SOLUTION: If f varies jointly as q2 and h, and f=24 when q=2 and h=2, find f when q=3 and h=5

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Question 1156640: If f varies jointly as q2 and h, and f=24 when q=2 and h=2, find f when q=3 and h=5
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39621) About Me  (Show Source):
Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
.

What is this mysterious and undefined symbol " q2 " in your post ?

If you want to express   q%5E2,  write   q^2.

Do not write  q2.   It is  INCORRECT.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


I will guess that the "q2" in your question is "q squared"....

We commonly use the "^" symbol (shift-6) to denote exponentiation. So

"If f varies jointly as q^2 and h..."

Another tutor suggests using the given information to find the constant of variation to find an explicit formula. That is a perfectly good method; and if you are working many problems with the same quantities, it is probably the best way.

But for working a single problem, I prefer a different path to the answer.

The value of f for the given inputs is 24.
The value for q changes from 2 to 3; that is a factor of 3/2. Since the variation is with q^2, this change in q changes the value of f by a factor of 9/4.
The value of h changes from 2 to 5; a factor of 5/2. This changes the value of f by a factor of 5/2.

So....
ANSWER: The new value of f is %2824%29%2A%289%2F4%29%2A%285%2F2%29+=+135