of a Plane - Definition, General Forms, and Examples
- Equivalent Fractions – Explanation & Examples
- Equivalent matrices - Explanation & Examples
- EUCLID OF ALEXANDRIA - The Father of Geometry
- Evaluating limits - Methods, Explanation, and Examples
- Evaluating Trig Functions: Explanation and Examples
- Evariste Galois
- Even and Odd Functions - Properties & Examples
- Even Odd Identities - Examples and Explanation
- Exact Equations - General Form, Solutions, and Examples
- Expanded Notation – The Way to Expand Numbers
- Expanding Expressions – Techniques & Examples
- Expanding logarithms - Properties, Examples, and Explanation
- Experimental Probability - Explanation & Examples
- Exponential derivative - Derivation, Explanation, and Example
- Exponential function - Properties, Graphs, & Applications
- Exterior Angle Theorem – Explanation & Examples
- Factor by Grouping – Methods & Examples
- Factor Theorem – Method & Examples
- Factorial - Explanation & Examples
- Factoring Quadratic Equations – Methods & Examples
- Factoring Trigonometric Expressions - Examples and Explanation
- Factoring Trinomial – Method & Examples
- Factoring Trinomials by Trial and Error – Method & Examples
- Factoring Trinomials with Two Variables – Method & Examples
- Factors - All Factors of a Number
- Factor of -6: Prime Factorization, Methods, Tree and Examples
- Factor of 12: Prime Factorization, Methods, Tree and Examples
- Factor of 176: Prime Factorization, Methods, Tree, and Examples
- Factor of 21: Prime Factorization, Methods and Examples
- Factors of -40: Prime Factorization, Methods, Tree, and Examples
- Factors of -48: Prime Factorization, Methods, Tree, and Examples
- Factors of 10: Prime Factorization, Methods, Tree, and Examples
- Factors of 100: Prime Factorization, Method, Tree, and Examples
- Factors of 105: Prime Factorization, Methods, Tree, and Examples
- Factors of 108: Prime Factorization, Methods, Tree, and Examples
- Factors of 11: Prime Factorization, Methods, Tree, and Examples
- Factors of 112: Prime Factorization, Methods, Tree, and Examples
- Factors of 119: Prime Factorization, Methods, Tree, and Examples
- Factors of 120: Prime Factorization, Methods, Tree, and Examples
- Factors of 121: Prime Factorization, Methods, Tree, and Examples
- Factors of 125: Prime Factorization, Methods, Tree, and Examples
- Factors of 126: Prime Factorization, Methods, Tree, and Examples
- Factors of 128: Prime Factorization, Methods, Tree, and Examples
- Factors of 13: Prime Factorization, Methods, Tree, and Examples
- Factors of 130: Prime Factorization, Methods, Tree, and Examples
- Factors of 135: Prime Factorization, Methods, Tree, and Examples
- Factors of 136: Prime Factorization, Methods, Tree, and Examples
- Factors of 14: Prime Factorization, Methods, Tree, And Examples
- Factors of 140: Prime Factorization, Methods, Tree, and Examples
- Factors of 144: Prime Factorization, Methods, Tree, and Examples
- Factors of 147: Prime Factorization, Methods, and Examples
- Factors of 15: Prime Factorization, Methods and Examples
- Factors of 150: Prime Factorization, Methods, and Examples
- Factors of 16: Prime factorization, Methods, Tree and Examples
- Factors of 160: Prime Factorization, Methods, and Examples
- Factors of 162: Prime Factorization, Methods, Tree, and Examples
- Factors of 168: Prime Factorization, Methods, Tree, and Examples
- Factors of 169: Prime Factorization, Methods, Tree, and Examples
- Factors of 17: Prime Factorization, Methods, Tree, and Examples
- Factors of 18: Prime Factorization, Methods, Tree, and Examples
- Factors of 180: Prime Factorization, Methods, Tree, and Examples
- Factors of 19: Prime Factorization, Methods, Tree, and Examples
- Factors of 192: Prime Factorization, Methods, Tree and Examples
- Factors of 196: Prime Factorization, Methods, Tree, and Example
- Factors of 2: Prime Factorization, Methods, Tree, and Examples
- Factors of 20: Prime factorization, Methods, Tree, and Examples
- Factors of 200: Prime Factorization, Methods, Tree, and Examples
- Factors of 210: Prime Factorization, Methods, Tree, and Examples
- Factors of 216: Prime Factorization, Methods, and Example
- Factors of 22: Prime Factorization, Methods, Tree, And Examples
- Factors of 224: Prime Factorization, Methods, Tree and Examples
- Factors of 225: Prime Factorization, Methods, Tree, and Examples
- Factors of 23: Prime Factorization, Methods, Tree, and Examples
- Factors of 24: Prime Factorization, Methods, Tree, and Examples
- Factors of 240: Prime Factorization, Methods, Tree and Example
- Factors of 25: Prime Factorization, Methods, Tree, and Examples
- Factors of 252: Prime Factorization, Methods, Tree, and Examples
- Factors of 26: Prime Factorization, Methods, Tree, and Examples
- Factors of 27: Prime Factorization, Methods, Tree, and Examples
- Factors of 28: Prime Factorization, Methods, Tree, and Examples
- Factors of 289: Prime Factorization, Methods, Tree, and Examples
- Factors of 29: Prime Factorization, Methods, Tree, and Examples
- Factors of 3: Prime Factorization, Methods, Tree, and Examples
- Factors of 30: Prime Factorization, Methods, Tree, and Examples
- Factors of 300: Prime Factorization, Methods, Tree, and Examples
- Factors of 31: Prime Factorization, Methods, Tree, and Examples
- Factors of 32: Prime Factorization, Methods, and Examples
- Factors of 33: Prime Factorization, Methods, Tree, and Examples
- Factors of 336: Prime Factorization, Methods, Tree, and Examples
- Factors of 34: Prime Factorization, Methods, Tree, and Examples
- Factors of 35: Prime Factorization, Methods, Tree, and Examples
- Factors of 36: Prime Factorization, Methods, Tree, and Examples
- Factors of 37: Prime Factorization, Methods, Tree, and Examples
- Factors of 38: Prime Factorization, Methods, Trees, And Examples
- Factors of 384: Prime Factorization, Methods, Tree, and Examples
- Factors of 39: Prime Factorization, Methods, Tree, And Examples
- Factors of 4: Prime Factorization, Methods, Tree, and Examples
- Factors of 40: Prime Factorization, Methods, Tree, and Examples
- Factors of 41: Prime Factorization, Methods, Tree, and Examples
- Factors of 42: Prime Factorization, Methods, Tree, and Examples
- Factors of 43: Prime Factorization, Methods, Tree, and Examples
- Factors of 432: Prime Factorization, Methods, Tree, and Examples
- Factors of 44: Prime Factorization, Methods, Tree, And Examples
- Factors of 45: Prime Factorization, Methods, Tree, and Examples
- Factors of 46: Prime Factorization, Methods, Tree, and Examples
- Factors of 47: Prime Factorization, Methods, Tree, and Examples
- Factors of 48: Prime Factorization, Methods, and Examples
- Factors of 49: Prime Factorization, Methods, Tree, and Examples
- Factors of 5: Prime Factorization, Methods, Tree, and Examples
- Factors of 50: Prime Factorization, Methods, Tree, and Examples
- Factors of 500: Prime Factorization, Methods, Tree, and Examples
- Factors of 51: Prime Factorization, Methods, Tree, and Examples
- Factors of 512: Prime Factorization, Methods, Tree, and Examples
- Factors of 52: Prime Factorization, Methods, Tree, And Examples
- Factors of 53: Prime Factorization, Methods, Tree, and Examples
- Factors of 54: Prime Factorization, Methods, Tree, and Examples
- Factors of 55: Prime Factorization, Methods, Tree, and Examples
- Factors of 56: Prime Factorization, Methods, Tree, and Examples
- Factors of 57: Prime Factorization, Methods, Tree, and Examples
- Factors of 576: Prime Factorization, Methods, Tree, and Examples
- Factors of 58: Prime Factorization, Method, Tree, and Examples
- Factors of 6: Prime Factorization, Methods, Tree, and Examples
- Factors of 60: Prime Factorization, Methods, Tree, and Examples
- Factors of 600: Prime Factorization, Methods, and Examples
- Factors of 61: Prime Factorization, Methods, Tree, and Examples
- Factors of 62: Prime Factorization, Methods, Tree, and Examples
- Factors of 625: Prime Factorization, Methods, Tree, and Examples
- Factors of 63: Prime factorization, Methods, Tree, and Examples
- Factors of 64: Prime Factorization, Methods, Tree, and Examples
- Factors of 65: Prime Factorization, Methods, Tree, And Examples
- Factors of 66: Prime Factorization, Methods, Tree, and Examples
- Factors of 67: Prime Factorization, Methods, Tree, and Examples
- Factors of 68: Prime Factorization, Methods, Tree, and Examples
- Factors of 69: Prime Factorization, Methods, Tree, and Examples
- Factors of 7: Prime Factorization, Methods, Tree, and Examples
- Factors of 70: Prime Factorization, Methods, Tree, and Examples
- Factors of 72: Prime Factorization, Methods, Tree and Examples
- Factors of 73: Prime Factorization, Methods, Tree, and Examples
- Factors of 74: Prime Factorization, Methods, Tree, and Examples
- Factors of 75: Prime Factorization, Methods, Tree, and Examples
- Factors of 76: Prime Factorization, Methods, Tree, and Examples
- Factors of 78: Prime Factorization, Methods, Tree, and Examples
- Factors of 8: Prime Factorization, Methods, Tree, and Examples
- Factors of 80: Prime Factorization, Methods, Tree, and Examples
- Factors of 81: Prime Factorization, Methods, Tree, and Examples
- Factors of 83: Prime Factorization, Methods, Tree, and Examples
- Factors of 84: Prime Factorization, Methods, Tree, and Examples
- Factors of 85: Prime Factorization, Methods, Tree, and Examples
- Factors of 87: Prime Factorization, Methods, Tree, and Examples
- Factors of 88: Prime Factorization, Methods, Tree, and Examples
- Factors of 89: Prime Factorization, Methods, Tree, And Examples
- Factors of 9: Prime Factorization, Methods, Tree, and Examples
- Factors of 90: Prime Factorization, Methods, Tree, and Examples
- Factors of 900: Prime Factorization, Methods and Examples
- Factors of 91: Prime Factorization, Methods, Tree, and Examples
- Factors of 93: Prime Factorization, Methods, Tree, and Examples
- Factors of 94: Prime Factorization, Methods, Tree, and Examples
- Factors of 96: Prime Factorization, Method, Tree, and Examples
- Factors of 98: Prime Factorization, Method, Tree, and Examples
- Factors of 99: Prime Factorization, Methods, Tree, and Examples

- Factors & Multiples – Differences & Examples
- Fibonacci Leonardo (of Pisa) - Italian Number Theorist
- Finding Common Factors – Explanation & Examples
- Finite Sets – Explanation & Examples
- First Order Linear Differential Equation - Form, Solution, and Examples
- Flight Time Calculator + Online Solver With Free Steps
- Foil Method – Explanation & Examples
- Forms of Linear Equations – Explanation & Examples
- Fractional Exponents – Explanation & Examples
- Fractions – Definition & Types
- Fractions to Decimals – Conversion Methods and Examples
- Frequency Distribution
- Frequency statistic – Explanation & Examples
- Frequency table
- Function Notation – Explanation & Examples
- Fundamental counting principle - Explanation & Examples
- Fundamental Theorem for Line Integrals - Theorem and Examples
- Fundamental Theorem of Calculus - Parts, Application, and Examples
- G. H. Hardy: Ramanujan's Mentor
- Gauss jordan elimination - Explanation & Examples
- Geometric Construction - Explanation & Examples
- Geometric Nets – Explanation & Examples
- Geometric probability - Explanation and Examples
- Geometric sequence - Pattern, Formula, and Explanation
- Geometric Series - Definition, Formula, and Examples
- Geometry
- Georg Cantor - The Man Who Founded Set Theory
- George Boole: Inventor of Boolean Logic
- George Peacock - History, biography and accomplishments
- Girard Desargues’s Phenomenal Contributions To Geometry
- Glossary of Mathematical Terms & Definition
- Golden Ratio – Explanation and Examples
- Gottfried Wilhelm Leibniz - The True Father of Calculus?
