1.

 Two variables x and y are related by the equation . Given that

 the variable x is increasing at the rate of 0.1 unit/s, find the rate at which variable

 y changes when x = 2.

 

 The area of a circular disc increases at a constant rate of 0.05 cm²/s. Find the

 rate at which its radius is increasing when the area is 25 cm². Give your

 answer correct to 3 significant figures.

 

 Water is being poured into a container at a rate of 3 cm³/s. The volume, V cm³, of

 the water in the container, when the depth is x cm, is given by

 V = 0.005x³ + 1.2x². Find

 (a) the rate of increase in the depth of water when x = 5 cm,

 (b) the depth of water when the rate of increase in the depth is 0.15 cm/s.

 Give your answers correct to 2 decimal places.

 

A circular ink blot starts with a radius of 3 cm. As the ink soaks into the paper, the

blot expands so that after t seconds, the radius, r cm, is given by r = 3 + 0.1t.

(i) Write down an expression for the area, A cm², of the blot after t seconds.

(ii) Find the rate of increase of the area of the blot that after 4 seconds, leaving

your answer in terms of .