Question

If y varies jointly with w squared and b squared, and y = 108 when w = 2 and b = 3, find b when y = 48 and w = 1.

a) 2
b) 3
c) 4
d) 5

Answer 1

To solve the problem, we find the constant of variation using the initial conditions. Then, we use this constant to find the required value of 'b' when 'y' and 'w' are given in the second set of conditions. The correct answer is that 'b' equals 4 when 'y' = 48 and 'w' = 1.

Step-by-step explanation:

If y varies jointly with w squared and b squared, this means that y = k(w^2)(b^2), where k is the constant of variation. From the given information, we can find the constant of variation when y = 108, w = 2, and b = 3. Substituting these values into the equation gives us 108 = k(2^2)(3^2). Simplifying this, we get k = 108 / (4 × 9), so k = 3.

To find the value of b when y = 48 and w = 1, we plug these values along with our constant k into the equation: 48 = 3(1^2)(b^2). Therefore, b^2 = 48 / 3, and b^2 = 16, which means that b = 4.