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Solve the simultaneous equations: y + 4x + 1 = 0, and y^2 + 5x^2 + 2x = 0.

"Solve the simultaneous equations" is another way of saying find the unknown variables. In this case, they are x and y. When looking at the second equation, y^2+5x^2+2x=0, we can see that we have t...
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Given that the graph f(x) passes through the point (2,3) and that f'(x)=6x^2-14x+3, find f(x).

For this question we already have the derivative of f(x), and so if we integrate it we should get to a general equation with a constant on the end, however we want to get to an exact solution which we should...
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Find the surface area of a hand held fan (modeled with negligible depth) with radius 8 cm and a 60 degree angle at the centre

60 degrees = π/3 radians A = 1/2r 2 θr = 8θ = π/3 1/2 x 8 2 x π/3 = 33.5103216... cm 2 33.5103216... x 2 = 67.0 cm 2 to 3 s.f.
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How do I differentiate (x^2 + 3x + 3)/(x+3)

In order to differentiate this fraction, you will need to use the quotient rule, which if you don't remember is: y = u/v then dy/dx = (v du/dx − u dv/dx)/ v^2) First you need to identify your initial variabl...
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The line, L, makes an angle of 30 degrees with the positive direction of the x-axis. Find the equation of the line perpendicular to L, passing through (0,-4).

What is the question asking us? -To find the equation of a straight line, and to do that we need two pieces of information, what are they? 1. the gradient of the line and 2. a point on the line. Now from the...
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