Question 1156640
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I will guess that the "q2" in your question is "q squared"....<br>
We commonly use the "^" symbol (shift-6) to denote exponentiation.  So<br>
"If f varies jointly as q^2 and h..."<br>
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.<br>
But for working a single problem, I prefer a different path to the answer.<br>
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.<br>
So....
ANSWER: The new value of f is {{{(24)*(9/4)*(5/2) = 135}}}<br>