- Graphing Cubic Functions – Explanation & Examples
- Graphing Exponential Functions – Explanation & Examples
- Graphing Linear Equations – Explanation & Examples
- Graphing Linear Inequalities – Explanation & Examples
- Graphing Linear Inequalities – Explanation & Examples
- Graphing Quadratic Functions - Explanation & Examples
- Graphing Reciprocal Functions – Explanation & Examples
- Graphing Trig Functions - Examples and Explanation
- Graphs of Logarithmic Function – Explanation & Examples
- Greater than – Explanation & Examples
- Greatest Common Factor
- Greatest Integer Function - Explanation & Examples
- GREEK MATHEMATICS & MATHEMATICIAN - Numerals and Numbers
- Green's theorem - Theorem, Applications, and Examples
- Half Angle Formula: Examples and Explanation
- Harmonic series - Properties, Formula, and Divergence
- HELLENISTIC MATHEMATICS
- Henri Poincare and The Chaos Theory
- Hippocrates of Chios – History, biography and accomplishments
- Histogram
- Home
- Homogeneous Differential Equation - Definition, Solutions, and Examples
- Horizontal asymptote - Properties, Graphs, and Examples
- Horizontal Compression - Properties, Graph, & Examples
- Horizontal Stretch - Properties, Graph, & Examples
- Hurt Gödel: The Eccentric Genius
- Hyperbola - Properties, Components, and Graph
- Hyperbolic functions - Graphs, Properties, and Examples
- Hypotenuse Leg Theorem – Explanation & Examples
- Identity matrix - Explanation & Examples
- Identity Property – Explanation with Examples
- Implicit differentiation - Definition, Process, and Examples
- Improper Integrals - Definition, Types, and Examples
- Independent events - Explanation & Examples
- index
- INDIAN MATHEMATICS & MATHEMATICIANS
- Infinite series - Properties, Partial Sum, and Conditions
- Infinite Sets – Explanation & Examples
- Integers – Explanation & Examples
- Integral Calculus - Definition,Techniques, and Application
- Integral Properties - Definition, Process, and Proof
- Integral Test - Definition, Conditions, and Examples
- Integrals of Inverse Trig Functions - Definition, Formulas, and Examples
- Integrating Exponential Functions - Formulas, Process, and Examples
- Integrating Factor - Definition, Method, and Examples
- Integration by Parts - Definition, Derivation, and Examples
- Integration of Hyperbolic Functions - Definition, Formulas, and Examples
- Intercepted Arc – Explanation & Examples
- Interquartile Range
- Intersecting lines - Explanations & Examples
- Intersection of Line and Plane - Definition, Explanation, and Examples
- Intersection of sets - Definition and Examples
- Introduction to Logarithms – Explanation & Examples
- Inverse Laplace Transform - Definition, Formulas, and Examples
- Inverse matrix - Explanation & Examples
- Inverse of 2x2 matrix - Explanation & Examples
- Inverse of a 3x3 matrix - Explanation & Examples
- Inverse of a Function – Explanation & Examples
- Inverse trig derivatives - Derivation, Explanation, and Examples
- Inverse Trig Graphs: Examples and Explanation
- Inverse Trigonometry: Explanation and Examples
- Inversely Proportional – Explanation & Examples
- Isaac Newton: Math & Calculus
- ISLAMIC MATHEMATICS
- Isolate the Variable (Transposition) – Techniques & Examples
- Iterated Integral - Definition, Formula, and Examples
- Julia Robinson and Yuri Matiyasevich: Computability Theory & Computational Complexity Theory
- L'Hôpital's rule - Conditions, Formula, and Examples
- Lagrange Multipliers - Definition, Optimization Problems, and Examples
- Laplace Transform - Definition, Formula, and Applications
- Law of Cosines - Explanation & Examples
- Law of Detachment
- Law of Sines: Detailed Explanation and Examples
- Law of Syllogism
- Least Common Multiple – LCM Definition & Examples
- Least Squares
- Length of a Vector - Definition, Formulas, and Examples
- Leonhard Euler - Swiss Mathematician
- Less than – Explanation & Examples
- Limit laws - Definition, Properties, and Examples
- Limits calculus - Definition, Properties, and Graphs
- Limits of rational functions - Examples and Explanation
- Limits of trig functions - Properties, Techniques, and Examples
- Line graph
- Line Integral - Definition, Properties, and Examples
- Linear Graph
- Linear Programming – Explanation & Examples
- List of Important Mathematicians & Timeline
- Local Extrema - Examples and Explanation
- Locus of a Moving Point
- Logarithm Rules – Explanation & Examples
- Logistic Equation - Explanation & Examples
- Maclaurin Series - Definition, Expansion Form, and Examples
- Madhava - The Founder of The Kerala School
- Math Calculators
- 1 Rep Max Calculator + Online Solver With Free Steps
- 2 Step Equation Calculator + Online Solver With Free Steps
- 3 Systems of Equations Calculator + Online Solver With Free Steps
- Absolute Value Calculator + Online Solver With Free Steps
- Acid Base Calculator + Online Solver With Free Easy Steps
- Adding and Subtracting Polynomials Calculator + Online Solver With Free Steps
- Age Difference Calculator + Online Solver With Free Steps
- Alpha Calculator + Online Solver With Free Steps
- Arc Length Calculator Calculus + Online Solver With Free Steps
- Area of Region Calculator + Online Solver With Free Steps
- Arrhenius Equation Calculator + Online Solver With Free Steps
- Atomic Mass Calculator + Online Solver With Free Steps
- Average Value of a Function Calculator + Online Solver with Free Steps
- Basal Metabolic Rate Calculator + Online Solver With Free Steps
- Batting Average Calculator + Online Solver With Free Steps
- Big O Calculator + Online Solver With Free Steps
- Biking Calorie Calculator + Online Solver With Free Steps
- Binary to Decimal Calculator + Online Solver With Free Steps
- Bits Calculator + Online Solver With Free Steps
- Blood Alcohol Content Calculator + Online Solver With Free Steps
- Body Type Calculator + Online Solver With Free Steps
- Boolean Algebra Calculator + Online Solver With Free Steps
- Box and Whisker Plot Calculator + Online Solver With Free Steps
- BPS Calculator (Basis Point Calculator) + Online Solver With Free Steps
- Byte Calculator + Online Solver With Free Steps
- Calculator Checksum + Online Solver With Free Steps
- Carb Calculator + Online Solver With Free Steps
- Center of Circle Calculator + Online Solver With Free Steps
- Centripetal Force Calculator
- Characteristic Polynomial Calculator + Online Solver With Free Steps
- Child Spacing Calculator + Online Solver With Free Steps
- Choose Calculator + Online Solver With Free Steps
- Circle Area Calculator + Online Solver With Free Steps
- Circle Graph Calculator + Online Solver With Free Easy Steps
- Coin Flip Calculator + Online Solver With Free Steps
- Coin Toss Probability Calculator + Online Solver With Free Steps
- Combination and Permutation Calculator + Online Solver With Free Steps
- Common Difference Calculator + Online Solver With Free Steps
- Complex Number Division Calculator + Online Solver With Free Steps
- Composite Function Calculator + Online Solver With Free Steps
- Compound Inequality Calculator + Online Solver With Free Steps
- Constrained Optimization Calculator + Online Solver With Free Steps
- Convergence Test Calculator + Online Solver With Free Steps
- Convert Double Integral to Polar Coordinates Calculator + Online Solver With Free Steps
- Cubic Equation Calculator + Online Solver With Free Steps
- Cubic Inch Calculator + Online Solver With Free Steps
- Cubic Regression Calculator + Online Solver With Free Steps
- Curl Calculator + Online Solver With Free Steps
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### Posts

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- 2pir – Comprehensive Explanation and Detailed Examples
- 3.16 repeating as a fraction. Convert 3.16 to a fraction.
- 8 and n as factors, which expression has both of these?
- A -10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis. Find the following:
- A +9 nC charge is located at the origin. What is the strength of the electric field at the position (x,y)=(−5.0 cm,−5.0 cm)
- A 0.145 kg baseball pitched at 40 m/s is hit on a horizontal line drive straight back toward the pitcher at 50 m/s. If the contact time between bat and ball is 1 ms, calculate the average force between the bat and ball during contest.
- A 0.500-kg mass on a spring has velocity as a function of time given by the following equation. Find the following:
- A 1500 kg car takes a 50m radius unbanked curve at 15 m/s.
- A 2.0 kg piece of wood slides on the surface. The curved sides are perfectly smooth, but the rough horizontal bottom is 30 m long and has a kinetic friction coefficient of 0.20 with the wood. The piece of wood starts from rest 4.0 m above the rough bottom. Where will this wood eventually come to rest?
- A 2.0 kg, 20cm-diameter turntable rotates at 100 rpm on friction-less bearings. Two 500 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is the turntable’s angular velocity, in rpm, just after this event?
- A 2.4 m aqueous solution of an ionic compound with the formula MX2 has a boiling point of 103.4 C. Calculate the Van’t Hoff factor (i) for MX2 at this concentration.
- A 20.0 g marble slides to the left with a velocity of magnitude 0.200 m/s on the frictionless, horizontal surface of an icy, New York sidewalk and has a head-on elastic collision with a larger 30.0 g marble sliding to the right with a velocity of magnitude 0.300 m/s. Find the magnitude of the velocity of 30.0 g marble after the collision.
- A 20.0 mL sample of 0.150 M ethylamine is titrated with 0.0981 M HCI. What is the pH after the addition of 5.0 mL of HCl? For ethylamine, pKb = 3.25.
- A and B are n x n matrices. Mark each statement True or False. Justify your answer.
- A ball is thrown vertically upward with an initial velocity of 96 feet per second.
- A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at 10, the average attendance had been 27,000. When ticket prices were lowered to10,the average attendance had been 27,000. When ticket prices were lowered to 8, the average attendance rose to 33,000. How should ticket prices be set to maximize revenue?
- A bat locates insects by emitting ultrasonic “chirps” and then listening for echoes from the bugs. Suppose a bat chirp has a frequency of 25 kHz. How fast would the bat have to fly, and in what direction, for you to just barely be able to hear the chirp at 20 kHz?
- A bicycle with 0.80 m diameter tires is coasting on a level road at 5.6 m/s. A small blue dot has been painted on the tread of the rear tire. What is the speed of the blue dot when it is 0.80 m above the road? Also, calculate the angular speed of the tires.
- A bicycle with 0.80 m diameter.
- A bird flies in the xy-plane with a position vector given below .The positive y-direction is vertically upward. At the bird is at the origin. Calculate the velocity vector of the bird as a function of time.
- A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 24 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 175m) the block swings toward the outside of the curve, then the string makes an angle theta with the vertical. Find theta.
- A block is on a frictionless table, on earth. The block accelerates at 5.3 m/s^{2} when a 10 N horizontal force is applied to it. The block and table are set up on the moon. The acceleration due to gravity at the surface of the moon is 1.62 m/s^{2}. A horizontal force of 5N is applied to the block when it is on the moon. The acceleration imparted to the block is closest to:
- A block oscillating on a spring has an amplitude of 20 cm. What will the amplitude be if the total energy is doubled?
- A block oscillating on a spring has an amplitude of 20 cm. What will the block’s amplitude be if its total energy is doubled?
- A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat.
- A boat on the ocean is 4 miles from the nearest point on a straight shoreline; that point is 6 miles from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant.
- A bridge is built in the shape of a parabolic arch. The bridge has a span of 130 feet and a maximum height of 30 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center.
- A canoe has a velocity of 0.40 m/s southeast relative to the earth. The canoe is on a river that is flowing 0.50 m/s east relative to the earth. Find the velocity (magnitude and direction) of the canoe relative to the river.
- A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by x(t) = bt^2 – ct^3 , where b = 2.40 m/s2 and c = 0.120 m/s3 (a) Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s. (b) Calculate the instantaneous velocity of the car at t=0, t = 5.0 s, and t = 10.0 s. (c) How long after starting from rest is the car again at rest?
- A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by x(t)=bt^2-ct^3, where b=2.40 m/s^2 and c=0.120 m/s^3. (a) Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s. (b) Calculate the instantaneous velocity of the car at t=0, t = 5.0 s, and t = 10.0 s. (c) How long after starting from rest is the car again at rest?
