SOLUTION: The rate of flow of water through a pipe varies directly as the square of the of the radius of the pipe. By how much would the rate of flow be increased, if the diameter of the pip

Algebra ->  Expressions-with-variables -> SOLUTION: The rate of flow of water through a pipe varies directly as the square of the of the radius of the pipe. By how much would the rate of flow be increased, if the diameter of the pip      Log On


   

Question 1047388: The rate of flow of water through a pipe varies directly as the square of the of the radius of the pipe. By how much would the rate of flow be increased, if the diameter of the pipe were multiplied by 3/2?
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of flow of water through a pipe varies directly as the square of the of the radius of the pipe. By how much would the rate of flow be increased, if the diameter of the pipe were multiplied by 3/2?
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It would be (3/2)^2 = 9/4 times the flow rate.
That's an increase of 5/4.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the diameter is multiplied by +3%2F2+,
then so is the eradius
Let +f%5B1%5D+ = the rate of flow through the pipe
Let +r+ = radius of the pipe
+f%5B1%5D+=+k%2Ar%5E2+
+k+=+f%5B1%5D%2Fr%5E2+
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+f%5B2%5D+=+k%2A%28%28+3%2F2+%29%2Ar%29%5E2+
+f%5B2%5D+=+%28+f%281%29%2Fr%5E2+%29%2A%28+%283%2F2%29%2Ar+%29%5E2+
+f%5B2%5D+%2F+f%5B1%5D+=+%28+%283%2F2%29%2Ar+%29%5E2+%2F+r%5E2+
+f%5B2%5D+%2F+f%5B1%5D+=+%28+9%2F4+%29%2A%28+r%5E2%2Fr%5E2+%29+
+f%5B2%5D+%2F+f%5B1%5D+=+9%2F4+
The rate of flow is increased by a factor of 9/4