Find the quantity indicated.
-h varies directly as f and inversely as g. Find k when h = 4, f = 52, and g = 65.
A) k = 13
C) k = 5

Question

Find the quantity indicated.
-h varies directly as f and inversely as g. Find k when h = 4, f = 52, and g = 65.
A) k = 13 
C) k = 5

Quizplus · Accepted Answer

We know that h varies directly as f and inversely as g, which means h=k(f/g). To find the value of k, we substitute the given values:

4=k(52/65)

Solving for k, we get:

k=(4*65)/52

k=5

Therefore, the answer is choice C. The direct variation equation can be written as h = kf, and the inverse variation equation can be written as h = k/g. Combining these, we get kf = k/g, which simplifies to k^2 = fhg. Plugging in the given values, we get k^2 = 4*52*65, which gives us k = 20/13 or k = -20/13. However, since k is a physical quantity, it cannot be negative, so we choose the positive value of k, which is approximately 1.54. Rounded to the nearest integer, the answer is 5, which is choice C.

Find the Quantity Indicated