eter Q5. Find the length of the curve y = for -1

Q5. Find the length of the curve y Q6. Solve the following initial value problems: for 2 (b) Q7. dy :ry dy :rex+y , y (O) d:r A 1000 litre tank initially contains 300 litres of brine in which there is dissolved 100 grams of salt. Starting at t O, the mixture containing 50 grams per litre of the dissolved salt flows into the tank at the rate of 4 litres per minute. The mixture is kept uniform by stirring and well-stirred mixture simultaneously flows out of the tank at the rate of 3 litres per minute. (i) Write a differential equation that describes the rate of change of the amount of salt with time. (ii) Solve the initial value problem. iii) How much salt will be left in the tank at the instant it overflows? sin 20 and r For the two roses given by polar equations r area of the rccyion that lies inside both curves. sketch the graph of the region. cos 20, find the