### 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
- 17 Times Table - Explanation & Example
- 17th
- 18 Times Table - Explanation & Examples
- 18th
- 19 Times Table - Explanation & Examples
- 19th
- 19th_bolyai
- 2 Times Table - Explanation & Examples
- 20 Times Table - Explanation & Examples
- 20th
- 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 – Explanation & Examples
- Angle of Elevation
- 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
- Box and whisker plot
- Brahmagupta: Mathematician and Astronomer
- Calculus
- 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
- 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
- Convert Decimals to Fractions – Explanation & Examples
- 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 - Examples and Explanation
- Cosine – Explanation & Examples
- Coterminal Angles – 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
- 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
- Factors of -40: Prime Factorization, Methods, Tree, and Examples
- Factors of 101: Prime Factorization, Methods, and Example
- Factors of 102: Prime Factorization, Methods, and Example
- Factors of 103: Prime Factorization, Methods, and Example
- Factors of 104: Prime Factorization, Methods, and Example
- Factors of 106: Prime Factorization, Methods, and Example
- Factors of 107: Prime Factorization, Methods, and Example
- Factors of 109: Prime Factorization, Methods, and Example
- Factors of 110: Prime Factorization, Methods, and Example
- Factors of 119: Prime Factorization, Methods, Tree, and Examples
- Factors of 130: Prime Factorization, Methods, Tree, and Examples
- Factors of 18: Prime Factorization, Methods, Tree, and Examples
- Factors of 24: Prime Factorization, Methods, Tree, and Examples
- Factors of 289: Prime Factorization, Methods, Tree, and Examples
- Factors of 336: Prime Factorization, Methods, Tree, and Examples
- Factors of 36: Prime Factorization, Methods, Tree, and Examples
- Factors of 384: Prime Factorization, Methods, Tree, and Examples
- Factors of 48: Prime Factorization, Methods, and Examples
- Factors of 576: Prime Factorization, Methods, Tree, and Examples
- Factors of 59: Prime Factorization, Methods, and Example
- Factors of 600: Prime Factorization, Methods, and Examples
- Factors of 67: Prime Factorization, Methods, Tree, and Examples
- Factors of 71: Prime Factorization, Methods, and Example
- Factors of 79: Prime Factorization, Methods, and Example
- Factors of 82: Prime Factorization, Methods, and Example
- Factors of 83: Prime Factorization, Methods, Tree, and Examples
- Factors of 86: Prime Factorization, Methods, and Example
- Factors of 92: Prime Factorization, Methods, and Example
- Factors of 93: Prime Factorization, Methods, Tree, and Examples
- Factors of 95: Prime Factorization, Methods, and Example
- Factors of 97: Prime Factorization, Methods, and Example

- 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
- 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 & 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 Common Factor
- Greatest Integer Function - Explanation & Examples
- GREEK MATHEMATICS & MATHEMATICIAN - Numerals and Numbers
- greek_plato
- Green's theorem - Theorem, Applications, and Examples
- Half Angle Formula - Examples and Explanation
- Harmonic series - Properties, Formula, and Divergence
- hellenistic
- 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
- Inversely Proportional – Explanation & Examples
- Isaac Newton: Math & Calculus
- islamic
- 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 - Explanation & 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
- 2 Step Equation Calculator + Online Solver With Free Steps
- 3 Systems of Equations Calculator + Online Solver With Free Steps
- Acid Base Calculator + Online Solver With Free Easy Steps
- Alpha Calculator + Online Solver With Free Steps
- Arc Length Calculator Calculus + 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
- Big O Calculator + Online Solver With Free Steps
- Boolean Algebra 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
- Cubic Equation Calculator + Online Solver With Free Steps
- Curl Calculator + Online Solver With Free Steps
- Curvature Calculator + Online Solver With Free Steps
- Cylindrical Coordinates Integral Calculator + Online Solver With Free Steps
- Determinant Calculator 4x4 + Online Solver With Free Steps
- Difference Quotient Calculator + Online Solver with Free Steps
