Question
W is directly proportional to t^2 and inversely proportional to z^3. What t = 2 and z=4, w= 14.4.
Find w when t= 7 and z = 11
Find w when t= 7 and z = 11
Answers
GPT 3.5
To find the relationship between W, T, and Z, we can write the equation as:
W = k * T^2 / Z^3
Given that when T = 2 and Z = 4, W = 14.4, we can substitute these values into the equation:
14.4 = k * 2^2 / 4^3
14.4 = 4k / 64
14.4 * 64 = 4k
921.6 = 4k
k = 921.6 / 4
k = 230.4
Now, we can use this value of k to find W when T = 7 and Z = 11:
W = 230.4 * 7^2 / 11^3
W = 230.4 * 49 / 1331
W = 11289.6 / 1331
W ≈ 8.48
Therefore, when T = 7 and Z = 11, W is approximately equal to 8.48.
W = k * T^2 / Z^3
Given that when T = 2 and Z = 4, W = 14.4, we can substitute these values into the equation:
14.4 = k * 2^2 / 4^3
14.4 = 4k / 64
14.4 * 64 = 4k
921.6 = 4k
k = 921.6 / 4
k = 230.4
Now, we can use this value of k to find W when T = 7 and Z = 11:
W = 230.4 * 7^2 / 11^3
W = 230.4 * 49 / 1331
W = 11289.6 / 1331
W ≈ 8.48
Therefore, when T = 7 and Z = 11, W is approximately equal to 8.48.