- A car traveling at speed v takes distance d to stop after the brakes are applied. What is the stopping distance if the car is initially traveling at speed 7.0v? Assume that the acceleration due to the braking is the same in both cases.
- A cart is driven by a large propeller or fan, which can accelerate or decelerate the cart. The cart starts out at the position x=0m, with an initial velocity of +5m/s and a constant acceleration due to the fan. The direction to the right is positive. The cart reaches a maximum position of x=12.5m, where it begins to travel in the negative direction. Find the acceleration of the cart.
- A Cessna aircraft has a liftoff speed of 120 km/h. What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 240 m?
- A Christmas light is made to flash via the discharge of a capacitor
- A clay vase on a potter’s wheel experiences an angular acceleration of 5.69 rad/s^2 due to the application of a 16.0 nm net torque. find the total moment of inertia of the vase and potter’s wheel.
- A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs?
- A controversial issue in the sport of professional soccer is the use of instant replay to make difficult goal-line decisions. We asked 102 players, fans, coaches, and representative samples of executives to comment on using instant replay to determine goal lines.
- A cylinder with a movable piston records a volume of 11.6 L when 3.2 mol of oxygen is added. The gas in the cylinder has a pressure of 5.2 atm. The cylinder develops a leak and the volume of gas is now recorded to be 10.5 L at the same pressure. How many moles of oxygen are lost?
- A discounted amusement park ticket costs $12.95 less than the original price p. Write and solve an equation to find the original price.
- A dockworker applies a constant horizontal force of 80.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 11.0 m in 5.00 s.
- A flute player hears four beats per second when she compares her note to a 523 Hz tuning fork (the note C). She can match the frequency of the tuning fork by pulling out the tuning joint to lengthen her flute slightly. What was her initial frequency?
- A food safety guideline is that mercury in fish must be less than one part per million (ppm). Below is the amount of mercury (ppm) in tuna sushi sampled at various stores in major cities.
- A force acting on a particle moving in the xy plane is given by F=(2yi+x^2 j)N, where x and y are in meters.
- A gas mixture contains 75.2% nitrogen and 24.8% krypton by mass.
- A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers 32 MW of power. The minimum and maximum temperatures in the cycle are 310 and 900 K, and the pressure of air at the compressor exit is 8 times the value at the compressor inlet. Assuming an isentropic efficiency of 80 percent for the compressor and 86 percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heats with temperature.
- A golfer hits a golf ball at an angle of 25.0 to the ground. If the golf ball covers a horizontal distance of 301.5 m, what is the balls maximum height? (hint: at the top of its flight, the balls vertical velocity component will be zero.)
- A hammer in an out-of-tune piano.
- A high diver of mass 70.0 kg jumps off a board 10 m above the water. If, 1.0 s after entering the water his downward motion is stopped, what average upward force did the water exert?
- A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 75.0 cm. The power is off for 30.0 s, and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 200 complete revolutions.
- A horizontal rope is tied to a 50 kg box on frictionless ice. What is the tension in the rope if a. The box is at rest? b. The box moves at a steady 5.0 m/s? c. The box has v_{x}=5.0m/s and a_{x}=5.0m/s^2.
- A jet plane lands with a speed of 100 m/s and can accelerate at a maximum rate of 7m/s^2 as it comes to rest. Can this plane land on a small tropical island airport where the runway is 0.900 km long?
- A job candidate at a large job fair can be classified as unacceptable, provisional, or acceptable. Based on past experience, a high-quality candidate is expected to get 80 percent acceptable ratings, 15 percent provisional ratings, and 5 percent unacceptable ratings. A high-quality candidate was evaluated by 100 companies and received 60 acceptable, 25 provisional, and 15 unacceptable ratings. A chi-square goodness-of-fit-test was conducted to investigate whether the evaluation of the candidate is consistent with past experience. What is the value of the chi-square test statistic and number of degrees of freedom for the test?
- A juggler throws a bowling pin straight up with an initial speed of 8.20 m/s. How much time elapses until the bowling pin returns to the juggler’s hand?
- A light wave has a 670 nm wavelength in air. Its wavelength in a transparent solid is 420 nm. Calculate the speed and frequency of light in given solid.
- A linear regression equation has b = 3 and a = – 6. What is the predicted value of y for x = 4?
- A mail-order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit. The audit reveals that 86 of these orders were shipped on time. If the company really ships 90% of its orders on time, what is the probability that the proportion in an SRS of 100 orders is 0.86 or less?
- A major League baseball diamond has four bases forming a square whose sides measure 90 feet each. The pitcher’s mound is 60.5 feet from home plate on a line joining home plate and second base. Find the distance from the pitcher’s mound to first base. Round to the nearest tenth of a foot.
- A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground.
- A mass sitting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released s from rest with the spring compressed, it experiences a maximum acceleration of 15 m/s^2 . Find the value of
- A mountain lion can make a leap 10.0 m long, reaching a maximum height of 3.0 m. What is the speed of the mountain lion just as it leaves the ground?
- A movie stuntman (mass 80.0kg) stands on a window ledge 5.0m above the floor. Grabbing a rope attached to a chandelier, he swings down to grapple with the movie’s villian (mass 70.0 kg), who is standing directly under the chandelier.(assume that the stuntman’s center of mass moves downward 5.0 m. He releases the rope just as he reaches the villian. (a) with what speed do the entwined foes start to slide across the floor?
- A nozzle with a radius of 0.250 cm is attached to a garden hose with a radius of 0.750 cm. The flow rate through hose and nozzle is 0.0009. Calculate the speed of the water.
- A pair of honest dice is rolled once. Find the expected value of the sum of the two numbers rolled.
- A parallel-plate air capacitor has a capacitance of 920 pf. The charge on each plate is 3.90 μc.
- A particle moves along the curve y=2 sin(pi x/2). As the particle passes through the point (1/3, 1), its x-coordinate increases at a rate of sqrt{10} cm/s. How fast is the distance from the particle to the origin changing at this instant?
- A piano has been pushed to the top of the ramp at the back of a moving van. The workers think it is safe, but as they walk away, it begins to roll down the ramp. If the back of the truck is 1.0 m above the ground and the ramp is inclined at 20°, how much time do the workers have to get to the piano before it reaches the bottom of the ramp?
- A piece of sodium metal reacts completely with water is given below. The hydrogen gas generated is collected over water at 25.0 degree C. The volume of the gas is 246 mL measured at 1.00 atm. Calculate the number of grams of sodium used in the reaction. (Vapor pressure of water at 25 degree C=0.0313 atm.)
- A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is a maximum?
- A pin fin of uniform, cross-sectional area is fabricated of an aluminum alloy (k=160W/mK). The fin diameter is 4mm, and the fin is exposed to convective conditions characterized by h=220W/m^2K. It is reported that the fin efficiency is eta_f=0.65. Determine the fin length L and the fin effectiveness epsilon_f.
- A piston–cylinder device initially contains 0.07 cubic meter of nitrogen gas at 130 kPa and 180 degrees. The nitrogen is now expanded to a pressure of 80 kPa polytropically with a polytropic exponent whose value is equal to the specific heat ratio (called isentropic expansion). Determine the final temperature and the boundary work done during this process.
- A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.
- A plastic rod is charged to -60 nC by rubbing. (a) Were the electrons added or protons removed from the surface? Explain. (b) How many unit charges (electrons/protons) have been added?
- A point charge of magnitude q is at the center of a cube with sides of length L. What is the electric flux Φ through each of the six faces of the cube? What would be the flux Φ_1 through a face of the cube if its sides were of length L_{1}?
- A potter’s wheel having a radius of 0.50 m and a moment of inertia of 12 kg m^2 is rotating freely at 50 rev/min. The potter can stop the wheel in 6.0 s by pressing a wet rag against the rim and exerting a radially inward force of 70 N. Find the effective coefficient of kinetic friction between the wheel and the wet rag.
- A pound of plain M&M candies contains 96 g fat, 320 g carbohydrate, and 21 g protein. What is the fuel value in kJ in a 42-g (about 1.5 oz) serving? How many Calories does it provide.
- A pound of plain M&M candies contains 96g fat, 320g carbohydrate, and 21g protein. What is the fuel value in kJ in a 42g (about 1.5-oz) serving?
- A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 65.0 m/s at an angle of 37 degrees with the horizontal.
- A proton with an initial speed of 650,000 m/s is brought to rest by an electric field.
- A rectangular package to be sent by a postal service that has a maximum total length and perimeter (or girth) limit of 108 inches. A rectangular package is to be sent via this service. Calculate the dimensions of the package that covers the maximum volume. (Cross-sections may be assumed to be square)
- A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 400 feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum area?
- A rock climber stands on top of a 70m high cliff overhanging a pool of water. He throws stones vertically downward 1.2s apart and observes that the cause a single splash. The initial speed of the first stone was 2.5 m/s. How long after the release of the first stone does the second stone hit the water?
- A rocket is launched at an angle of 53 degrees above the horizontal with an initial speed of 200 m/s. The rocket moves for 2.00 s along its initial line of motion with an acceleration of 20.0 m/s^2. At this time, its engines fail and the rocket proceeds to move as a projectile. Calculate the following quantities.
- A rubber ball of mass m is dropped from a cliff. As the ball falls. it is subject to air drag (a resistive force caused by the air). The drag force on the ball has magnitude bv^2, where b is a constant drag coefficient and v is the instantaneous speed of the ball. The drag coefficient b is directly proportional to the cross-sectional area of the ball and the density of the air and does not depend on the mass of the ball. As the ball falls, its speed approaches a constant value called the terminal speed.
- A seafood festival organizer is interested in performing a statistical analysis as per details given below. Which test should be performed?
- A shopper in a supermarket pushes a cart with a force of 35.0N directed at an angle of 25 below the horizontal. The force is just sufficient to balance various friction forces, so the cart moves at constant speed.
- A simple random sample size of 100 is selected from a population with p= 0.40. What is the expected value of p? What is the standard error of p? Show the sampling distribution of p? What does the sampling distribution of p show?
- A ski lift has a one-way length of 1km and a vertical rise of 200m. The ski lift which is operating at a steady speed of 10km/h and chairs are separated by 20m. Three people can be seated on each chair with the average mass of each loaded chair is 250kg
- A slab of insulating material of uniform thickness d, lying between -d/2 to d/2 along the x-axis, extends infinitely in the y and z directions. The slab has a uniform charge density p. The electric field is zero in the middle of the slab, at x=0. What is ein(x), the magnitude of the electric field inside the slab as a function of x?
- A small airplane takes on 245 L of fuel. If the density of the fuel is 0.821 g/ml, what mass of fuel has the airplane taken on?
- A small plane is flying a banner in the shape of a rectangle. The area of the banner is 144 square feet. The width of the banner is 1/4 the length of the banner. What are the dimensions of the banner?
- A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 45 with the vertical. Air Resistance is negligible.
- A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 45 with the vertical. Air Resistance is negligible.
- A solenoid is designed to produce a magnetic field of 0.030 T at its center. It has radius 1.50 cm and length 50.0 cm, and the wire can carry a maximum current of 11.0 A. (a) What minimum number of turns per unit length must the solenoid have? (b) What total length of wire is required?
- A spherical hot air balloon is initially filled with air at 120 kPa and 20 degree Celsius with a velocity of 3 m/s through a 1 m diameter opening. How many minutes will it take to inflate this balloon to a 17 m diameter when the pressure and temperature of the air in the balloon remain the same as the air entering the balloon?
- A spherical interplanetary probe of 0.5m diameter contains electronics that dissipates 150 W. If the probe surface has an emissivity of 0.8 and the probe does not receive radiation from other surfaces, as, for example, from the sun, what is its surface temperature?
- A spring with Spring Constant k=340N/m is used to Weigh a 6.7-kg fish
- A standard deck of cards contains 52 cards. One card is selected from the deck.
- A stationary boat in the ocean is experiencing waves from a storm. The waves move at 55 km/h and have a wavelength of 160 m. The boat is at a crest of a wave. How much time elapses until the boat is first at the trough of a wave?
- A statistic is an unbiased estimator of a parameter. Select the best answer.
- A steel cylinder has a length of 2.16 in, a radius of 0.22 in, and a mass of 41 g. What is the density of the steel in g/cm^3?