- Dimensional Analysis Calculator + Online Solver With Free Steps
- Directional Derivative Calculator + Online Solver With Free Steps
- Disk Method Calculator + Online Solver With Free Steps
- Distributive Property Calculator + Online Solver With Free Steps
- Domain and Range Calculator + Online Solver With Free Steps
- Eigenvalue Calculator 2x2 + Online Solver with Free Steps
- Equivalent Expressions Calculator + Online Solver With Free Steps
- Euclidean Distance Calculator + Online Solver With Free Steps
- Evaluate the Definite Integral Calculator + Online Solver With Free Steps
- Even or Odd Function Calculator + Online Solver with Free Steps
- Focal Diameter Calculator + Online Solver With Free Steps
- General Solution Calculator + Online Solver With Free Steps
- Geometric Sequence Calculator + Online Solver With Free Easy Steps
- Hessian Matrix Calculator + Online Solver With Free Steps
- Infinite Series Calculator + Online Solver With Free Steps
- Instantaneous Rate of Change Calculator + Online Solver With Free Steps
- Instantaneous Velocity Calculator + Online Solver With Free Steps
- Intersection Calculator + Online Solver With Free Steps
- Interval of Convergence Calculator + Online Solver With Free Steps
- Invnorm Calculator Online + Online Solver With Free Steps
- Jacobian Matrix Calculator + Online Solver With Free Steps
- L'Hôpital's Rule Calculator + Online Solver With Free Steps
- Least Squares Solution Calculator + Online Solver With Free Steps
- Length of Polar Curve Calculator + Online Solver With Free Steps
- Lewis Structure Calculator + Online Solver With Free Steps
- Light Speed Calculator + Online Solver With Free Steps
- Linear Programming Calculator + Online Solver With Free Steps
- Matrix Null Space Kernel Calculator + Online Solver With Free Steps
- Mean Value Theorem Calculator + Online Solver With Free Steps
- Miller Indices Calculator + Online Solver With Free Steps
- Mixture Problem Calculator + Online Solver With Free Steps
- Multiplicity Calculator + Online Solver With Free Steps
- Multiply Rational Expressions Calculator + Online Solver With Free Steps
- Multivariable Critical Point Calculator + Online Solver With Free Steps
- Net Ionic Equation Calculator + Online Solver with Free Steps
- Nth Derivative Calculator + Online Solver With Free Steps
- Parametric Arc Length Calculator + Online Solver With Free Steps
- Parametric Equation Calculator + Online Solver With Free Steps
- Parametric To Cartesian Equation Calculator + Online Solver
- Partial Derivative Calculator + Online Solver With Free Steps
- Partial Fraction Calculator + Online Solver With Free Steps
- Period Calculator Math + Online Solver with Free Steps
- PH and POH Calculator + Online Solver With Free Easy Steps
- Piecewise Laplace Transform Calculator + Online Solver with Free Steps
- Polar Derivative Calculator + Online Solver With Free Steps
- Polar Double Integral Calculator + Online Solver With Free Steps
- Polar Form Calculator + Online Solve With Free Easy Steps
- Power Series Calculator + Online Solver With Free Steps
- Product Rule Calculator + Online Solver With Free Steps
- Product Sum Calculator + Online Solver With Free Steps
- Quadratic Formula Calculator + Online Solver With Free Steps
- Rate Constant Calculator + Online Solver With Free Steps
- Rational Expression Calculator + Online Solver With Free Steps
- Rearranging Equations Calculator + Online Solver With Free Steps
- Rectangular to Polar Equation Calculator + Online Solver With Free Steps
- Recursive Sequence Calculator + Online Solver With Free Steps
- Reflection Calculator + Online Solver With Free Steps
- Repeating Decimal Calculator + Online Solver With Free Steps
- Root Finder Calculator + Online Solver With Free Steps
- Secant Line Calculator + Online Solver With Free Steps
- Sequence Convergence Calculator + Online Solver With Free Steps
- Sequence Formula Calculator + Online Solver With Free Steps
- Shell Method Calculator + Online Solver With Free Steps
- Simplify the Complex Fraction Calculator + Online Solver With Free Steps
- Solids Of Revolution Calculator + Online Solver With Free Steps
- Solubility Calculator + Online Solver With Free Steps
- Solve for X Calculator + Online Solver With Free Steps
- Stoichiometry Calculator + Online Solver With Free Steps
- Summation Calculator + Online Solver With Free Steps
- Surface Area Calculator Calculus + Online Solver With Free Steps
- Table of Values Calculator + Online Solver With Free Steps.
