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
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.
To solve this problem, we need to find the constant of proportionality first.
Given:
W ∝ t^2
W ∝ 1/z^3
Using the given values when t = 2, z = 4 and w = 14.4, we can find the constant of proportionality:
14.4 = k * (2^2) * (4^-3)
14.4 = k * 4 * (1/64)
14.4 = k * (4/64)
14.4 = k * (1/16)
k = 14.4 * 16
k = 230.4
Now we can find the value of w when t = 7 and z = 11:
W = k * (t^2) * (1/z^3)
W = 230.4 * (7^2) * (1/11^3)
W = 230.4 * 49 * (1/1331)
W ≈ 230.4 * 49 * 0.00075
W ≈ 8.4
Therefore, when t = 7 and z = 11, the value of w is approximately 8.4.