Approximation|Definition & Meaning Definition An approximation means that the result is closer to the actual value but not equal. An approximation can be made by either rounding off to the nearest 10 or 100 or rounding them to the nearest decimal place. You can approximate a number if the value is very high or low. […]
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Apex | Definition & Meaning
Apex|Definition & Meaning Definition An apex, in geometry, is the vertex that is at the most heightened point of a certain shape. The term is generally used to direct to the vertex opposite to the base. The phrase Apex is taken from the Latin for peak, summit, tip, extreme end, and top. An apex is […]
Angle Bisector | Definition & Meaning
Angle Bisector|Definition & Meaning Definition An angle bisector is a line that cuts an angle made by two adjoining lines equally. This means that the angle is made by two joining lines or made up of three points A, B, and C, with the angle between line AB and line BC, cut in half by […]
Amplitude | Definition & Meaning
Amplitude|Definition & Meaning Definition Amplitude is defined as the height from the middle value of a periodic function to the maximum or the minimum value of the function. It is the height from the center of the periodic signal to the trough or the crest of a wave. It defines how much something is enhanced […]
Addition | Definition & Meaning
Addition|Definition & Meaning Definition The act of adding two or more numbers together is defined as addition or an arithmetic operation that is applied to acquire the total or sum of desired numbers/items. When the addition operation is applied to two whole numbers, their combined value is the total amount or sum. In simple words, […]
Add | Definition & Meaning
Add|Definition & Meaning Definition Add, or addition is a mathematical operation used to add numbers. The outcome of addition is what is referred to as the sum of the supplied numbers. For example, if we add the numbers 4 and 5, we get the number 9, which is the sum of both. Adding is the process of combining two […]
Accuracy | Definition & Meaning
Accuracy|Definition & Meaning Definition Accuracy is a term used to define how close different results or attempts are as close to the correct value. Let us take an example of a reading of the thickness of metal. The correct value is close to 1mm. but the physical measurements read either 1.3 mm, 1.2 mm, or 0.8 mm. Hence, this concludes that the […]
Common Fraction | Definition & Meaning
Common Fraction|Definition & Meaning Definition A common fraction has integers (non-decimal values such as 1, 5, 10, etc.) for both the numerator (dividend) and the denominator (divisor) terms. Since fractions represent division, the common fraction represents the division of two integers. Sometimes called a vulgar fraction, it is the opposite of a decimal fraction, where […]
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.
This question aims to find the volume of the solid whose base forms an elliptical region. The cross-section perpendicular to the x-axis forms isosceles right triangles with hypotenuse as seen in the line shown in Figure 1. The concept of this question is based on the basic geometry of shapes like the area and volume […]
Find a vector function that represents the curve of intersection of the cylinder and the plane.
[Cylinder x^2+y^2=4] [Surface z=xy] The aim of this question is to find the vector function of the curve that is generated when a cylinder is intersected by a surface. The basic concept behind this article is the Vector-Valued Function and representation of different geometrical figures in parametric equations. A vector-valued function is defined as a […]
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?
This problem aims to find the velocity of a car running on a curved surface. Also, we are to find the coefficient of friction between the car’s tires and the road. The concept required to solve this problem is related to introductory dynamic physics, which includes velocity, acceleration, coefficient of friction, and centripetal force. We […]
Suppose that X is a normal random variable with mean 5. If P(X>9)=0.2, approximately what is Var(X)?
This question aims to find the probability of a normally distributed random variable $X$. A random variable is one whose value is determined by the results of a statistical experiment. The normal distribution, also known as the Gaussian distribution or the z-distribution, has a mean of zero and a standard deviation of one. Data in a […]
Find the surface area of the torus shown below, with radii r and R.
The main objective of this question is to find the surface area of the given torus with the radii represented by r and R. This question uses the concept of the torus. A torus is basically the surface revolution generated as a result of rotating the circle in the three-dimensional space. Expert Answer In this […]
Viewed from a point above the north pole, is the angular velocity positive or negative?
