Question 997019: The amount of a particular pollutant p from a power plant in the air above the plant depends on the wind speed s, among other things, with the relationship between p and s approximated by p=16-0.04s^2, with s in miles per hour.
a) find the value(s) of s that will make p=0
b)what does p=0 mean in this application?
c)what solution to 0=16-0.04s^2 makes sense in the context of this application?
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Solve for s:
0= 16-0.04s^2 Now, .04 is the same as 1/25 (do the math). So, rewrite:
16-0.04 s^2= 16-s^2/25:
0= 16-s^2/25 Let's flip the equation to make it more elegant:
16-s^2/25= 0
The left hand side factors into a product with four terms:
-1/25((s-20)(s+20))= 0 Multiply both sides by -25 (and -25*0= 0)
(s-20) (s+20) = 0
Split into two equations:
s-20 = 0 or s+20 = 0
Add 20 to both sides:
s = 20 or s+20 = 0
Subtract 20 from both sides:
s = 20 or s = -20
Since s is squared, both numbers give you the same result: 20*20=400 and -20*-20 also= 400. However, we are measuring the amount of a pollutant p in the air so the number we are looking for has to be 0 or higher. Therefore, 20 is your answer.
Proof:
16-0.04(20)^2= 0
16-0.04(400)= 0
16-16= 0 We have the correct answer
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