Make \(r\) subject of the formula given that \(\frac{x}{r+a}=\frac{a}{r}\)

A circle with radius 5cm has its radius increasing at the rate of 0.2m/s. What will be the corresponding increase in the area?

Find the derivative of y = sin2(5x) with respect to x.

If y = x2 - (1/x). find dy/dx

Find the maximum value of y in the equation y = 1 - 2x - 3x2

The time taken to do a piece of work is inversely proportional to the number of men employed. if it takes 45 men to do a piece of work in 5 days, how long wi...

Evaluate ∫sin 3x dx

Solve for x in the equation x3 - 5x2 - x + 5 = 0

Find the range of values of x for which \( \frac{(x+2)}{4}-\frac{2x-3}{3}<4 \)