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The point P lies on a curve with equation: x=(4y-sin2y)^2. (i) Given P has coordinates (x, pi/2) find x. (ii) The tangent to the curve at P cuts the y-axis at the point A. Use calculus to find the coordinates of the point A.

To find the x coordinate of point P, we simply substitute in the value of y at P into the equation of the curve and solve for x = 4pi^2. (ii) To start, we can differentiate x with respect to y, by using the ...
TF
Answered by Tobias F. • Maths tutor
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Solve the following simultaneous equations: 2x - y = 7 and x^2 + y^2 = 34

First, clearly write the two equations above one another, and label them (1) and (2). Rearrange the linear equation (the one with no squared variables) to make y the subject of the equation. You should get y...
TF
Answered by Tobias F. • Maths tutor
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What other A Level subjects would be useful towards applying to do a Mathematics degree?

To compliment Mathematics, Further Mathematics would be an ideal subject to take. It is not essential, however the additional practice would benefit your understanding of Mathematics, easing you into even hi...
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Answered by Vene F. • Maths tutor
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The point P lies on the curve C: y=f(x) where f(x)=x^3-2x^2+6x-12 and has x coordinate 1. Find the equation of the line normal to C which passes through P.

First we must find the y coordinate of the point P: We know the x-coordinate is x1=1 so the y coordinate must satisfy the equation y1=f(1) which gives y1=-7. So we now know P is at (1,-7). We now need to fin...
KH
Answered by Kieran H. • Maths tutor
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Find all solutions of x^2-x-6 using the quadratic formula

From the given quadratic, we have a=1, b=-1, and c=-6. We substitute these values into the quadratic formula, x=-b+-sqrt(b^2-4ac)/2a, giving us x=-1+-sqrt(-1^2-4 1 -6)/2*1. This simplifies to x=1+-5/2. Keepi...
JH
Answered by Jack H. • Maths tutor
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