EXERCISE 20D 1 a andb are variables related by the equatiomb?' : 40 At the instant wheru : 5 bis increasing at 1 unit per second. What is happening attat this instant? 2 The length of a rectangle is decreasinglacm per minute.However, the area of the rectangle remains constant aUO cm2. At what rate is the breadth increasing at the instant when the rectangle is a square? 3 A stone is thrown into a lake and a circular ripple moves out at a constant lspnesL 10f Find the rate at which the circle's area is increasing at the instant when: a t: 2seconds b t: 4seconds. 1| Air is pumped into a spherical weather balloon at a constant rbe In? per minute. Find the rate of change in its surface area at the instant when the radius of the ballnnn is 5 For a given mass of gas in a pistqnlfl'f' : 400 where pis V the pressure in N/ih andV is the volume in% Suppose the pressure increases at a constant rate3 sz per minute. Find the rate at which the volume is changing at instant when the pressure 50 N/m2. 6 Wheat runs from a hole in a silo at a constant rate and forms a conical heap whose base radius is treble its height. Aftet minute, the height of the heap2s cm. Find the rate at which the height is rising at this instant. 7 A trough of lengtl III has a uniform cross-section which is an . equilateral triangle with sides of lenglhm. Water leaks from the bottom of the trough at a constant ratd).ibn3/min. 1m Find the rate at which the water level is falling at the instant when the water is20 cm deep. end View 8 Two jet aeroplanes y on parallel courses which 1am apart. Their air speeds a260 m f1 and 250 m 571 respectively. How fast is the distance between them changing at the instant when the slower jet ikm ahead of the faster one? 9 A ground-level oodlight locatedO m from the foot of a building shines in the direction of the building. A 2 m tall person walks directly from the oodlight towards the building atl In 51. How fast is the person's shadow on the building shortening at the instant when the person is: L ! I' 40 m ->I a 20 m from the building I: 10 m from the building