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What is e^ln(x)?

The definition of the natural logarithm ln(x) is that it is the area under the curve y = 1/t between t = 1 and t = x. As a result, the value of ln(e) is 1. Since e^ln(x) = x, the graph of the function y = e^ln(x) is a straight line through the origin with a gradient of 1. It has the line equation y = x.

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What are some basic operations with polynomials?

Examples of polynomials are: (2X + 3Y), (7Z - 3X + 2Y) and 7X4. Just like integers, polynomials can be added and subtracted. When adding and subtracting polynomials, only like terms can be added and subtracted. Like terms are those with the same exponent or terms with the same degree. Multiplication and division of polynomials are also done using the same rules of multiplication and division of integers.

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How do you solve basic fraction equations?

For a simple fraction example, take x/3 + 3/5 = 4. The first thing to do is convert 3/5 to a decimal for easier calculations; it converts to 0.6. This leaves the equation as x/3 + 0.6 = 4. Subtracting 0.6 from 4 leaves 3.4, so the equation is now x/3 = 3.4. Multiply both sides by 3, leaving the solution as 10.2. Remember that if the denominators of fractions are the same, you can work with the numerators as normal.\nTo solve proportional equations, use the cross-multiplication method of multiplying numerators by opposite denominators, then solving for the variable. For example, the equation 3/..

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How do you convert cubic meters to cubic feet?

Cubic meters and cubic feet are both units of volume. They are often used to express the concentration of a chemical in a volume of air or the volume of a container. A cubic meter is a metric volume, which is equal to 1000 liters or a million cubic centimeters. A cubic foot is an imperial unit of volume that is often used in the United States.\nMultiplying a volume in cubic meters by 35.315 gives the volume in cubic feet. To perform the reverse calculation, divide the volume in cubic feet by 35.315 to obtain the volume in cubic meters. To convert cubic centimeters to cubic feet, first divide t..

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How do you do linear equations?

A linear equation describes a straight line. In a simple linear equation, operations can be undone by performing the same operation to both sides. For the equation x + 3 = 10, the +3 can be undone by subtracting the same number, 3, from both sides of the equation.x + 3 - 3 = 10 - 3x = 7Where there is more than one operation performed on the variable, they must be undone in a specific order: addition and subtraction before multiplication and division. The equation 3x + 4 = 10, therefore, involves four steps.3x + 4 - 4 = 10 - 43x = 63x/3 = 6/3x = 2Other variations may include variables on both s..

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What is a computation method in math?

While the four basic math functions are all part of the computation method, the answers are referred to differently. The addition of two or more numbers provides a sum, subtraction provides a difference, multiplication ends with a product, and division results in a quotient. In general American education, the computation method is taught with addition first, followed by subtraction, multiplication and finally, the concept of division.

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What are factor pairs?

The order of the numbers in the pair does not matter. The factor pair three and four is the same as four and three. When the product is divided by one member of the factor pair, the answer is always the other member. For a number under 50, finding its factor pairs is relatively simple. For each number, one is partnered with the number itself in a factor pair. Next, two is tried to see if it divides evenly into the number. Finally, three is tried and all subsequent numbers are systematically tried until all the factor pairs have been identified.

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What is the integral of cos x 2?

The half-angle identity for the function states that cos^2(x) = 1/2 + (1/2)cos(2x). Factoring out 1/2 gives the equation of 1/2 the integral of 1 + cos(x). Integrating 1 + cos(x) results in the equation x + (1/2)sin(2x). Multiplying x + (1/2)sin(2x) times the 1/2 outside the integral gives the above solution. The expression cos^2(x) is typically written without the exponentiation mark and with the 2 in superscript. An integral is also called an antiderivative due to the relationship between integration and differentiation.

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How do you teach 3D geometric shapes to kids?

Train the kids to chant names of common 3D shapes such as cones, spheres, cubes and cylinders repetitively. In between the chants, give examples of familiar objects that look like the shapes. For instance, have them repeat the word "cube," and then note that a cube looks like a box. Include additional information such as number of vertices and faces to the chants.\nShow children pictures of differently colored 3D geometric shapes. Many videos can help children recognize 3D geometric shapes through interactive step-by-step processes. Alternatively, engage the children in games that enhance mast..

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How do you get pre-algebra help?

Algebra.com separates its math problems by grade level. The website offers lessons, free tutors, answer keys and a large selection of practice algebra and pre-algebra problems for 1st grade through 8th grade.\nKhan Academy is a popular online learning center offering lessons on a huge variety of subjects. Its Math Foundations section has many pre-algebra topics, including negative numbers, absolute value, factoring and radicals. Site users can register for a free account and take a simple test to assess the specific skills that need to be reinforced. Then, as new skills are developed, the diff..

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