Make r the subject of the formula $\frac{x}{r+a}=\frac{a}{r}$

If the 9^th term of an AP is fives times the 5^th term, find the relationship between a and d

Find the maximum value of y in the equation $y=1-2x-3{{x}^{2}}$

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

If $P=\left( \begin{matrix}   2 & 1  \\   -3 & 0  \\\end{matrix} \right)$ and I is a 2 × 2 unit matrix. Evaluate ${{p}^{2}}-2p+4I$

The time taken to 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 will it take 25 men?

Solve the equation${{x}^{3}}-5{{x}^{2}}-x+5=0$ 

Use the graph above to find the value if $px+qy\le 4$

If $y={{x}^{2}}-\frac{1}{x},$find $\frac{dy}{dx}$

A circle with radius 5cm has its radius increasing at the rate of 0.2cms^-1. What will be the corresponding increase in the area?