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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=4pi² 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...

Answered by George N. • Maths tutor

3466 Views

The parametric equations of a curve are: x = cos2θ y = sinθcosθ. Find the cartesian form of the equation.

x = cos2θ y = sinθcosθcos2θ = cos²θ - sin²θ cos²θ + sin²θ = 12cos²θ = 1 + cos2θ cos²θ = 1/2(1 + x)2sin²θ = 1 - cos...

Answered by Amelia N. • Maths tutor

8016 Views

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

Answered by Olufayojimi O. • Maths tutor

3160 Views

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. ...

Answered by Olufayojimi O. • Maths tutor

11975 Views

(a) By using a suitable trigonometrical identity, solve the equation tan(2x-π/6)^2 =11-sec(2x-π/6)giving all values of x in radians to two decimal places in the interval 0<=x <=π .

say (2x-π/6)=qtan²q = sec²q-1so sec²q-1= 11 - sec q sec²q + sec q -12 = 0(sec q -3) (sec q + 4) = 0sec q = 3 or -4because 0<=x<= πso -π/6 <= q <= 11...

Answered by Zhaohui Z. • Maths tutor

8493 Views