Problem:
If f varies directly as g and inversely as the square of h, and f = 20 when g = 50 and h = 5, find f when g = 18 and h = 6.
Solution:
To translate into variation statement a relationship involving combined variation between two quantities.
The statement, "If f varies directly as g and inversely as the square of h" translated into combined variation is f = kg/h² where k is the constant of variation.
Solve if f is 20 when g is 50 and h is 5. So, find the constant using the equation of a combined variation.
- f = kg/h²
- (20) = k(20)/(5)²
- 20 = 20k/25
- 20 × 25 = 20k
- 500 = 50k
- 50k/50 = 500/5
- k = 100
The constant of the variation is 100. In equation of variation.
Find f when g is 18 and h is 6. Substitute the equation using the constant of the variation that you obtained.
- f = 100g/h²
- f =100(18)/(6)²
- f = 1800/36
- f = 50
Answer:
∴ Therefore, the value of f is 50 to the combined variation.
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