The weight W kg of a metal bar varies jointly as its length L meters and the square of its diameter d meters. If w = 140 when d = 42/3 and L = 54, find d in...
The weight W kg of a metal bar varies jointly as its length L meters and the square of its diameter d meters. If w = 140 when d = 42/3 and L = 54, find d in terms of W and L.
Answer Details
We are told that the weight W of a metal bar varies jointly as its length L and the square of its diameter d, which can be expressed as:
W = kLd2
where k is a constant of variation. We need to find an expression for d in terms of W and L, given that W = 140 when d = 4/3 and L = 54.
To find the value of k, we can substitute the given values into the equation and solve for k as follows:
140 = k × 54 × (4/3)^2
140 = k × 54 × 16/9
k = 140 × 9 / (54 × 16)
k = 35 / 64
Now we can substitute the value of k into the original equation and solve for d in terms of W and L:
W = kLd2
d2 = W / (kL)
d = √(W / (kL))
Substituting the value of k, we get:
d = √((64/35) × W / L)
Simplifying, we get:
d = √((64W) / (35L))
Therefore, the expression for d in terms of W and L is: