Question

A store has been selling calculators at ₹ 350 each. A market survey indicates that a reduction in price (p) of calculator increases the number of units (x) sold. The relation between the price and quantity sold is given by the demand function p = 450 – (1/2)x.

Engine displacement is the measure of the cylinder volume swept by all the pistons of a piston engine. The piston moves inside the cylinder bore The cylinder bore in the form of circular cylinder open at the top is to be made from a metal sheet of area 75π cm².

In order to set up a rain water harvesting system, a tank to collect rain water is to be dug. The tank should have a square base and a capacity of 250 m³. The cost of land is ₹ 5,000 per square metre and cost of digging increases with depth and for the whole tank, it is ₹ 40,000 h², where h is the depth of the tank in metres. x is the side of the square base of the tank in metres.

A volleyball player serves the ball which takes a parabolic path given by the equation h(t) = −(7/2)t² + (13/2)t + 1, where h(t) is the height of ball at any time t (in seconds), (t ≥ 0).