– The radius of the earth is measured to be $6.37times{10}^6m$. It completes one rotation around its orbit in $24$ hours. – Part (a) – Calculate the angular speed of the earth. – Part (b) – If the rotation of the earth is viewed from a location above the north pole, will the angular velocity […]
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).
This problem aims to familiarize us with different methods to solve a differential. The concept required to cater to this problem mostly relates to ordinary differential equations. We define an ordinary differential equation or most commonly known as ODE, as an equation that has one or additional functions of a single independent variable given with […]
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.
This question aims to develop a practical understanding of Newton’s laws of motion. It uses the concepts of tension in a string, the weight of a body, and the centripetal/centrifugal force. Any force acting along a string is called the tension in the string. It is denoted by T. The weight of a body with […]
How far, in meters, will the vehicles slide after the collision?
A car with mass mc=1074kg is traveling west through an intersection at a magnitude of veloctiy of vc=15m/s when a truck of mass mt=1593 kg traveling south at vt=10.8 m/s fails to yield and collides with the car. The vehicles become stuck together and slide on the asphalt, which has a coefficiet of friction of […]
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.
Write an expression from the given data to calculate the mass of the planet concerning G and the variables given in the statement. Also calculate the mass of the planet in Kg if T=26 hours and R=2.1X10^8m. This problem aims to familiarize us with the objects revolving around a specific pivot point. The concepts required to solve this problem are mostly […]
How much work is done on the package by friction as it slides down the circular arc from A to B?
– A railway station has a loading yard for goods transport, a small 0.2kg documents package is released from rest to a point A on a booking place which is one-quarter of a circle having the radius of 1.6 m. The package size is much smaller compared to a radius of 1.6 m. Therefore, the […]
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?
This article aims to find the area of a sector. This article uses the concept of the area of a sector. The reader should know how to find the area of the sector. Area of sector of a circle is the amount of space enclosed within the boundary of the sector of circle. The sector always starts from […]
The solid lies between planes perpendicular to the x-axis at x=-1 and x=1.
– A Square is formed from the cross-section of given two planes perpendicular to the $x-axis$. Base of this square extends from one semicircle $y=sqrt{1-x^2}$ to another semicircle $y=-sqrt{1-x^2}$. Find the volume of the solid. The main purpose of this article is to find the volume of the given solid that is lying between two […]
In a poker hand consisting of 5 cards, find the probability of holding 3 aces.
This article aims to determine the probability of holding $3$ aces in a poker hand of $5$. The article uses the background concept of probability and combination. To solve problems like this, the idea of combinations should be clear. A combination combines $n$ things $k$ at once without repetition. The formula to find the combination is: [binom […]
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.
what is the speed of the rock when the string passes through the vertical position? what is the tension in the string when it makes an angle of $45$ with the vertical? what is the tension in the string as it passes through the vertical? The purpose of this question is to find the speed […]
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?
The main purpose of this question is to find the density of the air enclosed in the sphere if the radius of the sphere is halved. A sphere is a $3-$dimensional body with a circular shape. It is divided into three $x-$axis, the $y-$axis, and the $z-$axis. This is the primary distinction between a sphere […]
Using the two equations E=hv and c=lambda v derive an equation expressing E in terms of h,c and lambda.
This question aims to express the quantum of energy $(E)$ in terms of the speed of light $(c)$, the wavelength $(lambda)$, and Planck’s constant $(h)$. The frequency can be expressed as the number of oscillations in one unit of time and it is calculated in Hz (hertz). The wavelength is regarded as the measure of […]
How many ways are there to distribute six indistinguishable balls into nine distinguishable bins?
The objective of this question is to find the number of ways the six indistinguishable balls can be distributed into nine distinguishable bins. A mathematical method for determining the number of potential groupings in a set of objects in which the selection order becomes irrelevant is referred to as combination. The objects can be chosen […]
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.