- A student standing in a canyon yells “echo” and her voice produces a sound wave of the frequency of f=0.54 kHz. The echo takes t=4.8 s to return to the student. Assume the speed of sound through the atmosphere at this location is v=328 m/s
- A system consisting of one original unit plus a spare can function for a random amount of time X. If the density of X is given (in units of months) by the following function. What is the probability that the system functions for at least 5 months?
- A tank of water with depth of 20.0 cm and a mirror at its bottom has a small fish floating motionless 7.0 cm under the surface of the water. (a) What is the apparent depth of the fish when viewed at normal incidence? (b) What is the apparent depth of the image of the fish when viewed at normal incidence?
- A traveling wave along the x-axis is given by the following wave function.
- A trough is 12 feet long and 3 feet across the top. Water is being pumped into the trough at 2 cubic feet per minute. How fast is the water level rising when the depth h is 1 foot? The water is rising at a rate of 3/8 inch per minute when h = 2 feet. Determine the rate at which water is being pumped into the trough.
- A uniform lead sphere and a uniform aluminum sphere have the same mass. What is the ratio of the radius of the aluminum sphere to the radius of the lead sphere?
- A uniform steel bar swings from a pivot at one end with a period of 1.2 s. How long is the bar?
- A variable force of 5x^-2 pounds moves an object along a straight line from the origin. Calculate the work done.
- A very thin oil film (n=1.25) floats on water (n=1.33). What is the minimum width of the oil film required to produce a strong reflection for green light with 500nm wavelength.
- A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins in the environment.
- A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m. The length of each propeller blade is 12 m. A tip of the propeller breaks off when the propeller is vertical. The fragment flies off horizontally, falls, and strikes the ground at P. Just before the fragment broke off, the propeller was turning uniformly, taking 1.2 s for each rotation. In the above figure, the distance from the base of the pylon to the point where the fragment strikes the ground is closest to:
- About 0.1 ev is required to break a “hydrogen bond” in a protein molecule.
- Absolute Value of -8: A Detailed Explanation With Examples
- According to census data in 1950 the population of the US amounted to 151.3 million persons.
- After the reaction, how much octane is left?
- Air enclosed in a sphere has density 1.4 kg/m^3. What will the density be if the radius of the sphere is halved, compressing the air within?
- An aerosol spray can with a volume of 250 mL contains 2.30 g of propane gas (C3H8) as a propellant.
- An airplane flies at an altitude of 5 miles toward a point directly over an observer.
- An aluminum engine block has a volume of 4.77 L and a mass of 12.88 kg. What is the density of the aluminum in grams per cubic centimeter?
- An astronaut on a distant planet wants to determine its acceleration due to gravity. The astronaut throws a rock straight up with a velocity of + 15 m/s and measures a time of 20.0 s before the rock returns to his hand. What is the acceleration (magnitude and direction) due to gravity on this planet?
- An atomic nucleus initially moving at 420 m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350 m/s. If the alha particle has a mass of 4.0u and the original nucleus has a mass of 222u. What speed does the alpha particle have when it is emitted?
- An electron with an initial speed of 6.00 x10^5 m/s is brought to rest by an electric field. Did the electron move into a region of higher potential or lower potential? What was the potential difference that stopped the electron? What was the initial kinetic energy of the electron, in electron volts?
- An element of atomic number 88 decays radioactively to an element of atomic number 82.
- An equation that expresses a relationship between two or more variables, such as H=9/10(220-a), is called a/an? The process of finding such equations to describe real-world phenomena is called mathematical ? Such equations, together with the meaning assigned to the variables, are called mathematical ?
- An iceberg (specific gravity 0.917) floats in the ocean (specific gravity 1.025 ). What percent of the volume of the iceberg is under water?
- An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T. The spaceship enters a geosynchronous orbit at a distance of R.
- An object is 1.0 cm tall and its inverted image is 4.0 cm tall. What is the exact magnification?
- An object is placed 30 cm to the left of a converging lens that has a focal length of 15 cm. Describe what the resulting image will look like (i.e, image distance, magnification, upright or inverted images, real or virtual images)?
- An object moving in the xy-plane is acted on by a conservative force described by the potential-energy function U(x,y) where ‘a’ is a positive constant. Derive an expression for the force f⃗ expressed in terms of the unit vectors i^ and j^.
- An oil pump is drawing 44kw of electric power. Find out the mechanical efficiency of the pump.
- An open tank has a vertical partition and on one side contains gasoline with a density p= 700 kg/m^3 at a depth of 4m. Arectangular gate that is 4 m high and 2 m wide and hinged at one end is located in the partition. Water is slowly added to the empty side of the tank. At what depth, h, will the gate start to open?
- An urn contains 5 white and 10 black balls. A fair die is rolled and that number of balls is randomly chosen from the urn. What is the probability that all of the balls selected are white? What is the conditional probability that the die landed on 3 if all the balls selected are white?
- Angle Bisector Theorem – Definition, Conditions and Examples
- Applied Calculus: Comprehensive Definition and Detailed Examples
- Approximate the sum of the series correct to four decimal places.
- Aqueous Iodide ion is oxidized to i2(s) by hg22+(aq).
- Argon is compressed in a polytropic process with n=1.2 from 120 kPa and 30°C to 1200 kPa in a piston-cylinder device. Determine the final temperature of the argon.
- As part of your work out, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. When you push the platform, you compress the springs. You do 80.0 J of work when you compress the springs 0.200m from their uncompressed length. What magnitude of force must you apply to hold the platform in this position?
- Assume that A is row equivalent to B. Find bases for Nul A and Col A.
- Assume that a procedure yields a binomial distribution.
- Assume that adults with smartphones are randomly selected in meetings and classes. Find the probability of them using smartphones in classes or meetings.
- Assume that random guesses are made for eight multiple choice questions on an SAT test.
- Assume that T is a linear transformation. Find the standard matrix of T.
- Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 16 days. a) What percentage of pregnancies should last between 270 and 280 days? b) At least how many days should the longest 25% of all pregnancies last? c) Suppose a certain obstetrician is currently providing prenatal care to 60 pregnant women. Let y̅ represent the mean length of their pregnancies. According to the Central Limit Theorem, what’s the distribution of this sample mean, y̅? Specify the model, mean, and standard deviation. d) What’s the probability that the mean duration of these patient’s pregnancies will be less than 260 days?
- At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of $40$ freshmen sharing a common lounge area.
- At a certain location wind is blowing steadily at 12 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 60m diameter blades at that location. Take the air density to be 1.25kg/m^3.
- At NASA’s Jet Propulsion Laboratory’s 25-foot space simulator facility, a series of overhead arc lamps can generate a light intensity of 2500 $\dfrac {W} {m ^ 2} $ on the facility floor. (This simulates the intensity of sunlight near Venus.) Find the average momentum density (momentum per unit volume) in the light at the floor.
- At one point in a pipeline the water’s speed is 3.00 m/s and the gauge pressure is 5.00 x 10^4 Pa. Find the gauge pressure at a second point in the line, 11.0 m lower than the first, if the pipe diameter at the second point is twice that at the first.
- At what point does the curve have maximum curvature? What happens to the curvature as x tends to infinity y=lnx?
- At what point does the curve have maximum curvature? y = 7 ln(x)
- Based on the normal model N(100, 16), describing IQ scores. What percent of people’s IQ would you expect to be:
- Box Method for Factoring Trinomials: A Step-by-Step Guide
- Boxes A and B are in contact on a horizontal friction-less surface. Box A has mass 20 kg and box B has mass 5kg.A horizontal force of 250N is exerted on box A. What is the magnitude of the force that box A exerts on box B?
- Boxes A and B are in contact on a horizontal, frictionless surface. Box A has mass 20.0 kg and box B has mass 5.0 kg. A horizontal force of 250 N is exerted on box A. What is the magnitude of the force that box A exerts on box B?
- Calculate net price factor and net price.
- Calculate the double integral of the expression 6x/(1 + xy) dA, where R = [0, 6] × [0, 1].
- Calculate the frequency of each of the following wave lengths of electromagnetic radiation.
- Calculate the frequency of each of the following wavelengths of electromagnetic radiation.
- Calculate the frequency of each of the following wavelengths of electromagnetic radiation.
- Calculate the iterated integral: $\int_{0}^{3} \int_{0}^{1} 4xy (\sqrt{x^2 + y^2}) \, dydx$
- Calculate the magnitude of the linear momentum for the following cases:
- Calculate the Molar Solubility of Ni(OH)2 when Buffered at ph=8.0
- Calculate the pH of a buffer that is 0.12 M in lactic acid and 0.11 M in sodium lactate.
- Calculate the ratio of effusion rates for Ar and Kr.
- Calculate the ratio of NaF to HF required to create a buffer with pH =4.20.
- Calculate the ratio of NaF to HF required to create a buffer with pH=4.15.
- Calculate the total kinetic energy, in Btu, of an object with a mass of 10 lbm when its velocity is 50 ft/s.
- Calculate the total potential energy, in Btu, of an object that is 20 ft below a datum level at a location where g=31.7 ft/s^2 and which has mass of 100lbm.
- Caltech vs MIT: Which One of These Universities Is Better?
- Can two events with nonzero probabilities be both independent and mutually exclusive?
- Cavalieri’s Principle – Definition, Conditions and Applications
- Change from rectangular to cylindrical coordinates. (let r ≥ 0 and 0 ≤ θ ≤ 2π.) (a) (−9, 9, 9)
- Choose the point on the terminal side of -210°.
- Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that a newborn baby is a boy is 1/2.
- Closed Under Addition – Property, Type of Numbers, and Examples
- Co-planar circles that have a common center are called:
- Coefficient Matrix — Explanation and Examples
- Coffee is draining from a conical filter into a cylindrical coffee pot of radius 4 inches at the rate of 20 cubic inches per minute. How fast is the level in the pot rising when the coffee in the cone is 5 inches deep. How fast is the level in the cone falling then?
- Compilers can have a profound impact on the performance of an application. Assume that for a program, compiler A results in a dynamic instruction count of 1.0E9 and has an execution time of 1.1 s, while compiler B results in a dynamic instruction count of 1.2E9 and an execution time of 1.5 s.
- Complex number in rectangular form what is (1+2j) + (1+3j)? Your answer should contain three significant figures.
- Complex number in rectangular form. What is (1+2i)+(1+3i)?
- Compute 4.659×10^4−2.14×10^4. Round the answer appropriately.
- Compute the distance d from y to the line through u and the origin.
- Compute the following binomial probabilities directly from the formula for b(x, n, p).
- Compute the reactance of a 0.450 H inductor at the frequency of 60.0 Hz. Compute the reactance of a 2.50 microfarad capacitor at the same frequencies.
- Compute the y-intercept if x-bar = 57, y-bar = 251, sx= 12, sy= 37 and r = 0.341.
- Congruent Supplementary Angles – Definition, Measure and Explanation
- Consider a binomial experiment with n=20 and p=0.70.
- Consider a normal population distribution with the value of σ known.
- Consider a sample with data values of 10, 20, 12,17, and 16. Compute the range and interquartile range.
- Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. Determine the wavelength of light that is associated with this transition. Will the light be absorbed or emitted?
- Consider a vehicle moving with constant velocity v. Find the Power dissipated by form drag.
- Consider an object moving along the parametrized curve with equations: x(t) = e^t + e^{-t} and y(t) = e^{-t}
- Consider the case when the constant a=4. plot the graph of y=4/x.
- Consider the following convergent series.
- Consider the function below. C(x) = x^{1/5}(x + 6). (If an answer does not exist, enter DNE).
- Consider the function below. f(x)=x^2 e^-x. Find minimum and maximum value of the function.
- Consider the three circuits shown below. All the resistors and all the batteries are identical. Which of the statements are true and which ones are false?
- Construct a graph corresponding to the linear equation y=2x−6.
- Construct a matrix whose column space contains (1, 1, 5) and (0, 3, 1) while it’s null space contains (1, 1, 2).
- Convert 4/25 into a decimal and percent.
- Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. The equation is given as follows:
- Cosine Theorem – Explanation & Examples
- Data that is words only and cannot be ranked
- David is driving a steady 25.0 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.00 m/s^2 at the instant when David passes. How far does Tina drive before passing David, and what is her speed as she passes him?
- Descartes Rule of Signs in Finding Roots of a Polynomial
- Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix.
- Describe in words the region of R3 represented by the equations or inequalities, x = 10.
