Question

1.Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p​ dollars, the revenue R​ (in dollars) is R(p)=−5p2+15,000p.

​(a) At what prices p is revenue​ zero?

​(b) For what range of prices will revenue exceed $1,500,000​?

2. A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance s​ (in feet) of the ball from the ground after t seconds is s=80t-16t2. ​(a) At what time t will the ball strike the​ ground? ​(b) For what time t is the ball more than 84 feet above the​ ground?

Answer 1

Answer 2

The solutions are given below

Question -1) Given that RCD) = -5.52+ 15000 6 (a) RSb) = -5.62 +15000 $ -5b1b-3000) 56. b-3000 =0 p=t = 3ooo Thuss at price pzo and þ= 3ooo dollars the will be Zevo. or or revenue (6) Now, RCB) = 1500-300 5627 15000p=1500000 62 + 3000b=300,000 22.-36005 + 300,000 =0 Now, using the formula ba -bit/6²-yar 20 Here...al, b = -3000 LE 350,000 þ= -(3000) £ V3.000) - Yo): 300,000 2.1 1500 - 100X195 100/195 + 1500 = 103.57 2896 · 46 Thus, RE) > 1500,050 Rob p> 103.57 and þ<2896.46 ie. RCb) > 1560,000 if 103.57<p < 2896.46 to

Thit the =0 Question=2) s(t) = got- 16th (a) For ball to s(t) ground Qot-16th 20 16t(5-t) o >tzo and 5-tzo st and ta5 so the ball will be hitting the t=5 seconds. And t = selconds its Intial positions so ball the nd at t = 5 seconds. ground at will hêt (6) Now, Sit)=8u Sot -16t2 = 04 16t2_886 +8 uzo > 4t2-20t + 21 20 4+2 -14t-66 +2130 3 2t(2t -7)-3(21-7)=0 » 2t-3) (21-7) t =3 and t = 7 2 ball will be above 84 between t=3/2 and t= 7/2 sec Oy slt) 284 E 2 2 from the ground Usec. if 3 < t < 7