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A curve with equation y = f(x) passes through the point (4,25). Given that f'(x) = (3/8)*x^2 - 10x^(-1/2) + 1, find f(x).

f'(x) = (3/8) x^2 - 10x^(-1/2) + 1Each term must be integrated (increase the power by 1 and divide by the new power), remembering to include + c.f(x) = (3/8) (x/3)^3 - 10*(2x)^(1/2) + x + cf(x) = (1/8) x^3 -...
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Answered by Oliver W. • Maths tutor
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Find the roots of 2x^2-2x=3, leaving your answer in it's simplest exact form.

First we need to rearrange our equation so it is in the correct form of ax 2 +bx+c=0.So we'd move the 3 over to the left hand side to give us 2x2-2x-3=0.We need to use the quadratic formula. Using x=( -b+/-(...
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Answered by Jake A. • Maths tutor
4971 Views

Solve the inequality x^2 + 4x ≥ 77

First step is to rearrange to make the quadratic easier to work with: in a familiar form. x 2 + 4x ≥ 77, -77 from both sides x 2 + 4x - 77 ≥ 0 Now the quadratic can be solved, by simplifying into double brac...
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Answered by Alex D. • Maths tutor
5598 Views

Show that the square of any odd number is an odd number

We can talk about any integer (or whole number) with the variable n. n could be any integer, 2, 3 or 100 or 5 billion and 1!If n is any integer, then what numbers could be written as 2n? These are the even n...
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Answered by Alice T. • Maths tutor
5426 Views

Solve simultaneously, 2x-3y=16 and x+2y=-6

In order to solve this we need to make two of the terms the same and use an elimination method so we are left with only one unknown rather than two. We will multiply x + 2y = -6 by 2 in order to get 2x + 4y ...
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Answered by Gemma G. • Maths tutor
6272 Views