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Given that x = cot y, show that dy/dx = -1/(1+x^2)

Identify that we are looking at dy/dx, not dx/dy and realise the relationship that dy/dx=1/(dx/dy)2)Try find dx/dy;cot = 1/tan or (tan)^-1Hence, x=(tan y )^-1 implying dx/dy = (-...

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Time, T, is measured in tenths of a second with respect to distance x, is given by T(x)= 5(36+(x^2))^(1/2)+4(20-x). Find the value of x which minimises the time taken, hence calculate the minimum time.

To solve this problem we first must look into the given formula for time (T). It is stated, in the question, that the time taken is dependent on distance x. From this we can infer that the following probl...

Answered by Aziz H. • Maths tutor

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Find the equation to the tangent to the curve x=cos(2y+pi) at (0, pi/4)

Normally to find a tangent we want to work out dy/dx, but since this equation is x=something, it's much easier to work out dx/dy first, then we get dy/dx by doing 1/(dx/dy)=dy/dx.
By the chain rule, ...

Answered by Sarah J. • Maths tutor

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Find the angle between two lines with vector equations r1 = (2i+j+k)+t(3i-5j-k) and r2 = (7i+4j+k)+s(2i+j-9k)

Explain the dot product and the relation : a.b= ¦a¦¦b¦cos(x) where a.b is the dot product of two vectors, ¦a¦ and ¦b¦ are the magnitude of a and b respectively and x is the angle between them. Si...

Answered by Muhammad S. • Maths tutor

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Find the intersection coordinates of both axis with the function: f(x)=x^2-3x+4/3

Find the y₁ coordinate, where x₁ = 0, this is the intersection with y-axis. f(0)=4/3, therefore one intersection P_y=[0,4/3]Find the x_1,2 coordinates, where y = ...

Answered by Martin S. • Maths tutor

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