Expert: Richard J. Raridon - 4/27/2008

Question
i am 28yrs.  i actually have 4 problems i wanted to see if i could get help setting up and get answers for.
                                                       1.  the cost of removing P% of the air pollution from the he stack emissions from sanding and lathing at ricky's rockers is modeled by the following function:
C(p)=120,000p/1-p
a) what percent of the air pollution can ricky's rockers remove if they are willing to spend $600,000?
b) if the usepa requires ricky's rockers to remove at least 95% of their pollution, how much will they have to spend on pollution control?
c) can ricky's rockers remove 100% of their pollution, Why?

2.  at ricky's rockers Frank, needs to fix a leak in a pipe on the air pollution control equipment at the factory. Frank has a ladder that is 20 feet long and he knows according to the osda safety manual that to make a safe climb he must have the base of the ladder at least 6 feet from the base of the building. if the pipe on the building that he wants to repair is 16 feet high does the ladder reach the pipe so frank can safely make the repair?
(use the pythagorean theorem)

3.  Frustrated with dealing with the usepa about the air pollution at his plant. ricky took his cell phone and threw it off the top of his office building, the height of the falling cell phone at time (t) is described by the function: h(t)= -16tsquared + 64t +192
a) when will ricky's cell phone be at a height of 240 feet?
b) how many seconds will it take before ricky's phone hits the ground?

4.  ricky had thought about selling his business. he knows that it has appreciated at 6% per year. his capital was $128,000. how much could ricky ask for his business after being in business for 12 years?

Answer
1. This problem is not stated correctly since 1-p would be negative for p greater than 1.  You need to divide the percent by 100 to get the fraction.  Also, never put commas in an equation.  So if you re-write C = 120000p/(1-p) and solve for p you get p=C/(120000+C) so for (a) you have p = 0.833 or 83.3%
(b) C = 120000(0.95)/(1-0.95) = $2,280,000
(c) no since you would be dividing by 0 giving you infinity
2. 20^2 = 6^2 +x^2 so x = 19 ft
3. (a) 240 = -16t^2+64t+192 or t^2-4t+3 = 0 = (t-1)(t-3) so t = 1s,3s
(b) 0 = -16t^2 +64t+192 or t^2-4t-12 = 0 = (t-6)(t+2) so t = 6s
4. 128000(1.06)^12 = $257,561