This question aims to find the moment of inertia about the given axis of rotation. Inertia is a property of a body that opposes any force which attempts to move it or to change the magnitude or direction of its velocity if it is in motion. Inertia is a non-resistant property that allows a body to oppose active factors such as forces […]
The earth’s radius is 6.37×106 m; it rotates once every 24 hours.
Calculate the angular speed of the earth. Calculate the direction (positive or negative) of the angular velocity. Assume you are viewing from a point exactly above the north pole. Calculate the tangential speed of a point on the earth’s surface located on the equator. Calculate the tangential speed of a point on the earth’s surface […]
Identify the surface whose equation is given. ρ=sinθsinØ
The aim of this question is to find the surface corresponding to the Spherical Coordinates $p=sintheta sinphi$ by utilizing the Cartesian Coordinate system and Equation of Sphere. First, we will explain the concept of Sphere, its Equation, and its Coordinates in the Cartesian Coordinate System. A Sphere is defined as a $3D$ geometrical structure have […]
Factors of 23: Prime Factorization, Methods, Tree, and Examples
Factors of 23: Prime Factorization, Methods, Tree, and Examples Factors of 23 refer to the numbers that give off no reminder; the answer is in whole numbers when the numbers are divided by 23. The answer should never be in decimals, fractions, or any other form if it is a numerical factor. Finding the factors […]
Factors of 51: Prime Factorization, Methods, Tree, and Examples
Factors of 51: Prime Factorization, Methods, Tree, and Examples Factors of 51 are those numbers that, when multiplied together, equal to 51 or by which 51 can completely be divided in half. Therefore, a number divides 51 with a 0 as the remainder is considered a factor. To analyze factors, list all the numbers that are less […]
Factors of 180: Prime Factorization, Methods, Tree, and Examples
Factors of 180: Prime Factorization, Methods, Tree, and Examples Factors of 180 can be referred to as the numbers that may fully divide 180 or whose result is 180 when two numbers are multiplied together. Therefore, an integer is said to be a factor if it divides 180 by itself with a remainder of 0. […]
Factors of 20: Prime factorization, Methods, Tree, and Examples
Factors of 20: Prime factorization, Methods, Tree, and Examples The factors of 20 are all the numbers, which when multiplied together, their answer is 20. They can also be called numbers that when divided with a specific number give zero as a remainder and the answer is always an integer. Thus, factors of a number […]
Factors of 16: Prime factorization, Methods, Tree and Examples
Factors of 16: Prime factorization, Methods, Tree, and Examples A factor in mathematics is always a whole number that divides another number and gives off no remainder i.e. remainder will always be zero. Factors of 16 are the numbers that are completely divisible by the number itself. There are two super easy methods to find […]
Math Calculators
Math Calculators The Math Calculators are the solution to all your math problems. With a single click, you can save time and get rid of complicated calculations that take up so much homework space in an already busy schedule! We have provided you with the platform where you can have access to various Math Calculators […]
Base (Geometry) | Definition & Meaning
Base (Geometry)|Definition & Meaning Definition The base of a shape is the surface on which the whole shape lies on. Bases are used for polygons, triangles, prisms, etc. The unit of the base of the figure is m, cm, inch, or ft. Geometry and Its Importance in Mathematics Geometry is one of the most fundamental […]
Glossary of Mathematical Terms & Definition
GLOSSARY OF MATHEMATICAL TERMS AND DEFINITIONS A B C D E F G H I J K L M N O P Q R S T U V W X Y […]
what is 33 percent of 75 + Solution with Free Steps
what is 33 percent of 75 + Solution with Free Steps 33 percent of 75 is equal to 24.75. In short multiplication result of 0.33 by 75 and you will get 24.75. This problem has many practical applications one of them is, for example, a fruit seller has 75 oranges at the start of the […]