- Describe in words the surface whose equation is given as:
- Describe in words the surface whose equation is given:
- Describe in words the surface whose equation is given. r = 6
- Describe in words the surface whose equation is given. φ = π/6
- Describe the zero vector (the additive identity) of the vector space.
- Determine a region whose area is equal to the given limit. Do not evaluate the limit.
- Determine if b is a linear combination of the vectors formed from the columns of the matrix A.
- Determine if the columns of the matrix form a linearly independent set. Justify each answer.
- Determine the current (magnitude and direction) in the 8.0 and 2.0-? resistors in the drawing.
- Determine the dimensions of nul a and col a for the matrix shown below.
- Determine the head of the vector whose tail is given. Make a sketch.
- Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution.
- Determine the magnitude of the current in the (a) 8.0-ω and (b) 2.0-ω resistors in the drawing.
- Determine the missing coordinates of the points on the graph of the function. y=arctan
- Determine the set of points at which the function is continuous.
- Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.
- Determine whether each of these functions is a bijection from R to R.
- Determine whether f is a function from Z to R for given functions
- Determine whether the equation represents y as a function of x. x+y^2=3
- Determine whether the Geometric series is Convergent or Divergent. 10 − 4 + 1.6 − 0.64 + ….
- Determine whether the given vectors are orthogonal, parallel, or neither. u = ⟨6, 4⟩, v = ⟨-9, 8⟩
- Determine whether the planes are parallel, perpendicular, or neither. If the planes are neither parallel nor perpendicular, find the angle between them.
- Determine whether the sequence converges or diverges. If it converges, find the limit.
- Determine which plot shows the strongest Linear Correlation.
- Determine zα for the following of α. (Round your answers to two decimal places.)
- Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix.
- Did the electron move into a region of higher potential or lower potential?
- Differentiate y = sec(θ) tan(θ).
- Double Angle Theorem – Identities, Proof, and Application
- During contract negotiations, a company seeks to change the number of sick days employees may take, saying that the annual “average” is 7 days of absence per employee. The union negotiators counter that the “average” employee misses only 3 days of work each year. Explain how both sides might be correct, identifying the measure of center you think each side is using and why the difference might exist.
- Each limit represents the derivative of some function f at some number a.
- Elimination Method – Steps, Techniques, and Examples
- Empirical Probability – Definition, Application, and Examples
- Enter the solubility-product expression for Al(OH)3 (s)
- Estimate the angle to the nearest one-half radian.
- Ethyl chloride vapor decomposes by the first-order reaction shown below. The activation energy is 249kj/mol, and the frequency factor is 1.6×10^14 s^{-1}. Find the value of the rate constant at 710 K. What fraction of the ethyl chloride decomposes in 15 minutes at this temperature? Find the temperature at which the rate of the reaction would be twice as fast.
- Evaluate 512/2
- Evaluate the difference quotient for the given function. Simplify your answer.
- Evaluate the double integral y^2 dA, D is the triangular region with vertices (0, 1), (1,2), (4,1)
- Evaluate the double integral. 4xy^2 dA, d is enclosed by x=0 and x=4−y^2 d.
- Evaluate the indefinite integral as a power series. integral tan^-1(x)/(x) dx. What is the radius of convergence?
- Evaluate the line integral, where c is the given curve. $\int_{c} xy ds$, c : x = t^2, y = 2t, 0 ≤ t ≤ 2.
- Evaluate the Line integral, where C is the given curve. c xy ds, c: x = t^3, y = t, 0 ≤ t ≤ 3.
- Events A and B are Mutually Exclusive. Which of the following statements is also true?
- Expand the expression (x+1)^3.
- Expanded Form Exponents — Explanation and Examples
- Explain why the function is differentiable at the given point. Then find the linearization L(x, y) of the function at that point.
- Explain why the function is discontinuous at the given number a. The function is given as:
- Explicit Formula – Explanation and Examples
- Express the plane z=x in cylindrical and spherical coordinates.
- Extreme Value Theorem – Explanation and Examples
- Factoring Monomials — Explanation and Examples
- Factoring Quadratics Made Easy: Methods and Examples
- Figure ABCD is a Trapezoid with point A (0, −4). What rule would rotate the figure 270° clockwise?
- Fill in each blank so that the resulting statement is true.
- Fill in the blank with a number to make the expression a perfect square.
- Find 10 partial sums of the series. (Round your answer to five decimal places)
- Find a basis for the eigenspace corresponding to each listed eigenvalue of A given below:
- Find a basis for the space of 2×2 lower triangular matrices.
- Find a basis for the space spanned by the given vectors: v1, v2, v3, v4, and v5.
- Find a Cartesian equation for the curve and identify it.
- Find a function f such that f'(x)=3x^3 and the line 81x+y=0 is tangent to the graph of f.
- Find a function whose square plus the square of its derivative is 1.
- Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and area of the triangle PQR.
- Find a polynomial of the specified degree that has the given zero. Degree 4 with zeros -4, 3, 0, and -2.
- Find a polynomial with integer coefficients that satisfies the given conditions
- Find a single vector x whose image under t is b
- Find a vector $A$ with representation given by the directed line segment $AB$. Draw $AB$ and the equivalent representation starting from the origin $A(4, 0, -2), B(4, 2 ,1)$.
- Find a vector equation and parametric equations for the line segment that joins P to Q. P(-1, 0, 1) and Q(-2.5, 0, 2.1).
- Find a vector function that represents the curve of intersection of the cylinder and the plane.
- Find a2, the magnitude of the centripetal acceleration of the star with mass m2 under the following constraints.
- Find all polar coordinates of point p = (6, 31°).
- Find all the second partial derivatives of v=xy/x-y.
- Find an equation for the plane consisting of all points that are equidistant from the points (1,0,-2) and (3,4,0).
- Find an equation of a parabola that has curvature 4 at the origin
- Find an equation of the plane tangent to the following surface at the given point:
- Find an equation of the plane. The plane through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1)
- Find an equation of the tangent line to the curve at the given point. y = sqrt(x) , (81, 9)
- Find an equation of the tangent line to the curve at the given point. y = x , (81, 9)
- Find an explicit description of nul A by listing vectors that span the null space.
- Find an expression for the function whose graph is the given curve. The expression of the curve is x^2 + (y – 4)^2 = 9.
- Find an expression for the square of the orbital period.
- Find an orthogonal basis for the column space of the matrix given below:
- Find parametric equations for the path of a particle that moves along the circle
- Find Partial Derivatives ∂z/∂x and ∂z/∂y Given z = f(x)g(y), find z_x+z_y .
- Find the annual percent increase or decrease that y =0.35(2.3)^{x) models.
- Find the area of the parallelogram whose vertices are listed. (0,0), (5,2), (6,4), (11,6)
- Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1)
- Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1)
- Find the area of the part of the plane as shown below that lies in the first octant.
- Find the area of the region bounded by the graphs of the given equations.
- Find the area of the region enclosed by one loop of the curve. r = sin(12θ).
- Find the area of the region enclosed by the inner loop of the curve:
- Find the area of the region that is inside r=3cos(Θ) and outside r=2-cos(Θ).
- Find the area of the region that lies inside both curves.
- Find the area of the region that lies inside both curves. r2 = 50 sin(2θ), r = 5
- Find the area of the region that lies inside the first curve and outside the second curve.
- Find the Area of the Shaded Region of a Circle: Clear Examples
- Find the area under the given curve over the indicated interval.
- Find the average value of f over the given rectangle. f(x,y)= x^2y. R has vertices (-1,0),(-1,5),(1,5),(1,0)
- Find the best approximation to z by vectors of the form c1v1 + c2v2
- Find the centroid of the region in the first quadrant bounded by the given curves y=x^3 and x=y^3
- Find the change of coordinates matrix from B to the standard basis in R^n.
- Find the coefficient of x^5 y^8 in (x+y)^13.
- Find the constant a such that the function is continuous on the entire real line.
- Find the coordinates of the vertex for the parabola defined by the given quadratic function.
- Find the critical value z a/2 that corresponds to a 93% confidence level.
- Find the curvature of r(t) = 7t, t2, t3 at the point (7, 1, 1).
- Find the curve’s unit tangent vector. Also, find the length of the indicated portion of the curve.
- Find the differential dy when y=rad(15+x^2).Evaluate dy for the given values of x and dx. x = 1, dx = −0.2
- Find the differential of each function. (a) y=tan (7t), (b) y=3-v^2/3+v^2
- Find the dimension of the subspace spanned by the given vectors:
- Find the directional derivative of f at the given point in the direction indicated by the angle θ.
- Find the domain and range of the following functions.
- Find the domain and range of these functions.
- Find the domain of the vector function. (Enter your answer using interval notation).
- Find the equation of the sphere centered at (-4, 1, 4) with radius 3. Give an equation which describes the intersection of this sphere with the plane z = 6.
- Find the exact length of the curve. x = et + e−t, y = 5 − 2t, 0 ≤ t ≤ 4
- Find the exact value of each of the remaining trigonometric functions of theta.
- Find the exponential function f(x) = a^x whose graph is given.
- Find the exponential model that fits the points shown in the graph. (Round the exponent to four decimal places)
- Find the first partial derivatives of the function f(x, y) = (ax + by)/(cx + dy)
- Find the general solution of the given differential equation. Give the largest over which the general solution is defined.
- Find the general solution of the given differential equation. y(6) − y” = 0
- Find the general solution of the given higher-order differential equation: y^{4} + y^{3} + y^{2} = 0
- Find the largest area of an isosceles triangle inscribed in a circle of radius 3.
- Find the least common multiple of x^3-x^2+x-1 and x^2-1. Write the answer in factored form.
- Find the least integer n such that f(x) is O(x^n) for each of these functions.
- Find the length and width of a rectangle that has the given area and a minimum perimeter.
- Find the length of the curve for the given expression
- Find the linearization L(x) of the function at a.
- Find the local maximum and minimum values and saddle points of the function.
- Find the maximum and minimum values attained by the function f along the path c(t).
- Find the parametric equation of the line through a parallel to b.
- Find the partial derivate of the given function
- Find the particular solution that satisfies the differential equation and the initial condition.
- Find the planes tangent to the following surfaces at the indicated points.
- Find the point at which the given lines intersect. Find an equation of the plane that contains these lines.
- Find the point on the hyperbola xy = 8 that is closest to the point (3,0).
- Find the point on the line y = 4x + 3 that is closest to the origin.
- Find the point on the line y=2x+3 that is closest to the origin.
- Find the point on the line y=5x+3 that is closest to the origin.
- Find the point(s) on the surface at which the tangent plane is horizontal.
- Find the points on the cone z^2 = x^2 + y^2 that are closest to the point (2,2,0).
- Find the points on the surface y^2 = 9 + xz that are closest to the origin.
- Find the principal unit normal vector to the curve at the specified value of the parameter: R(t) = ti + (4/t)j where t=2
- Find the probability P (E or F), if E and F are mutually exclusive.
- Find the product of the following equation. Express it in standard form. Give the value of a followed by the value of b separated by a comma.
- Find the rate of change of f at p in the direction of the vector u.
- Find the regression equation for predicting final score from midterm score, based on the following information:
- Find the scalar and vector projections of b onto a.
- Find the scalar and vector projections of b onto a. a=i+j+k, b=i−j+k
- Find the surface area of the torus shown below, with radii r and R.
- Find the symmetric difference of {1, 3, 5} and {1, 2, 3}.
- Find the Taylor polynomial T3(x) for the function f centered at the number a. f(x) = x + e^{−x}, a = 0
- Find the tension in each cord in the figure (figure 1) if the weight of the suspended object is w.
- Find the two positive numbers such that the sum of the first number squared and the second number is 57 and the product is a maximum.
- Find the unit tangent and unit normal vectors T(t) and N(t).
- Find the value of x and y.
- Find the value of x or y so that the line passing through the given points has the given slope.
- Find the value(s) of h for which the vectors are linearly dependent. Justify your answer.
- Find the values of b such that the function has the given maximum value.
- Find the values of x such that the angle between the vectors (2, 1, -1) and (1, x, 0) is 40.
- Find the vectors T, N, and B at the given point. r(t)= and point .
- Find the vectors T, N, and B, at the given point.
- Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position.
- find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 3, 0), (-2, 0, 2),(-1, 3, -1).
- Find the volume of the solid generated by revolving the shaded region about the y-axis.
