SOLUTION: Word problems are so difficult for me to understand! Please help! Thanks. For an engine with a displacement of 2.8L, the function given by the equation d=Cn^-2 can be used to dete

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Question 469699: Word problems are so difficult for me to understand! Please help! Thanks.
For an engine with a displacement of 2.8L, the function given by the equation d=Cn^-2 can be used to determine the diameter size of the carburetor's opening, d, in millimeters, where n is the number of rpm's at which the engive achieves peak performace and C is a constant.
a. solve the equation for n.
b. Suppose the carburetor's opening is 84 mm and rpm's are 4480. Find the value of C that makes the equation true.
c. use the value of c that you found to determine the rpm's at which the engine produces peak power when the carburetor's opening is 81 mm.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+d+=+C%2An%5E%28-2%29+
(a)
Solve for n
Take the log of both sides
using the rule:
+log%28a%5Eb%29+=+b%2Alog%28a%29+
+log%28d%29+=+%28-2%29%2AC%2Alog%28n%29++
+log%28n%29+=+log%28d%29+%2F+%28-2%2AC%29+
Now use the above rule in reverse
+log%28n%29+=+log%28d%5E%281%2F%28-2C%29%29+
Use the rule:
If +log%28a%29+=+log%28b%29+,
then +a+=+b+
+n+=+d%5E%281%2F%28-2C%29%29+
------------------
(b)
+d+=+84+
+n+=+4480+
Find C
+n+=+d%5E%281%2F%28-2C%29%29+
+4480+=+84%5E%281%2F%28-2C%29%29+
Let +1%2F%28-2C%29+=+x+
+84%5Ex+=+4480+
+x%2Alog%2884%29+=+log%284480%29+
+x+=+log%284480%29+%2F+log%2884%29+
+x+=+3.6513+%2F+1.92428+
+x+=+1.8975+
+1%2F%28-2C%29+=+1.8975+
+-2C+=+1%2F1.8975+
+C+=+-1%2F3.7950+
+C+=+-.2635+