Question 1202703: F varies directly with m and inversely with the square of D If d=5 when f=24 and m=20 find d when f=18.75 and m=40
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
You can use the definition of how d, f, and m are related, along with the given set of values, to find the constant of proportionality and then use that constant with the new values of f and m to find the new value of d.
That would be a reasonable thing to do if you were going to use the relationship between d, f, and m multiple times on multiple problems.
However, to solve this single problem, there is no need to find the constant of proportionality. You can solve the problem by using the given variation to see how the value of one variable changes when the values of the other variables change.
In this problem, the variation as given defines how f varies with d and m; but we are to find the new value of d, given new values of f and m. So solve the given variation to see how d varies with f and m:
Note "k" is just a constant of variation, which we are not going to use, so here we don't need to write "sqrt(k)"....
This statement says that d varies directly as the square root of m/f.
From the first set of data to the second, m changes by a factor of 40/20 = 2, and f changes by a factor of 18.75/24 = 75/96 = 25/32, so m/f changes by a factor of 2/(25/32) = 64/25. And since d varies directly as the square root of m/f, d changes by a factor of 8/5.
And since the given value of d was 5, the new value of d is 5*(8/5) = 8.
ANSWER: 8
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