- Find the Volume of the Solid that is enclosed by the Cone and the Sphere
- Find the work W done by the force F in moving an object from a point A in space to a point B in space is defined as W = F.. Find the work done by a force of 3 newtons acting in the direction 2i + j +2k in moving an object 2 meters from (0, 0, 0) to (0, 2, 0).
- Find transient terms in this general solution to a differential equation, if there are any
- Find two functions f and g such that (f ∘ g)(x) = h(x).
- Find two numbers whose Difference is 100 and whose Product is a Minimum
- Find two positive real numbers whose product is a maximum. The sum is 110.
- Find two sets A and B such that A ∈ B and A ⊆ B.
- Find two unit vectors that make an angle of 45° with the vector v = (4, 3).
- Find two vectors in opposite directions that are orthogonal to the vector u. U=(-1/4)i +(3/2)j
- Find x such that the matrix is equal to its own inverse.
- Find yʹ and yʹʹ. y=xln(x)
- Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(1, 0, -1), B(3, -2, 0), C(1, 3, 3).
- For 589-nm light, calculate the critical angle for the following materials surrounded by air. (a) fluorite (n = 1.434) ° (b) crown glass (n = 1.52) ° (c) ice (n = 1.309)
- For a test of $ho$: $p$ = $0.5$, the $z$ test statistic equals $1.74$. Find the $z$ test statistic equals $p$-value for $ha$: $p$ > $0.5$.
- For a test of Ho: p=0.5,the z test statistic equals -1.74. Find the p-value for Ha: p<0.5.
- For all x≥0 if 4x≤g(x)≤2x^4−2x^2+4 for all x, evaluate lim x→1 g(x) as as x→1?
- For an electrostatic precipitator, the radius of the central wire is 90.0 um, the radius of the cylinder is 14.0 cm, and a potential difference of 50.0 kV is established between the wire and the cylinder. What is the magnitude of the electric field midway between the wire and the cylinder wall?
- For how long a time t could a student jog before irreversible body damage occurs?
- For the equation, write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. Keeping the restrictions in mind, solve the equation.
- For the matrix A below, find a nonzero vector in nul A and a nonzero vector in col A.
- For the matrix, list the real eigenvalues, repeated according to their multiplicities.
- For the two vectors in the figure (Figure 1) , find the magnitude of the vector product
- For waves on a string there are two formulae.
- For what value of the constant c is the function f continuous on (-∞, ∞)?
- For which positive integers k is the following series convergent?
- Formic acid, HCOOH, is a weak electrolyte. What solutes are present in the aqueous solution of formic acid. Write its equilibrium equation
- From the half-life for 14C decay, 5715 year, determine the age of the artifact.
- Function Operations – Explanation and Examples
- Give full and correct answer in how many ways can a set of two positive integers less than 100 be chosen?
- Given a data set consisting of 33 unique whole number observations, its five-number summary is: [12,24,38,51,64]. How many observations are less than 38?
- Given a mortgage of $48,000 for 15 years with a rate of 11%, what are the total finance charges?
- Given a standard normal distribution, find the area under the curve that lies (a) to the left of z=-1.39; (b) to the right of z=1.96 ; (c) between z=-2.16 and z = -0.65; (d) to the left of z=1.43 ; (e) to the right of z=-0.89; (f) between z=-0.48 and z= 1.74.
- Given equation is dy/dt=ay+by^2, sketch the graph versus y. Determine critical points, and classify those points asymptotically stable or unstable.
- Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of X+Y.
- Given that z is a standard normal random variable, compute the following probabilities
- Given the equation c=2πr solve for r. Which of the following options is correct?
- Given the following functions, find f of g of h.
- Given the proportion a/b = 8/15, what “ratio” completes the equivalent proportion a/8.
- Given V = LxWxH, solve for L.
- Glide Reflection – Definition, Process and Examples
- Greatest Common Monomial Factor — Explanation and Examples
- Halfplane: Definition, Detailed Examples, and Meaning
- Hinge Theorem – In-Depth Explanation and Detailed Examples
- Horizontal Shift – Definition, Process and Examples
- How do I interpret this equation 5+1×10=? Is the answer 15 or 60?
- How do you translate “91 more than the square of a number” into an algebraic expression?
- How do you write y = 2x – 9 in standard form?
- How far, in meters, will the vehicles slide after the collision?
- How Hard is Calculus? A Comprehensive Guide
- How many atoms are in 1.75 mol CHCl3?
- How many different 7 card hands can be chosen from a standard 52 card deck?
- How many electrons per second enter the positive end of battery #2 for the following circuit:
- How many hydrogen atoms are in 35.0 grams of hydrogen gas?
- How many liters of a 0.0550m KCl solution contain 0.163 moles of KCl?
- How many square feet is Rhode island?
- How many strings are there of four lowercase letters that have the letter (x) in them?
- How many subsets with an odd number of elements does a set with 10 elements have?
- How many ways are there to choose four members of the club to serve on an executive committee?
- How many ways are there to distribute six indistinguishable balls into nine distinguishable bins?
- How much work is done on the package by friction as it slides down the circular arc from A to B?
- How to Complete Tables – Explanation and Examples
- How To Find 16 Square Root: Detailed Explanation
- How To Find Square Root of 9/16: Examples and Explanation
- How to Find the Volume of the Composite Solid?
- Identify the surface whose equation is given. ρ=sinθsinØ
- If 2 + sqrt(3) is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root.
- If a and b are mutually exclusive events with p(a) = 0.3 and p(b) = 0.5, then p(a ∩ b) =
- If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). (a) Calculate the ideal speed to take a 80 m radius curve banked at 15.0. (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 25.0 km/h?
- If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes.
- If electrical energy costs $0.12, per kilowatt-hour, how much do the following events cost?
- If f and g are both even functions, is f + g even? If f and g are both odd functions, is f+g odd? What if f is even and g is odd? Justify your answers.
- If f is continuous and integral 0 to 4 f(x)dx = 10 , find integral 0 to 2 f(2x)dx.
- If f is continuous and integral from 0 to 9 f(x)dx=4
- If f(2)=10 and f'(x)=x^2f(x) for all x, find f”(2).
- if f(x) + x2[f(x)]5 = 34 and f(1) = 2, find f ‘(1).
- If the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic meters.
- If the ethyl benzoate used to prepare triphenylmethanol is wet, what by product is formed?
- If we triple the average kinetic energy of the gas atoms, what is the new temperature in ∘c?
- If X is a normal random variable with parameters µ=10 and σ^2=26 , compute P[X<20]
- If X is an exponential random variable parameter, λ = 1 , compute the probability density function of the random variable Y defined by Y = logX.
- If xy + 3ey = 3e, find the value of y” at the point where x = 0.
- If xy+6e^y=6e, find the value of y” at the point where x=0.
- If xy+8e^y=8e , find the value of y” at the point where x=0.
- If you double the net force on an object, you’ll double its
- Implicit Function Theorem – Explanation and Examples
- In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point. If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. What is the height of the shelf above the point where the quarter leaves your hand?
- In a poker hand consisting of 5 cards, find the probability of holding 3 aces.
- In a random sample of soldiers who fought in the Battle of Preston, 774 soldiers were from the New Model Army, and 226 were from the Royalist Army. Use a 0.05 significance level to test the claim that fewer than one quarter of the soldiers were Royalist.
- In a study designed to prepare new gasoline.
- In a study of the accuracy of fast food drive-through orders, Restaurant A had 298 accurate orders and 51 non-accurate ones.
- In an experiment in space, one proton is fixed and other is released from rest (point A), from a distance of 5 mm away. What is the initial acceleration of the proton after it is released?
- In formulating hypotheses for a statistical test of significance, the null hypothesis is often, choose the correct option.
- In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of 6.0 m/s in 1.5 s. Assuming that the player accelerates uniformly, determine the distance he runs.
- In government data, a household consists of all occupants of a dwelling unit, while a family consists of 2 or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States.
- In how many different orders can five runners finish a race if no ties are allowed?
- In how many ways can 8 people be seated in a row if:
- In open-heart surgery, a much smaller amount of energy will defibrillate the heart. (a) What voltage is applied to the capcitor of a heart defibrilator that 40.0J of energy? (b) Find the amount of the stored charge.
- In regression analysis, the variable that is being predicted is the
- In the exponential growth or decay function y = y0e^kt, what does y0 represent?
- Incenter Theorem – Definition, Conditions and Examples
- Indirect Measurement – Explanation and Examples
- Intercept form Quadratic — Explanation and Examples
- Inverse Function Theorem – Explanation & Examples
- Inverse Variation – Explanation & Examples
- Is -1 a Rational Number? Detailed Explanation With Sample
- Is -6 a Rational Number? A Detailed Guide
- Is Statistics Harder Than Calculus?
- Is there a point between a 10 nC charge and a 20 nC charge at which the electric field is zero? What is the electric potential at this point if both charges are separated by 15 cm?
- Is Trigonometry Hard?
- It can be shown that the algebraic multiplicity of an eigenvalue lambda is always greater than or equal to the dimension of the eigenspace corresponding to lambda. Find h in the matrix A below such that the eigenspace for lambda = 4 is two-dimensional.
- Justine works for an organization committed to raising money for Alzheimer’s research. From past experience, the organization knows that about 20% of all potential donors will agree to give something if contacted by phone. They also know that of all people donating, about 5% will give 100 dollars or more. On average, how many potential donors will she have to contact until she gets her first 100 dollars donor?
- LASIK eye surgery uses pulses of laser light to shave off tissue from the cornea, reshaping it. A typical LASIK laser emits a 1.0-mm-diameter laser beam with a wavelength of 193 nm. Each laser pulse lasts 15 ns and contains 1.0 mJ of light energy.
- LASIK eye surgery uses pulses of laser light to shave off tissue from the cornea, reshaping it. A typical LASIK laser emits a 1.0-mm-diameter laser beam with a wavelength of 193 nm. Each laser pulse lasts 15 ns and contains 1.0 mJ of light energy.
- Let C be the curve intersection of the parabolic cylinder x^2=2y and the surface 3z=xy. Find the exact length of C from the origin to the point (6,18,36).
- Let f be a fixed 3×2 matrix, and H be the set of matrices A belonging to a 2×4 matrix. If we assume that the property FA = O holds true, show that H is a subspace of M2×4. Here O represents a zero matrix of order 3×4.
- Let F(x, y, z)=xi+yj+zk. Evaluate the integral of F along each of the following paths.
- Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).
- Let P(x,y) be the terminal point on the unit circle determined by t. Then find the value for sin(t), cos(t) and tan(t).
- Let vectors A =(2, -1, -4), B =(−1, 0, 2), and C =(3, 4, 1). Calculate the following expressions for these vectors:
- Let W be the set of all vectors of the form shown, where a, b, and c represent arbitrary real numbers
- Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.
- Let x represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. What are the possible values of x?
- Let x represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. What are the possible values of X?
- Line AB contains points A(4, 5) and B(9, 7). What is the slope of line AB?
- Line of Reflection – Explanation and Examples
- Linear vs Nonlinear Function: Explanation and Examples
- List five integers that are congruent to 4 modulo 12.
- Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data.
- Look at the normal curve below, and find μ, μ+σ, and σ.
- Martha invited 4 friends to go with her to the movies. Find the ways in which Martha can be sitted in the middle.
- Match the function with its graph (labeled i-vi)
- Match the parametric equations with the graphs. Give reasons for your choices.
- Match the vector field F with the correct plot. F(x,y) = (x, -y)
- Midpoint Theorem – Conditions, Formula, and Applications
- Multiplication Property of Inequality – Explanation and Examples
- Nathaniel is using the quadratic formula to solve the given equation.
- Nitrogen is compressed by an adiabatic compressor from 100 kPa and 25°C to 600 kPa and 290°C. Calculate the entropy generation for this process, in kJ/kg∙K.
- Now consider an excited-state hydrogen atom, what is the energy of the electron in the n=4 level?
- On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a rough patch that reduces her speed to 1.65 m/s due to a friction force that is 25% of her weight. Use the work–energy theorem to find the length of this rough patch.
- One number is 2 more than 3 times another. Their sum is 22. Find the numbers.
- Parseval’s Theorem – Definition, Conditions and Applications
- Perform the indicated operation and simplify the result. Leave your answer in factored form.
