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The tangent to a point P (p, pi/2) on the curve x=(4y-sin2y)^2 hits the y axis at point A, find the coordinates of this point.

p=4pi 2 differentiating with respect to y we have dx/dy = 2(4y-sin2y)(4-2cos2y) substituting in the value of y =pi/2 we have dx/dy = 24pi, which means dy/dx =1/pi24using (y-y_1)=m(x-x_1) we have y-pi/2=1/24p...
GN
Answered by George N. • Maths tutor
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The parametric equations of a curve are: x = cos2θ y = sinθcosθ. Find the cartesian form of the equation.

x = cos2θ y = sinθcosθcos2θ = cos 2 θ - sin 2 θ cos 2 θ + sin 2 θ = 12cos 2 θ = 1 + cos2θ cos 2 θ = 1/2(1 + x)2sin 2 θ = 1 - cos2θ sin 2 θ = 1/2 (1 - x)y 2 = sin 2 θcos 2 θy 2 = ( 1/2(1 + x)) . (1/2 (1 - x))...
AN
Answered by Amelia N. • Maths tutor
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If a motor uses 500J to raise a box of 25N, how high has the box been lifted?

Work done = Force x distance the applied force has moved, hence 500 = 25d where d = unknown distance. Therefore the distance moved is 500/25 = 20m
OO
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find dy/dx of x^1/2 + 4/(x^1/2) + 4

This can be rewritten as x 1/2 + 4x -1/2 + 4, hence dy/dx = (1/2)x -1/2 - 2x -3/2
OO
Answered by Olufayojimi O. • Maths tutor
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A farmer has 30 boxes of eggs. There are 6 eggs in each box. Write, as a ratio, the number of eggs in two boxes to the total number of eggs. Give your answer in its simplest form.

The question asked for the ratio between the number of eggs in 2 boxes and the total number of eggs. From the question we know that the total number of eggs is the same as the number of eggs in 30 boxes. Hen...
OO
Answered by Olufayojimi O. • Maths tutor
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