A candle that is 10 inches tall is lit As the candle burns i

A candle that is 10 inches tall is lit. As the candle burns, its height decreases at a rate of 1.6 inches per hour. Let t = the time in hours that the candle has been burning. Write an expression for the quantity described below in each part. Each expression should be written in terms of the appropriate variable. a. 15 minutes less than twice the time the candle has been burning. (Your expression should represent a number of hours.)

Solution

Sol:

Let length of canndle burnt in t hours= x

Given Rate of burning = 1.6 inches /hour

=> dx/dt=1.6

=> dx = 1.6 dt

Integrating both sides we have x=1.6 t + c

c=0 as x=0 at t=0

thus after (2t-1/4)hour lenth of candel burnt = 1.6*(2t-1/4)= 3.2 t - .4

thus remaining length after (2t-1/4)hour = 10-(3.2 t - .4)= 10.4- 3.2t is required answer