- Perimeter of a Parallelogram – Explanation & Examples
- Perimeter of a Rectangle – Explanation & Examples
- Perimeter of a Rhombus – Explanation & Examples
- Perimeter of a Square – Explanation & Examples
- Perimeter of a Triangle – Explanation & Examples
- Perpendicular Bisector Theorem – Explanation and Examples
- Population y grows according to the equation dy/dt = ky, where k is a constant and t is measured in years. If the population doubles every ten years, then the value of k is?
- Prime Polynomial: Detailed Explanation and Examples
- Properties of Rational Exponents – Explanation and Examples
- Prove or disprove that if a and b are rational numbers, then a^b is also rational.
- Prove or disprove that if a and b are rational numbers, then a^b is also rational.
- Prove or disprove that the product of two irrational numbers is irrational.
- Prove that if m and n are integers and m x n is even, then m is even or n is even.
- Prove that if n is a positive integer, then n is even if and only if 7n + 4 is even.
- Pythagorean Identities – Formula, Derivation, and Applications
- Rachel has good Distant vision but has a touch of Presbyopia. Her near point is $0.80$ m.
- Rational Root Theorem – Explanation & Examples
- Read the numbers and decide what the next number should be. 5, 15, 6, 18, 7, 21, 8.
- Rectangle has area 16 m^2. Express the perimeter of the rectangle as a function of the length of one of its sides.
- Recursive Formula – Definition, Formula, and Examples
- Reflection Function – Explanation and Examples
- Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increading t.
- Resistivity measurements on the leaves of corn plants are a good way to assess stress and overall health. The leaf of a corn plant has a resistance of 2.4M Ω measured between two electrodes placed 23 cm apart along the leaf. The leaf has a width of 2.7 cm and is 0.20 mm thick. What is the resistivity of the leaf tissue?
- Resolve the force F2 into components acting along the u and v axes and determine the magnitudes of the components.
- Right Prism: Definition, Explanation and Examples
- Rigid Transformation – Definition, Types, and Examples
- Rolle’s Theorem – Explanation and Examples
- Ropes 3m and 5m in length are fastened to a holiday decoration that is suspended over a town square. The declaration has a mass of 5kg. The ropes, fastened at different heights, make angles of 52 degrees and 40 degrees with the horizontal. Find the tension in each wire and the magnitude of each tension.
- Sampling Variability – Definition, Condition and Examples
- Satellite A orbits a planet with a speed of 10,000 m/s. Satellite B is twice as massive as satellite A and orbits at twice the distance from the center of the planet. What is the speed of satellite B? Assume that both orbits are circular.Satellite A orbits a planet with a speed of 10,000 m/s. Satellite B is twice as massive as satellite A and orbits at twice the distance from the center of the planet. What is the speed of satellite B? Assume that both orbits are circular.
- Segment BC is Tangent to Circle A at Point B. What is the length of segment BC?
- Select which of the following standard enthalpy of formation values is not zero at 25°C:
- Seven women and nine men are on the faculty in the mathematics department at a school.
- Several factors are involved in the creation of a confidence interval. In regards to the concept of confidence level, margin of error and sample mean, which of the following statements are true?
- Shape of Distribution – Definition, Features, and Examples
- Show that a root of x2 – 5x – 1 = 0 is real.
- Show that if A^2 is the zero matrix, then the only eigenvalue of A is 0.
- Show that the equation has exactly one Real root 2x+cosx=0.
- Show that the equation has exactly one real root.
- Show that the equation represents a sphere and find its center and radius.
- Show that the product of a number and seven is equal to two more than the number.
- Side Splitter Theorem – Rules, Application and Examples
- Simon is making wreaths to sell. He has 60 bows, 36 silk roses, and 48 silk carnations.
- Simplify tan(sin^{-1}(x))
- Sketch the graph of a function that satisfies the given conditions given as follows:
- Sketch the region bounded by the curves, and visually estimate the location of the centroid:
- Sketch the vector field f by drawing a diagram like this figure. f(x, y) = (yi + xj)/(x2 + y2)
- Solve differential equation ty’+(t+1)y=t , y(ln2)=1 , t>0
- Solve the differential equation by variation of parameters. y” + y = sin x.
- Solve the differential equation dp/dt=p−p^2
- Solve the equation explicitly for y and differentiate to get y’ in terms of x.
- Solve the exponential equation 3^x = 81 by expressing each side as a power of the same base and then equating exponents.
- Solve the given differential equation by variation of parameters.
- Solve the initial value problem for r as a vector function of t.
- Solve the system of equations and show all work.
- Solve the system of equations below.
- Solving 1 Divided by Infinity
- State how many mole ratios can be written for chemical reaction involving three substances.
- Suppose f and g are continuous functions such that g(2)=6 and lim[3f(x)+f(x)g(x)]=36. Find f(2), x→2
- Suppose f” is continuous on (−∞, ∞). If f ‘(3)=0 and f ”(3)=-3. What can you say about f?
- Suppose f(x) = 0.125x for 0 < x < 4. determine the mean and variance of x. round your answers to 3 decimal places.
- Suppose S and T are mutually exclusive events P(S)=20.
- Suppose that A and B are independent events such that the probability that neither occurs is a and the probability of B is b.
- Suppose that a population develops according to the logistic equation.
- Suppose that f(5)=1, f'(5)=6, g(5)=-3, and g'(5)=2. Find the following values of (fg)'(5), (f/g)'(5), and (g/f)'(5).
- Suppose that factory a produces 12 tables.
- Suppose that the height in inches of a 25-year-old man is a normal random variable with parameters μ=71 and σ^2=6.25.
- Suppose that X is a normal random variable with mean 5. If P(X>9)=0.2, approximately what is Var(X)?
- Suppose that you are rolling a six sided dice. Let A = get a number smaller than 2. What is P(Ac)?
- Suppose the CPI was 110 last year and is 121 this year.
- Suppose you are climbing a hill whose shape is given by the equation z=100 – 0.05x^2 – 0.1y^2, where x,y and z are measured in meters, and you are standing at a point with coordinates (60, 50, 1100). The positive x-axis points east and the positive y-axis points north. If you walk due south, will you start to ascend or descend? At what rate?
- Suppose you conduct a test and your p-value is equal to 0.93. What can you conclude?
- Suppose you conduct a test and your p-value turns out to be 0.08. What can you conclude?
- Suppose you have 1.0 mol of O_2 gas. How many coulombs of positive charge are contained in the atomic nuclei of this gas?
- Sydney Retailing (buyer) and Troy Wholesalers (seller) enter into the following transactions. May 11 Sydney accepts delivery of 25,000 dollars of merchandise it purchases for resale from Troy: invoice dated. Prepare journal entries that Sydney Retailing (buyer) records for these three transactions. Prepare journal entries that Troy Wholesalers (seller) records for these three transactions.
- The air in a bicycle tire is bubbled through water and collected at 25°C. If we assume that the air that has been collected at 25°C has a total volume of 5.45 L and pressure of 745 torr, calculate the moles of air that were stored in the bicycle tire?
- The amount 180.00 is what percent greater than 135.00?
- The amount of time Ricardo spends brushing his teeth follows a normal distribution with unknown mean and standard deviation. Ricardo spends less than one minute brushing his teeth about 40% of the time. He spends more than two minutes brushing his teeth 2% of the time. Use this information to determine the mean and standard deviation of this distribution.
- The asteroid belt circles the sun between the orbits of Mars and Jupiter.
- The base of S is an elliptical region with boundary curve 9x^2+4y^2=36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base. Find the volume of the Solid.
- The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of 45 degrees. With what speed must the animal leave the ground to reach that height?
- The cdf a certain college library checkout duration X is as follows:
- The components of a velocity field are given by u= x+y, v=xy^3 +16, and w=0. Determine the location of any stagnation points (V=0) in the flow field.
- The constant-pressure heat capacity of a sample of a perfect gas was found to vary with temperature according to the expression. Calculate q, w H and U when the temperature is raised from 25 degree to 100 degree.
- The current in a 50 mH inductor is known to be
- The current in a wire varies with time according to the relation $I=55A-\left(0.65\dfrac{A}{s^2}\right)t^2$.
- The density of acetic anhydride is 1.08 g/mL. How many moles are contained in 5 mL. Please show in detail how the answer was obtained.
- The diffuser in a jet engine is designed to decrease the kinetic energy of the air entering the engine compressor without any work or heat interactions. Calculate the velocity at the exit of a diffuser when air at 100 kPa and 30 C enters it with a velocity of 355m/s and the exit state is 200 kPa and 90C.
- The domain of every Rational function is the set of all Real numbers.
- The earth’s radius is 6.37×10^6 m; it rotates once every 24 hours.
- The electric potential at a point that is halfway between two identical charged particles is 300 V. What is the potential at a point that is 25% of the way from one particle to the other?
- The electric potential in a region of space is V=(350V.m)/√(x^2+y^2), where x and y are in meters.
- The figure shows a laser beam coming from the left, deflected by a 30-60-90 prism. What is the prism’s index of refraction?
- The following data represents the age of 30 lottery winners. 21 49 54 63 54 35 52 45 88 65 64 51 41 34 49 78 31 40 51 70 78 60 74 55 29 66 59 32 68 56 Complete the frequency distribution for the data. Bin Frequency 20-29 30-39 40-49 50-59 60-69 70-79 80-89
- The fox population in a certain region has an annual growth rate of 9 percent per year. It is estimated that the population in the year 2010 was 23,900. Find a function for the population and estimate the fox population in the year 2018.
- The graph of a function f is shown. Which graph is an antiderivative of f?
- The graph of f is shown. Evaluate each integral by interpreting it in terms of areas.
- The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral.
- The highest that george can suck water up a very long straw is 2.0 m . (this is a typical value.)
- The Humber bridge in England has the World’s longest single span, 1410 m .
- The integral represents the volume of a solid. Describe the solid. $\pi\int\limits_0^1(y^4−y^8)\,dy$
- The intensity L(x) of light x feet beneath the surface of the ocean satisfies the differential equation dL/dx = – kL, where k is a constant. As a diver you know from experience that diving to 18 ft in the Caribbean Sea cuts the intensity in half. You cannot work without artificial light when the intensity falls below a tenth of the surface value. About how deep can you expect to work without artificial light?
- The joint density of x and y is f(x y)=c(x^2-y^2)e^{-x}. Find the conditional distribution of Y, given X=x.
- The matter is more likely to exist in the ________ state as the pressure is increased or temperature is decreased.
- The measure of an angle is 6 less than 5 times its complement. What is the measure of compliment?
- The minute hand of a certain clock is 4 in long, Starting from the moment when the hand is pointing straight up, how fast is the area of the sector that is swept out by the hand increasing at any instant during the next revolution of the hand?
- The missing number in the series 9, ? , 6561, 43046721 is: 81, 25, 62, 31, 18.
- The molar solubility of pbBr2 at 25 °C is 1.0×10−2mol/l. Calculate ksp.
- The next number in the series 38, 36, 30, 28, 22 is ?
- The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of 8.8.
- The planet mercury’s surface temperature varies from 700K during the day to 90K at night. What are these values in Celsius and Fahrenheit?
- The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p= -1/6x + 100. Find a model that expresses the revenue R as a function of x.
- The probability density function of the net weight in pounds of a packaged chemical herbicide is f(x)=2.2 for 49.8 < x < 50.2 pounds. a) Determine the probability that a package weighs more than 50 pounds. b) How much chemical is contained in 90% of all packages?
- The probability density function of x the lifetime of a certain type of electronic device
- The relatively high resistivity of dry skin, about 1 × 10^6 ohm.m, can safely limit the flow of current into deeper tissues of the body. Suppose an electrical worker places his palm on an instrument whose metal case is accidentally connected to a high voltage. The skin of the palm is about 1.5 mm thick. Estimate the area of skin on the worker’s palm that would contact a flat panel, then calculate the approximate resistance of the skin of the palm.
- The seller of a loaded die claims that it will favor the outcome 6. We don’t believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain.
- The solid lies between planes perpendicular to the x-axis at x=-1 and x=1.
- The solubility of copper (I) chloride is 3.91 mg per 100.0 ml of solution. Calculate the value of K_sp.
- The speed of sound in air at 20 C is 344 m/s
- The three balls each weigh 0.5 lb and have a coefficient of restitution of e = 0.85. If ball A is released from rest and strikes ball B and then ball B strikes ball C, determine the velocity of each ball after the second collision has occurred. The balls slide without friction.
