If the distance $s$ travelled by a particle in time $t$ is given by $s=t^2-2t+5$,then its acceleration is

In $\Delta ABC$,sides $a$ and $b$ are kept constant such that there is an error $\alpha$ in angle $C$. What is the relative error in the area?

The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = 3x^2 + 36x + 5$. Find the marginal revenue when $x = 5$,where marginal revenue is defined as the rate of change of total revenue with respect to the number of items sold at an instant.

If the displacement,velocity,and acceleration of a particle at time $t$ are $x, v$,and $f$ respectively,then which of the following is true?

Water is dripping out at a steady rate of $1 \text{ cm}^3/\text{sec}$ through a tiny hole at the vertex of a conical vessel,whose axis is vertical. When the slant height of water in the vessel is $4 \text{ cm}$,find the rate of decrease of the slant height,where the semi-vertical angle of the conical vessel is $\frac{\pi}{6}$.

If the area of a circle increases at the rate of $\frac{1}{\sqrt{\pi}}$ sq. units/sec,then the rate (in units/sec) at which the perimeter of the circle changes,when perimeter is $\sqrt{\pi}$ units,is