- Triple Integral Calculator + Online Solver With Free Steps
- Valence Electron Calculator + Online Solver With Free Steps
- Variable Isolation Calculator + Online Solver With Free Steps
- Venn Diagram Calculator + Online Solver With Free Steps
- Zeros Calculator + Online Solver With Free Steps

- Math Lessons
- Math Transformations
- Mathematical induction - Explanation and Example
- Matrices
- Matrices - Explanation & Examples
- Matrix addition - Explanation & Examples
- Matrix equation - Explanation & Examples
- Matrix multiplication - Explanation & Examples
- Matrix subtraction - Explanation & Examples
- Mayan Mathematics - Numbers & Numerals
- Mean statistics – Explanation & Examples
- Mean value theorem - Conditions, Formula, and Examples
- Measures of Central Tendency
- Median mean mode
- Median statistics
- medieval
- Midpoint Formula – Explanation & Examples
- Mode statistics – Explanation & Examples
- Multiplication – Explanation & Examples
- Multiplication by a Scalar - Explanation and Examples
- Multiplication Chart – Explanation & Examples
- Multiplication Property of Equality – Examples and Explanation
- Multiplying and Dividing Integers – Methods & Examples
- Multiplying complex numbers - Techniques, Explanation, and Examples
- Multiplying Decimals – Explanation & Examples
- Multiplying Exponents – Explanation & Examples
- Multiplying Expressions – Methods & Examples
- Multiplying Fractions – Methods & Examples
- Multiplying Mixed Numbers – Methods & Examples
- Multiplying Numbers in Scientific Notation – Technique & Examples
- Multiplying Polynomials – Explanation & Examples
- Multiplying Radicals – Techniques & Examples
- Multiplying Rational Expressions – Techniques & Examples
- Mutually exclusive events - Explanation & Examples
- Negative Exponents – Explanation & Examples
- Negative Numbers – Explanation & Examples
- Negative reciprocal - Explanation and Examples
- Negative Vectors - Explanation and Examples
- Newton's method - Process, Approximation, and Example
- NICCOLò TARTAGLIA, GEROLAMO CARDANO & LODOVICO FERRARI
- Non Homogeneous Differential Equation - Solutions and Examples
- Normal Distribution – Explanation & Examples
- Normal Probability Plot - Explanation & Examples
- Normal vector - Explanation and Examples
- Nth term test - Conditions, Explanation, and Examples
- Number Properties - Definition & Examples
- Number Sequence – Explanation & Examples
- Numbers in Scientific Notation – Explanation & Examples
- Oblique asymptotes – Properties, Graphs, and Examples
- Obtuse Angle
- Odd and Even Numbers
- One sided limits - Definition, Techniques, and Examples
- One to one function - Explanation & Examples
- Opposite adjacent hypotenuse – Explanation & Examples
- Order of Operations – PEDMAS
- Ordering Fractions – Explanation & Examples
- Orthogonal vector - Explanation and Examples
- Parabola - Properties, Components, and Graph
- Parallel Lines - Definition, Properties, and Examples
- Parallel Planes - Explanation & Examples
- Parallel Vectors - Explanation and Examples
- Parametric Curves - Definition, Graphs, and Examples
- Parametric equations - Explanation and Examples
- Parametrize a circle - Equations, Graphs, and Examples
- Parametrize a line - Equations, Graphs, and Examples
- Parent Functions - Types, Properties & Examples
- Partial Derivatives - Definition, Properties, and Example
- Partial Fraction Decomposition – Explanation & Examples
- Partial Fractions - Definition, Condition, and Examples
- Pascal's triangle - Definition, Patterns, and Applications
- Paul Cohen: Set Theory and The Continuum Hypothesis
- Percent Difference – Explanation & Examples
- Percent Error – Explanation & Examples
- Percentage Change – Explanation & Examples
- Percentage Conversion – Methods & Examples
