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What is a 12-faced shape called?

The other Platonic solids are the tetrahedron, made up of 4 triangles; the hexahedron, made up of 6 squares; the octahedron, made up of 8 triangles; and the icosahedron, made up of 20 triangles. These shapes have been recognized as special since antiquity. Mathematicians and philosophers have long admired them for their symmetry and mathematical beauty. Role-playing games sometimes use dice made in the shapes of the five Platonic solids.

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Who discovered fractions?

The need for fractions began with observations of nature. People divided days, months and seasons. As societies grew, people needed a way to measure goods and merchandise for trade when there was no money or currency. The Egyptians were the first society to study fractions by using unit fractions.\nA unit fraction has a numerator of 1 and a positive integer for the denominator. Instead of numerals, the Egyptians used symbols representing numbers in fractions. European mathematicians believed fractions came from the Greeks until the Rhind Papyrus, which contained the work of Egyptian mathematic..

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What is the square root of 320?

There are two methods of finding the square root of a number. The prime factorization method is best used when the given number happens to be a perfect square. The continuous division method is a good method for all numbers.\nThe best way to find the square root of a number like 320 is to use the method of division and get the answer up to at least two decimal places. This method can be used to get the square root of any number. To divide 320, one must divide in pairs two numbers starting from the right. Hence, begin with one as the divisor, as 2 x 2 = 4. This yields a remainder of two. One ca..

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What is the exterior angle theorem?

The exterior angle theorem comes from Euclid’s “Elements,” Book 1, Proposition 16. The formal proof for the theorem uses the triangle sum theorem. For a triangle ABC with interior angles a, b and c, it follows that the sum of these angles is 180 degrees. Extending a side of the triangle at any given vertex creates an exterior angle d. Using the supplementary-angle theorem, which states that the sum of two adjacent angles formed by the intersection of two lines equals 180 degrees, the sum of angle d and its adjacent angle must equal 180 degrees. Thus, the sum of the remaining two adjacent..

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What is a real-life example of a scalene triangle?

The scalene shape is stable and strong, making it a good choice for construction. Some ramps, such as those used in a skateboarding park, are also scalene triangles. These ramps provide a stable platform from which skateboarders can launch. The sail on a sailboat is also likely to be raised in the shape of a scalene triangle, with no side of the sail being the same length as any other side.

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What are some Vedic math tricks?

The crisscross system of multiplication is an alternative way of multiplying two-digit numbers together. A simple example includes multiplying 12 by 34. The first step is to multiply both of the one digits by each other, in this case the 2 and the 4. The answer, 8, is the ones digit of the final answer. The second step is to multiply the tens digit of the first number by the ones digit of the second number and vice versa. In this case, 1 (the tens digit of 12) multiplied by 4 (the ones digit of 34) equals 4, and 3 (the tens digit of 34) times 2 (the ones digit of 12) equals 6. The sum of the t..

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What type of games does Cool Math offer?

Access the complete list of CoolMath.com games from the More button below the Math Games section of the site's home page. Adobe Flash Player is required for many of the games to work.\nCoffee shop is a game that requires managing a budget, recipe and pricing model to run a successful coffee shop. Number Balls is a game that requires ordering numbers from the least value to the greatest value, while Freed Fribbit Addition requires rapid adding. Number twins requires pairing numbers so they add up to 10. Fractone is a fraction game that involves combining fractions until they add up to a va..

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What is the derivative of 2e^x?

E^x is an exponential function. The base for this function is e, Euler's number. This is an irrational number and is approximately 2.71. The number "e" should be treated like any other numerical base such as two or three. If the exponential function has a numerical base "a", the function can be written y = a^x. The derivative of this function is dy/dx = (a^x)ln(a). For example, the derivative of y=2^x is dy/dx=(2^x)ln(2). Thus the derivative of e^x is (e^x)ln(e). The natural log of e, ln(e), is one. Thus the derivative simplifies to e^x.\nIf the function contains anything more complicated..

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Why are decimals important?

Similarly, using the decimal system is less cumbersome than writing, adding, subtracting or multiplying mixed numbers with fractions. For example, it is easier to write ten and a half as 10.5 than as 10 1/2. Adding decimals like 10.5 and 29.75 is much easier than add 10 1/2 and 29 3/4, where you need to replace the fractions with common denominators before adding them. Likewise, it is easier to compare decimal numbers than fractions.The decimal system, which uses base 10, is a system used for calculation in the sciences and engineering disciplines that can require more precision. Additionally,..

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What is the derivative of ln(3x)?

The expression ln(3x) can be separated as ln(x) plus ln(3). The derivative of ln(3) is zero, because ln(3) is a constant, and the derivative of a constant is always zero. The derivative of x is always one over x, based on the rule that for f(x) = ln(x), the derivative is f(x) = 1/x.\nAnother way to solve for the derivative of ln(3x) is to substitute a variable for 3x, and multiply the derivative of the variable by the derivative of the natural log of the variable.

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