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Solve the simultaneous equations: x^2 + y^2 = 25 and y − 2x = 5

x 2 +y 2 =25, y-2x= 5 y = 5+2x -----> y 2 = (5+2x) 2 = 25 + 20x +4x 2 x 2 + 4x 2 + 20x + 25 = 25 5x 2 + 20 x = 0 x = 0 y = 5+(2*0) y=5
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Answered by Alex G. • Maths tutor
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a) Factorise the following expression (x^2)-49 b) Differentiate the following equation y = (x^2) - 49 and find the stationary points of the equation

a) (x+7)(x-7) b) y = (x^2) - 49 y' = 2x 0 = 2x x = 0 y = (0^2) - 49 y = -49, x = 0
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Answered by Thomas G. • Maths tutor
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Show that (sqrt(3) + sqrt(75))^{2} = 108

The key here is to simplify the left hand side. There are two different approaches to take here, one slightly faster but both perfectly legitimate. First approach: Remember the formula (a + b)^{2} = a^{2} + ...
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Answered by Callum B. • Maths tutor
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Compute the integral of f(x)=x^3/x^4+1

A basic function of integration states that: for a function f(x), the integral of f'(x)/f(x) = ln[f(x)] (the natural log of the modulus of f(x)). Take the denominator of f(x), x 4 +1. We will refer to this a...
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Answered by Tyla D. • Maths tutor
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A curve has parametric equations x = 1 - cos(t), y = sin(t)sin(2t) for 0 <= t <= pi. Find the coordinates where the curve meets the x-axis.

If the curve is meeting the x-axis, notice that this means y = 0. So we must solve sin(t)sin(2t) = 0 for t within the given bounds. Using a trigonometric identity sin(2t) = 2cos(t)sin(t), we obtain sin 2 (t)...
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Answered by Callum B. • Maths tutor
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