Problem:
If m varies directly as the square of n and m = 72 when n = 6, find m when n = 8.
Solution:
A direct variation is a relationship between two variables, x and y, that can be written as y = kx where k ≠ 0.
The statement, "m varies directly as the square of n" translated into directly variation is m = kn² where k is the constant of variation.
Solve if m is 72 and n is 6. So, find the constant using the equation of a combined variation.
- m = kn²
- (72) = k(6)²
- 72 = k(36)
- 72 = 36k
- 36k/36 = 72/36
- k = 2
The constant of the variation is 2. In equation of variation.
Find m when n is 8. Substitute the equation using the constant of the variation that you obtained.
- m = 2n²
- m = 2(8)²
- m = 2(64)
- m = 128
Answer:
∴ Therefore, the value of m is 128 to the directly variation.
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