- The three masses shown in the figure are connected by massless, rigid rods. Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page. Express your answer to two significant figures and include the appropriate units. Find the moment of inertia about an axis that passes through masses B and C. Express your answer to two significant figures and include the appropriate units.
- The three masses shown in the figure are connected by massless, rigid rods. Find the moment of inertia about an axis that passes through masses B and C.
- The two intervals (114.4, 115.6) is confidence interval for mean value defined as true average resonance frequency (in hertz) for all tennis rackets of a certain type. What is the value of the sample mean resonance frequency?
- The velocity function (in meters per second) is given for a particle moving along a line.
- The velocity in a certain flow field is given by the equation.
- The water gas shift reaction CO(g)+H_2 O⇌ CO_2(g)+H_2(g) is used industrially to produce hydrogen. The reaction enthalpy is ΔH^o=-41kj. To increase the equilibrium yield of hydrogen would you use high or low temperature?
- The wave speed on a string under tension is 200 m/s. What is the speed if he tension is doubled?
- The world’s fastest humans can reach speeds of about 11m/s. How high does such a sprinter have to climb to increase the gravitational potential energy by an amount equal to the kinetic energy at full speed?
- Thirteen people on a softball team show up for a game. How many ways are there to assign the 10 positions by selecting players from the 13 people who show up?
- Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force F. The magnitude of the tension in the string between blocks B and C is T=3.00N. Assume that each block has mass m=0.400kg. What is the magnitude F of the force? What is the tension tab in the string between block A and block B?
- Three uniform spheres are fixed at positions shown in the figure. Find the magnitude and direction of the force of gravity acting on a 0.055kg mass placed at the origin.
- To throw a discus, the thrower holds it with a fully outstretched arm. Starting from rest, he begins to turn with a constant angular acceleration, releasing the discuss after making one complete revolution. The diameter of the circle in which the discus moves is about 1.8 m. If the thrower takes 1.0 s to complete one revolution, starting from rest, what will be the speed of the discus at release?
- To win a prize at the country fair, you’re trying to knock down a heavy bowling pin by hitting it with a thrown object. Should you choose to throw a rubber ball or a beanbag of equal size and weight? Explain.
- Triangle Proportionality Theorem – Explanation and Examples
- Triangle Reflection – Definition, Techniques, and Examples
- True or False. The graph of a rational function may intersect a horizontal asymptote.
- Two 2.1cm diameter disks face each other, 2.9mm apart. They are charged to 10 nC. (a) What is the electric field strength between the disks?
- Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose that we win 2 for each black ball selected and we lose 2 for each black ball selected and we lose 1 for each white ball selected. Let X denote our winnings. What are the possible values of X, and what are the probabilities associated with each value?
- Two cards are drawn successively and without replacement from an ordinary deck of playing cards Compute the probability of drawing
- Two components of a minicomputer have the following joint PDF for their useful lifetimes X and Y:
- Two large parallel conducting plates carrying opposite charges of equal magnitude are separated by 2.20cm.
- Two light bulbs have constant resistances of 400 ohm and 800 ohm. If the two light bulbs are connected in series across a 120 V line, find the power dissipated in each bulb
- Two protons are aimed directly toward each other by a cyclotron accelerator with speeds of 3.50 * 10^5 m/s, measured relative to the Earth. Find the maximum electrical force that these protons will exert on each other.
- Two runners start a race at the same time and finish in a tie.
- Two small spheres spaced 20.0 centimeters apart have equal charges.
- Two snowcats in antarctica tow a housing unit to a new location at McMurdo Base, Antarctica. The sum of the forces Fa and Fb exerted on the unit by the horizontal cables is parallel to the line L. Determine Fb and Fa + Fb.
- Two stores sell watermelons. At the first store, the melons weigh an average of 22 pounds, with a standard deviation of 2.5 pounds. At the second store, the melons are smaller, with a mean of 18 pounds and a standard deviation of 2 pounds. You select a melon at random at each store.
- Unpolarized light with intensity I₀ is incident on two polarizing filters. Find intensity of the light after passing through second filter.
- Upside Down U in Math- Detailed Explanation
- Use a direct proof to show that the product of two odd numbers is odd.
- Use a double integral to find the area of the region inside the circle and outside the circle.
- Use a double integral to find the area of the region. The region inside the cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ).
- Use a double integral to find the area of the region. The region inside the circle (x-5)^2+y^2=25 and outside the circle x^2+y^2=25.
- Use a double integral to find the volume of the solid shown in the figure.
- Use a linear approximation (or differentials) to estimate the given number. (1.999)^5
- Use coordinate vectors to test the linear independence of the sets of polynomials. Explain your work.
- Use definition 2 to find an expression for the area under the graph of f as a limit. Do not evaluate the limit.
- Use L(x) to approximate the numbers √(3.9) and √(3.99). (Round your answers to four decimal places.)
- Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval.
- Use the Distributive Property To Remove the Parentheses
- Use the row of numbers shown below to generate 12 random numbers between 01 and 99. 78038 18022 84755 23146 12720 70910 49732 79606 Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?
- Use the table of values of f(x, y) to estimate the values of fx(3, 2), fx(3, 2.2), and fxy(3, 2).
- Using a directrix of y=−2 and a focus of (2, 6), what quadratic function is created?
- Using the two equations E=hv and c=lambda v derive an equation expressing E in terms of h,c and lambda.
- V_1 and V_2 are different vectors with lengths V_1 and V_2 respectively. Find the following:
- Verify that each given function is a solution of the differential equation:
- Vertex Formula: Complete Definition, Examples, and Solutions
- Vertical Angles Theorem – Definition, Applications, and Examples
- Viewed from a point above the north pole, is the angular velocity positive or negative?
- Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 20 kW of shaft power. The free surface of the upper reservoir is 45 m higher than that of the lower reservoir. If the flow rate of water is measured to be 0.03 m^3/s, determine mechanical power that is converted to thermal energy during this process due to frictional effects.
- What are the dimensions of the lightest open-top right circular cylinder can hold a volume of 1000 cm^3 ?
- What assumption(s) are frequently made when estimating a cost function?
- What does a 1:1 ratio mean?
- What does a 2:1 ratio mean?
- What Does Triangle ABC Is Similar to Triangle DEF Mean?
- What Does Zero Slope Mean? How To Calculate Zero Slope
- What Is -b/2a and Why Is It Important in Math?
- What is 0 on a Graph? Explanation and Examples
- What is 10∠ 30 + 10∠ 30? Answer in polar form. Note that the angle is measured in degrees here.
- What is 12/5 as a mixed fraction?
- What is 3.16 repeating as a fraction?
- What is a Frequency distribution of qualitative data and why is it useful?
- What is a Set of Ordered Pairs?
- What is an advantage of using a stem-and-leaf plot instead of a histogram? What is the disadvantage?
- What is Calculus 4?
- What is d/dx? A Detailed Explanation
- What Is n Choose 2?
- What is stated by the null hypothesis for the chi-square test for independence?
- What is the absolute value of 4i.
- What is the acceleration of the block when x= 0.160 m?
- What is the angle between the electric field and the axis of the filter?
- What is the antiderivative of the given expression.
- What is the block’s speed now?
- What is the current if the emf frequency is doubled?
- What is the difference between f(-x) and -f(x)?
- What is the electric flux through a spherical surface just inside the inner surface of the sphere?
- What is the flea’s Kinetic Energy as it leaves the ground? A 0.50 mg flea, jumping straight up, reach a height of 30 cm if there were no air resistance. In reality, air resistance limits the height to 20 cm.
- What is the height of the rocket above the surface of the earth at t=10.0 s ?
- What Is the Integral of Arctan x And What Are Its Applications?
- What is the Laplace transform of u(t-2)?
- What is the least common multiple of 2 and 4?
- What is the length of X in the diagram below?
- What is the passenger’s weight while the elevator is speeding up?
- What is the position vector r(t) as a function of angle Θ(t). Give your answer about R, Θ(t), and the unit vectors x and y corresponding to the coordinate system.
- What is the probability that a fair die never comes up an even number when it is rolled six times?
- What is the probability that a five-card poker hand does not contain the queen of hearts?
- What is the probability that the sum of the numbers on two dice is even when they are rolled?
- What is the quotient of the complex number (4-3i)/(-1-4i)?
- What is the smallest possible depth of a leaf in a decision tree for a comparison sort?
- What is the smallest value the angle θ can have with a rope without breaking it.
- What is the speed vgas of the exhaust gas relative to the rocket?
- What is the total area of the figure below?
- What is the total surface charge qext on the exterior surface of the conductor?
- What is the volume of the cone? Use π ≈ 3.14 and round your answer to the nearest hundredth. The height is 14in and diameter is 10in.
- What is the width of the central bright fringe?
- What is wrong with the following equation:
- What is x^0 – Detailed Explanation & Examples
- What minimum energy is required to excite a vibration in HCl?
- What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate?
- What values of b satisfy 3(2b + 3)2 = 36?
- When a honeybee flies through the air, it develops a charge of +16pC.
- When Does a Quadratic Function Have No Real Solution?
- When the current i is positive, the capacitor charge q is decreasing.
- Where is the greatest integer function f(x)= ⌊x⌋ not differentiable? Find a formula for f’ and sketch its graph.
- Whether the given study depicts an observational study or a designed experiment and to identify the response variable. The study is conducted to compare the battery lives of a brand-name battery and a generic plain-label battery in digital cameras. For this purpose, 30 digital cameras are randomly selected and divided into 2 groups, one of the groups uses the brand-name battery while the other one uses the generic plain-label battery. In both the cameras, pictures are taken under identical conditions by keeping all variables, except the battery-type, in control.
- Which equation could be used to calculate the sum of the geometric series?
- Which equation has a graph perpendicular to the graph of 7x=14y-8?
- Which expression is equivalent to the following complex fraction – 2/x + (5/y)/(3/y) – 2/x ?
- Which of the following are true about regression with one predictor variable? Check all the given options.
- Which of the following expressions are meaningful which are meaningless explain:
- Which of the following integrals are improper? (Select all that apply.)
- Which of the following is a linear function?
- Which of the following is NOT a conclusion of the Central Limit Theorem? Choose the correct answer below.
- Which of the following is not a requirement of the binomial probability distribution?
- Which of the following is the nth taylor polynomial tn(x) for f(x)=ln(1−x) based at b=0?
- Which of the following transformations are linear?
- Which of these functions from R to R are bijections?
- Which one of the following species has as many electrons as it has neutrons?
- Which pair of angles has congruent values for the sinx° and the cosy°?
- Which pair of numbers has an LCM of 16
- Which relation does not represent a function.
- Which Relation Is Not a Function? Explanation and Examples
- Which Table Represents a Direct Variation Function: A Full Guide
- Which Table Represents a Linear Function?
- Which table represents exponential growth.
- Would you expect distributions of these variables to be uniform unimodal or bimodal? Symmetric or skewed? Explain why.
- Write a reaction that shows what happens when methanol is treated with potassium hydroxide?
- Write an algebraic expression for each word phrase. 4 more than p
- Write an algebraic expression for: 6 more than a number c.
- Write out the first four terms of the maclaurin series of f(x).
- Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.
- Write the area A of a circle as a function of its circumference C.
- Write the area A of square as a function of its perimeter P.
- Write the first trigonometric function in terms of the second theta for in the given quadrant:
- X-coordinate: Complete Definition, Detailed Examples, and Meaning
- X~N(570, 103). Find the z-score corresponding to an observation of 470.
- y = x Reflection – Definition, Process and Examples
- y = x^2: A Detailed Explanation Plus Examples
- You are holding one end of an elastic cord that is fastened to a wall 3.5 m away. You begin shaking the end of the cord at 5 Hz, creating a continuous sinusoidal wave of wavelength 1.0 m. How much time will pass until a standing wave fills the entire length of the string?
- You live on a busy street, but as a music lover, you want to reduce the traffic noise.
- You roll a die. If it comes up a 6 you win 100. If not, you get to roll again. If you get a 6 the second time, you win 50. If not, you lose.
- Your iron works has contracted to design and build a 500 cubic foot, square-based, open-top, rectangular steel holding tank for a paper company. The tank is made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weigh as little as possible. What dimensions do you tell the shop to use?