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Further Mathematics
GCSE

Find the solution of 3^{4x} = 9^{(x-1)/2}.

First, recognise that 3^2 = 9. Recall the rule for multiplying indices, that (a^b)^c = a^{bc}. Then, substitute 3^2 in place of 9 to get 3^{4x} = (3^2)^{(x-1)/2}. Use the rule for multiplying indices, so ...

CO
1897 Views

f'(x) = 3x^2 - 5cos(3x) + 90. Find f(x) and f''(x).

Finding f(x) requires integrating the function f'(x), because f(x) is the integral of the given function f'(x). So {integralsymbol} f'(x) dx = {integralsymbol} (3x^2 - 5cos(3x) + 90) dx = x^3 - (5/3)sin(3...

CO
2022 Views

Prove that tan^2(x)=1/(cos^2(x))-1

tan^2(x)=1/(cos^2(x))-1 Left hand side of the equation (LHS)=tan^2(x) Use the identity tan(x)=sin(x)/cos(x) and substitute it into the LHS LHS=sin^2(x)/cos^2(x) Use the identity sin^2(x)+cos^2(x)=1 and re...

PA
2039 Views

How do I know I can multiply two matrices and if so, how do I do it?

Firstly you need to check if the matrices conform. Matrices are an array of elements within a pair of brackets, there are some number of columns, usually denoted m, and some number of rows, denoted n. The...

MD
7144 Views

If the equation of a curve is x^2 + 9x + 8 = y, then differentiate it.

First we must establish how to differentiate terms individually. This is done by using the simple method of multiplying the X by the power, and subtracting one away from the power. To make it easier we wi...

TT
2686 Views

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