Final answer:
To solve for e when d=32 and f=4 in the equation d = ke/f^3, we can substitute the values and solve for e using the given values of d = 24, e = 3, and f = 2.
Step-by-step explanation:
To solve the problem, we can use the equation d = ke/f^3, where k is a constant.
We are given that d varies directly as e and inversely as the cube of f, so we can write the equation as d = ke/f^3.
Using the given values of d = 24, e = 3, and f = 2, we can substitute these values into the equation to find k. Then, we can use this value of k to find e when d = 32 and f = 4.
Substituting the values of d = 32 and f = 4 into the equation d = ke/f^3, we can solve for e.
e = (k * d)/f^3
Finally, substitute the calculated value of k from the previous step and solve for e.