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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))...
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Answered by Amelia N. • Maths tutor
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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
3639 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. Hen...
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Answered by Olufayojimi O. • Maths tutor
13816 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)=qtan 2 q = sec 2 q-1so sec 2 q-1= 11 - sec q sec 2 q + sec q -12 = 0(sec q -3) (sec q + 4) = 0sec q = 3 or -4because 0&lt;=x&lt;= πso -π/6 &lt;= q &lt;= 11π/6q = 1.23 or 1.82 or 4.46 or 5.05so x...
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Answered by Zhaohui Z. • Maths tutor
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