EXAMPLES VIII 



129 



(80) The annual cost of giving a certain amount of electric 

 light to a certain town, the voltage being V and the candle-power 

 of each lamp C, is found to be 



A - a + -- for electric energy 



and 



i: 



m 



n - for lamp renewals. 



The given values are known when 

 C = 10. Find a, b, m, and n. If 

 C = 20, what value of V will give 

 minimum total cost ? (B. of E., 

 1907.) 



(31) If a crank is at the angle from a dead point, and = qt 

 where q is the angular velocity ; if x feet is the distance of the 

 piston from the end of its stroke, r feet is the length of the crank, 

 and I feet the length of the connecting rod ; then 



I 

 x = r(l - cos 0) + -j (1 - cos 20) 



Taking r = 1 and 1 = 5, what is the angular position of the crank 

 when the piston is moving with greatest velocity, and what is 

 the distance of the piston from the end of its stroke at that 

 instant ? 



