Find the square of the mode

Find the dimension of the rectangle of greatest areas which has a fixed perimeter p.

If $y=x\sin x$ find $\frac{dy}{dx}$ when $x=\tfrac{\pi }{2}$

Find the rate of change of the V of a sphere with respect to its radius r when r =1

Find the area bounded by the curve $y=4-{{x}^{2}}$and $y=2x+1$

Differentiate (2x + 5)² (x – 4) with respect to x

Evaluate $\int{2{{(2x-3)}^{\tfrac{2}{3}}}dx}$

If the gradient of the curve $y=2k{{x}^{2}}+x+1$ at x =  1 is 9. Find k 

In the figure above, PQR is a straight line segment, PQ = QT . Triangle PQT is an isosceles triangle. $\angle QPT$is 25^o . Calculate the value of $\angle RST$

The chord ST of a chord ST of a circle is equal to the radius r of the circle. Find the length of the arc ST.