what is 30 percent of 16 + Solution with Free Steps
what is 30 percent of 16 + Solution with Free Steps 30 percent of 16 is equal to 4.8. In short, the multiplication result of 0.3 by 16 will provide 4.8. This problem is applicable to real-time scenarios, for example, a customer buys 16 bananas from the store and later finds out that 30 percent […]
what is 20 percent of 411 + Solution With Free Steps
What Is 20 Percent of 411 + Solution With Free Steps 20 percent of 411 is 82.2. To obtain this answer, we multiply 0.20 by 411. In mathematics, a percentage (from Latin: percento, “hundred”) is a number or ratio expressed as a fraction of 100. A percentage is a dimensionless quantity; it has no unit of measure. We can analyze this problem in the context […]
what is 12 percent of 600 + Solution with Free Steps
what is 12 percent of 600 + Solution with Free Steps 12 percent of 600 is equal to 72. Results can be obtained simply by multiplying 0.12 by 600. The practical application to this problem is supposed the total number of registered students in some college are 600 and on any particular day, 12 percent […]
what is 65 percent of 600 + Solution with Free Steps
what is 65 percent of 600 + Solution with Free Steps 65 percent of 600 is equal to 390. In short, just multiply 0.65 by 600 and you will get 390. The problem is applicable in many practical scenarios for example you study in high school and the total number of the final exam is […]
what is 10 percent of 200 + Solution with Free Steps
what is 10 percent of 200 + Solution with Free Steps 10 percent of 200 is equal to 20. to achieve the answer simply multiply 0.10 by 200 and you will get 20. This problem of 10 percent of 200 has many practical real-life applications involving ratios and proportion. For example, suppose in a college […]
what is 4 percent of 60 + Solution with Free Steps
What is 4 percent of 60 + Solution with Free Steps The number 2.4 is the result of 4% of 60. The factor 0.4 multiplied by 60 will provide this answer. This question is practically applicable in a way, for example, you study in high school and there are 60 students in your class, and […]
What is 0.12 percent of 10000 + Solution with Free Steps
What is 0.12 percent of 10,000 + Solution With Free Steps 0.12 percent of 10,000 is equal to 12. To get 12 as your answer, simply multiply the fraction 0.0012 by the number 10,000. The calculation of 0.12 percent of 10,000 can be helpful in certain ways, suppose, you wish to buy a motorbike worth […]
What is 40 percent of 25 + Solution with Free Steps
What is 40 percent of 25 + Solution With Free Steps 40 percent of 25 is equal to 10. To get 10 as your answer, simply multiply the fraction 0.40 by the number 25. The above calculation of 40 percent of 25 might be seen as a valuable real-life example, let’s say, you wish to […]
What is 55 percent of 60 + Solution with Free Steps
What is 55 percent of 60 + Solution With Free Steps 55 percent of 60 is equal to 33. To get 33 as your answer, simply multiply the fraction 0.55 by the number 60. The simple calculation of 55 percent of 60 can sum up as a real-life example, suppose, you wish to rent a […]
What is 35 percent of 2375 + Solution with Free Steps
What is 35 percent of 2375 + Solution With Free Steps 35 percent of 2375 is equal to 831. To get 831 as your answer, simply multiply the fraction 0.35 by the number 2375. The calculation of 35 percent of 2375 can be viewed as a real-life example, imagine, you wish to buy a single-story […]
what is 30 percent of 500 + Solution with Free Steps
what is 30 percent of 500 + Solution with Free Steps 30 percent of 500 is equal to 150. In short, just multiply 0.30 by 500 and you will get 150. This question has many practical implementations, one of them for example, you work in some organization and your monthly salary is 500$. Your manager […]
What is 5 percent of 30 + Solution with Free Steps
What is 5 percent of 30 + Solution With Free Steps 5 percent of 30 is equal to 1.5. To get 1.5 as your answer, simply multiply the fraction 0.05 by the number 30. This simple calculation of 5 percent of 30 can sum up as a real-life example, consider, you wish to buy a […]