The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = x^2 + 6x + 5$. The marginal revenue,when $x = 20$,is . . . . . . .

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

$A$ rod of length $41 \ ft$ with an end $A$ on the floor and another end $B$ on the wall perpendicular to the floor is sliding away horizontally from the wall at the rate of $3 \ ft/min$. When the end $B$ is at a height of $9 \ ft$ from the floor, the rate at which the area of the triangle formed by the rod with the wall and the floor changes at that instant is (in $ft^2/min$):

The displacement $S$ of a moving particle at a time $t$ is given by $S=5+\frac{48}{t}+t^3$. Then its acceleration when the velocity is zero,is

If the surface area of a spherical bubble is increasing at the rate of $4 \text{ cm}^2/\text{sec}$,then the rate of change in its volume (in $\text{cm}^3/\text{sec}$) when its radius is $8 \text{ cm}$ is:

The rate of change of the volume of a sphere with respect to its surface area,when its radius is $2 \text{ cm}$,is . . . . . . $\text{cm}^3 / \text{cm}^2$.