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When is an arrangement a combination, and when a permutation?

An arrangement is a permutation when we care about the order of the elements in it, and a combination when we do not. So if we are for example choosing a group of 3 people from 10 students, we do not care ab...
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Answered by Liora W. • Maths tutor
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In what useful ways can you rearrange a quadratic equation?

Factorisation: x 2 - 5x + 6 = (x - 2)(x - 3) This method is the quickest to perform if the roots are simple but does rely on a bit of trial and error. The method lets you find the roots of a quadratic equati...
Answered by • Maths tutor
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Find the area under the curve with equation y = 5x - 2x^2 - 2, bounded by the x-axis and the points at which the curve reach the x-axis.

First, we must find the two points at which the curve crosses the boundary. To do this, set y=0 and solve.0 = 5x - 2x 2 - 20 = (2x - 1)(-x+2)This gives that x = 0.5 and x = 2Next, we integrate with these bou...
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Answered by Natassja K. • Maths tutor
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Why is the derivative of x^2 equal to 2x?

The derivative tells us how much the output of a function changes when we change the input by a tiny amount. For the function f(x) = x 2 , we can think of the input as being a line of length x, and the outpu...
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Answered by Luke I. • Maths tutor
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A function is defined by f(x)= e^(x^2+4), all real x. Find inverse of f(x) and its domain.

Let f(x)=y: y = e^(x 2 +4); To find the inverse of a function, you need to find x in terms of y. In this case, you need to bring the exponent to the base. So in order to bring x 2 +4 from the power, take nat...
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Answered by Elisa C. • Maths tutor
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