- Percentage of a Number – Explanation & Examples
- Percentage to Decimal – Conversion Method & Examples
- Perfect Square Trinomial – Explanation & Examples
- Perimeters of Polygons – Explanation & Examples
- Permutation - Explanation & Examples
- Pictograph – Explanation & Examples
- Pie chart
- Piecewise Functions - Definition, Graph, and Examples
- Pierre De Fermat Mathematician
- Place Value – Explanation & Examples
- Polar Coordinates - Definition, Conversion, and Examples
- Polar Curves - Definition, Types of Polar Curves, and Examples
- Polar form - General Form, Conversion Rules, and Examples
- Polar to rectangular equation - Equations, Graphs, and Examples
- Polygons
- Polynomial equation - Properties, Techniques, and Examples
- Polynomial functions - Properties, Graphs, and Examples
- Position Vector - Explanation and Examples
- Power function - Properties, Graphs, & Applications
- Power reducing identities - Formulas, Proof, and Application
- Power Rule - Derivation, Explanation, and Example
- Power Series - Definition, General Form, and Examples
- Precalculus
- prehistoric
- Prime & Composite Numbers – Explanation with Examples
- Prime Factorization – Explanation & Examples
- Privacy Policy
- Probability
- Probability Density Function – Explanation & Examples
- Probability of an Event - Explanation & Strategies
- Probability of multiple events - Conditions, Formulas, and Examples
- Probability with replacement - Explanation & Examples
- Probability Without Replacement - Explanation & Examples
- Product rule - Derivation, Explanation, and Example
- Properties of Equality – Explanation & Examples
- Properties of Logarithm – Explanation & Examples
- Proportions – Explanation & Examples
- Pythagoras of Samos | Famous Mathematician
- Pythagorean Theorem – Explanation & Examples
- Pythagorean Triples – Explanation & Examples
- Quadrantal Angles
- Quadratic Formula – Explanation & Examples
- Quadratic Inequalities – Explanation & Examples
- Quadric surfaces - Definition, Types, and Examples
- Quadrilaterals – Explanation & Examples
- Quadrilaterals in a Circle – Explanation & Examples
- Questions & Answers
- Quotient rule – Derivation, Explanation, and Example
- Radicals that have Fractions – Simplification Techniques
- Range statistics - Explanation & Examples
- Ratio Test - Definition, Conditions, and Examples on Series
- Rational function - Properties, Graphs, and Applications
- Rational function holes - Explanation and Examples
- Ratios – Explanation & Examples
- Reciprocal Function - Properties, Graph, and Examples
- Reciprocals – Definition & Examples
- Rectangular form - Definition, Example, and Explanation
- Recursive sequence - Pattern, Formula, and Explanation
- Reducing Fractions – Explanation & Examples
- Reference Angle - Explanation and Examples
- Reflection in Geometry
- Reflex Angle
- Reflexive Property of Equality – Explanation and Examples
- Related rates - Definition, Applications, and Examples
- Relations and Functions – Explanation & Examples
- Relative Frequency
- Remainder Theorem – Method & Examples
- René Descartes
- Resultant vector - Explanation and Examples
- Riemann Sum - Two Rules, Approximations, and Examples
- Right Angle
- ROMAN MATHEMATICS - Numerals & Arithmetic
- Root Test - Definition, Conditions, and Examples on Series
- Roots of complex numbers - Examples and Explanation
- Rotation in Geometry - Explanation and Examples
- Rounding Decimals – Methods & Example
- Rounding Numbers – Definition, Place-value Chart & Examples
- Row vector - Explanation & Examples
- Rules of Divisibility – Methods & Examples
- Rules of Exponents – Laws & Examples
- Sample Space - Explanation and Examples
- Sampling Distribution - Explanation & Examples
- Sas Triangle – Explanation & Examples
- Scalar matrix - Explanation & Examples
- Scatter Plot
