The cube of a number A is proportional to the fourth power of another number B. If B = 8, then A = 8. If B = 3, what is the value of A?3
Question
The cube of a number A is proportional to the fourth power of another number B. If B = 8, then A = 8. If B = 3, what is the value of A?3
Solution
The problem states that the cube of a number A is proportional to the fourth power of another number B. This can be written as A^3 = k * B^4, where k is the constant of proportionality.
Given that when B = 8, A = 8, we can substitute these values into the equation to find k:
8^3 = k * 8^4 512 = k * 4096 k = 512 / 4096 = 0.125
Now that we have the value of k, we can substitute B = 3 into the equation to find the value of A:
A^3 = 0.125 * 3^4 A^3 = 0.125 * 81 A^3 = 10.125
Taking the cube root of both sides gives:
A = cube root of 10.125 ≈ 2.15
So, when B = 3, the value of A is approximately 2.15.
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