Question

Use the procedure for solving variation problems to solve the exercise.

If y varies jointly as a and b and inversely as the square root of c, and y = 16 when a = 4, b = 4, and c = 4, find y when a = 5, b = 3, and c = 16.

A. 18
B. 20
C. 22
D. 24

Answer 1

To solve this variation problem, we can use the formula for joint variation. Substitute the given values into the equation to find the constant k, then use this value to find y when new values are given.

Step-by-step explanation:

To solve this variation problem, we can use the formula for joint variation. If y varies jointly as a and b and inversely as the square root of c, we can write the equation as:

y = k * (a * b) / sqrt(c)

To find the value of k, we can substitute the given values of y, a, b, and c into the equation:

16 = k * (4 * 4) / sqrt(4)

Simplifying this equation, we get:

k = 4

Now, we can use this value of k to find y when a = 5, b = 3, and c = 16:

y = 4 * (5 * 3) / sqrt(16) = 60 / 4 = 15

Therefore, y = 15 when a = 5, b = 3, and c = 16. The correct answer is not listed.