- Secant cosecant cotangent - Explanation & Examples
- Second Order Homogeneous Differential Equation - Forms and Examples
- Set builder notation - Explanation and Examples
- Set Equality – Explanation & Examples
- Set Notation – Explanation & Examples
- Set theory – Definition and Examples
- Sets & Set Theory
- Shell Method -Definition, Formula, and Volume of Solids
- Sieve of Eratosthenes – Prime Number Algorithm
- Similar Triangles – Explanation & Examples
- Simple Interest – Explanation & Examples
- Simplify matrix - Explanation & Examples
- Simplifying Expressions – Tricks & Examples
- Simplifying Radicals – Techniques & Examples
- Simplifying Rational Expressions – Explanation & Examples
- Simplifying Square Roots – Techniques and Examples
- Sine – Explanation & Examples
- Sine Graph - Examples and Explanation
- Singular matrix - Explanation & Examples
- Site Map
- Skew lines - Explanation & Examples
- Slope of a Line – Explanation & Examples
- Slopes of Parallel and Perpendicular Lines – Explanation & Examples
- Solving Absolute Value Equations – Methods & Examples
- Solving Cubic Equations – Methods & Examples
- Solving Equations – Techniques & Examples
- Solving for a Variable in a Formula – Literal Equations
- Solving Inequalities – Explanation & Examples
- Solving Logarithmic Equations – Explanation & Examples
- Solving Logarithmic Functions – Explanation & Examples
- Solving Multi-Step Equations – Methods & Examples
- Solving Single-step Inequalities – Methods & Examples
- Solving System of Equations – Methods & Examples
- Solving Two-Step Equations – Techniques & Examples
- sources
- Special Right Triangles – Explanation & Examples
- Spherical Coordinates - Definition, Graph, and Examples
- Square matrix - Explanation & Examples
- Square Roots – Explanation & Examples
- Squares & Perfect Squares – Explanation & Examples
- Squares & Square Roots – Difference & Examples
- Squeeze theorem - Definition, Proof, and Examples
- Ssa Triangle - Explanation & Examples
- Sss Triangle - Explanation & Examples
- Statistics
- Stem and leaf plot
- story
- Story Of Mathematics Acquires Mathforge.net; Strengthens Its Position In The Math Learning Industry
- Straight Angle
- Subset - Definition and Examples
- Substitution Property of Equality - Explanation and Examples
- Subtracting complex numbers - Techniques, Explanation, and Examples
- Subtracting Exponents – Explanation & Examples
- Subtracting Fractions – Methods & Examples
- Subtracting Mixed Numbers – Methods & Examples
- Subtraction – Explanation & Examples
- Subtraction Property of Equality – Explanation and Examples
- Sum and Difference Formulas - Examples and Explanation
- Sum Rule – Explanation and Examples
- Sumerian/Babylonian Mathematics
- Summary Statistics
- Supplementary Angles – Explanation & Examples
- Surface Area of a Cone – Explanation & Examples
- Surface Area of a cube – Explanation & Examples
- Surface Area of a cuboid – Explanation & Examples
- Surface Area of a Cylinder – Explanation & Examples
- Surface Area of a Prism – Explanation & Examples
- Surface Area of a Pyramid – Explanation & Examples
- Surface Area of a Solid – Explanation & Examples
- Surface Area of a Sphere – Explanation & Examples
- Surface Integral - General Form, Techniques, and Examples
- Symmetric difference - Definition and Examples
- Symmetric Property of Equality – Explanation and Examples
- Synthetic Division – Explanation & Examples
- System of Linear Inequalities – Explanation & Examples
- Tally chart – Explanation & Examples
- Tangent – Explanation & Examples
- Tangent Graph - Examples and Explanation
- Tangent Plane - Definition, Equation, and Examples
- Tangent to a Circle – Explanation & Examples
- Tautology
- Taylor Series - Definition, Expansion Form, and Examples
- Telescoping series - Components, Formula, and Technique
- Thales’ Theorem – Explanation & Examples
- The Binomial Distribution – Explanation & Examples
- The Cosine Rule – Explanation & Examples
- The Expected Value – Explanation & Examples
- The Inscribed Angle Theorem – Explanation & Examples
- The Number Line – Explanation & Examples
- The Percentile – Explanation & Examples
- The Poisson Distribution – Explanation & Examples
- The Population Mean – Explanation & Examples
- The Quartiles – Explanation & Examples
- The Random Variable – Explanation & Examples
- The Sample Mean – Explanation & Examples
- The Sample Variance – Explanation & Examples
- The Sine Rule – Explanation & Examples
- The Standard Deviation – Explanation & Examples
- Theoretical Probability - Explanation & Examples
- Transformations of Functions - Explanation & Examples
- Transitive Property of Equality – Explanation and Examples
- Translation in Geometry
- Tree Diagram: Explanation and Examples
- Triangle Inequality – Explanation & Examples
- Triangle Sum Theorem – Explanation & Examples
- Trig Addition Identities - Examples and Explanation
- Trigonometric derivatives - Derivation, Explanation, and Examples
- Trigonometric Equations - Examples and Explanation
- Trigonometric form - Definition, Example, and Explanation
- Trigonometric Functions – Explanation & Examples
- Trigonometric Identities - Examples and Explanation
- Trigonometric Ratios
- Trigonometric special angles – Explanation & Examples
- Trigonometric substitution - Forms, Technique, and Examples
- Trigonometry
- Trigonometry angles – Explanation & Examples
- Triple Integral - Definition, General Forms, and Examples
- Types of Angles – Explanation & Examples
- Types of Numbers – Difference and Classification
- Types of Triangles – Explanation & Examples
- Union of sets – Definition and Examples
- Union vs intersection - Explanation and Examples
- Unit Circle - Explanation and Examples
- Unit Circle Memorization
- Unit vector - Explanation and Examples
- Universal set - Definition and Examples
- Vector Addition - Explanation and Examples
- Vector Calculus - Definition, Summary, and Vector Analysis
- Vector Components - Explanation and Examples
- Vector dot product - Explanation and Examples
- Vector equations - Explanation and Examples
- Vector Fields - Definition, Graphing Technique, and Example
- Vector function - Definition, Properties, and Explanation
- Vector Geometry - Explanation and Examples
- Vector Magnitude – Explanation & Examples
- Vector multiplication - Types, Process, and Examples
- Vector Subtraction - Explanation and Examples
- Vectors
- Vectors Equation of a Line - Definition, General Forms, and Examples
- Venn diagram - Explanation & Examples
- Vertical Angles – Explanation & Examples
- Vertical asymptotes - Properties, Graphs, and Examples
- Vertical Compression - Properties, Graph, & Examples
- Vertical Stretch - Properties, Graph, & Examples
- Volume of Cones – Explanation & Examples
- Volume of Cubes – Explanation & Examples
- Volume of Cylinders – Explanation & Examples
- Volume of Prisms – Explanation & Examples
- Volume of Pyramid – Explanation & Examples
- Volume of Rectangular Prisms – Explanation & Examples
- Volume of Solids – Explanation & Examples
- Volume of Spheres – Explanation & Examples
- Washer Method - Definition, Formula, and Volume of Solids
- Weighted Average - Explanation and Examples
- What is a Vector? – Explanation & Examples
- Work Calculus - Definition, Definite Integral, and Applications
- Z-score - Explanation & Examples
- Zero Angle
- Zero Exponents – Explanation & Examples
- Zeros of a function - Explanation and Examples

### Posts

- (a) Find the average value f on the given interval. (b) Find c such that f_{ave} = f(c). Equation given below
- 12/5 as a mixed number.
- 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 0.500-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 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 ball is thrown vertically upward with an initial velocity of 96 feet per second.
- 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 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 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 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 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 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 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 gas mixture contains 75.2% nitrogen and 24.8% krypton by mass.
- 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-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 hurricane wind blows across a $6.00 \,m\times 15.0\, m$ flat roof at a speed of $130\, km/h$. Is the air pressure above the roof higher or lower than the pressure inside the house? Explain.
- 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 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 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 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 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 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 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 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 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 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 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 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 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 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.
- About 0.1 ev is required to break a “hydrogen bond” in a protein molecule.
- After the reaction, how much octane is left?
- An airplane flies at an altitude of 5 miles toward a point directly over an observer.
- 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 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 object is 1.0 cm tall and its inverted image is 4.0 cm tall. What is the exact magnification?
- 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^.
- Angle Bisector Theorem – Definition, Conditions and Examples
- Applied Calculus: Comprehensive Definition and Detailed Examples
- 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.
- 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 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.
- 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 what point does the curve have maximum curvature? What happens to the curvature as x tends to infinity y=lnx?
- Based on the normal model N(100, 16), describing IQ scores. What percent of people’s IQ would you expect to be:
- Boxes A and B are in 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?
- 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 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 NaF to HF required to create a buffer with pH =4.20.
- 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?
- 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.
- Cavalieri’s Principle – Definition, Conditions and Applications
- Choose the point on the terminal side of -210°.
- Closed Under Addition – Property, Type of Numbers, 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?
- Complex number in rectangular form. What is (1+2i)+(1+3i)?
- 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 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 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 above. All the resistors and all the batteries are identical.
- 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 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
- Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix.
- Describe in words the surface whose equation is given:
- Describe in words the surface whose equation is given. φ = π/6
- Determine if b is a linear combination of the vectors formed from the columns of the matrix A.
- Determine the current (magnitude and direction) in the 8.0 and 2.0-? resistors in the drawing.
- 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 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 Geometric series is Convergent or Divergent. 10 − 4 + 1.6 − 0.64 + ….
- Determine whether the planes are parallel, perpendicular, or neither. If the planes are neither parallel nor perpendicular, find the angle between them.
- Determine which plot shows the strongest Linear Correlation.
- 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?
- 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
- 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 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?
- Explain why the function is differentiable at the given point. Then find the linearization L(x, y) of the function at that point.
- Express the plane z=x in cylindrical and spherical coordinates.
- Extreme Value Theorem – Explanation and Examples
- 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 function f such that f'(x)=3x^3 and the line 81x+y=0 is tangent to the graph of f.
- Find a polynomial of the specified degree that has the given zero. Degree 4 with zeros -4, 3, 0, and -2.
- 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 function that represents the curve of intersection of the cylinder and the plane.
- Find all polar coordinates of point p = (6, 31°).
- 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 tangent line to the curve at the given point. y = sqrt(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 orthogonal basis for the column space of the matrix given below:
- Find Partial Derivatives ∂z/∂x and ∂z/∂y Given z = f(x)g(y), find z_x+z_y .
- 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 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 lies inside both curves. r2 = 50 sin(2θ), r = 5
- Find the Area of the Shaded Region of a Circle: Clear Examples
- 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 constant a such that the function is continuous on the entire real line.
- 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 dimension of the subspace spanned by the given vectors:
- 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 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 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 maximum and minimum values attained by the function f along the path c(t).
- 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 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 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 rate of change of f at p in the direction of the vector u.
- Find the surface area of the torus shown below, with radii r and R.
- 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 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 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 that is enclosed by the Cone and the Sphere
- 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 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)
- 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 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 what value of the constant c is the function f continuous on (-∞, ∞)?
- 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.
- 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 equation is dy/dt=ay+by^2, sketch the graph versus y. Determine critical points, and classify those points asymptotically stable or unstable.
- Given the proportion a/b = 8/15, what “ratio” completes the equivalent proportion a/8.
- Glide Reflection – Definition, Process and Examples
- 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 write y = 2x – 9 in standard form?
- How far, in meters, will the vehicles slide after the collision?
- 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 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 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
- 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 tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes.
- 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 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.
- Implicit Function Theorem – Explanation and Examples
- 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 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 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 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.
- Incenter Theorem – Definition, Conditions and Examples
- Indirect Measurement – Explanation and Examples
- Inverse Function Theorem – Explanation & Examples
- Inverse Variation – Explanation & Examples
- 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.
- 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 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 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?
- Look at the normal curve below, and find μ, μ+σ, and σ.
- 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
- One number is 2 more than 3 times another. Their sum is 22. Find the numbers.
- One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm. Determine the initial and final values of n associated with this emission.
- Parseval’s Theorem – Definition, Conditions and Applications
- 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
- 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 that if m and n are integers and m x n is even, then m is even or n 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.
- Recursive Formula – Definition, Formula, and Examples
- Reflection Function – Explanation and Examples
- 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?
- 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
- 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 the equation represents a sphere and find its center and radius.
- 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 the differential equation by variation of parameters. y” + y = sin x.
- 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.
- State how many mole ratios can be written for chemical reaction involving three substances.
- Suppose f” is continuous on (−∞, ∞). If f ‘(3)=0 and f ”(3)=-3. What can you say about f?
- 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 factory a produces 12 tables.
- Suppose that you are rolling a six sided dice. Let A = get a number smaller than 2. What is P(Ac)?
- 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 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 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 earth’s radius is 6.37×10^6 m; it rotates once every 24 hours.
- The electric potential in a region of space is V=(350V.m)/√(x^2+y^2), where x and y are in meters.
- 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 highest that george can suck water up a very long straw is 2.0 m . (this is a typical value.)
- 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 missing number in the series 9, ? , 6561, 43046721 is: 81, 25, 62, 31, 18.
- The next number in the series 38, 36, 30, 28, 22 is ?
- 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 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 solubility of copper (I) chloride is 3.91 mg per 100.0 ml of solution. Calculate the value of K_sp.
- 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 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 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?
- 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.
- Triangle Proportionality Theorem – Explanation and Examples
- Triangle Reflection – Definition, Techniques, and Examples
- 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 large parallel conducting plates carrying opposite charges of equal magnitude are separated by 2.20cm.
- 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 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.
- Use a double integral to find the area of the region. The region inside the circle and outside the circle.
- Use a double integral to find the volume of the solid shown by the figure.
- Use a linear approximation (or differentials) to estimate the given number. (1.999)^5
- 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?
- 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:
- Vertical Angles Theorem – Definition, Applications, and Examples
- 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 is 10∠ 30 + 10∠ 30? Answer in polar form. Note that the angle is measured in degrees here.
- What is a Frequency distribution of qualitative data and why is it useful?
- 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 stated by the null hypothesis for the chi-square test for independence?
- What is the current if the emf frequency is doubled?
- 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 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 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 speed vgas of the exhaust gas relative to the rocket?
- What is the total area of the figure below?
- 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 wrong with the following equation:
- What is x^0 – Detailed Explanation & Examples
- What minimum energy is required to excite a vibration in HCl?
- What values of b satisfy 3(2b + 3)2 = 36?
- When a honeybee flies through the air, it develops a charge of +16pC.
- 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.
- Which equation could be used to calculate the sum of the geometric series?
- 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 is a linear function?
- 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 pair of numbers has an LCM of 16
- Which relation does not represent a function.
- Which Relation Is Not a Function? Explanation and Examples
- 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 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~N(570, 103). Find the z-score corresponding to an observation of 470.
- y = x Reflection – Definition, Process and Examples
- 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.