Question

The weight Wkg of a metal bar varies jointly

Answer 1

Answer:

d = $\sqrt{\frac{216W}{35L} }$

Step-by-step explanation:

Given that W varies jointly as L and d² then the equation relating them is

W = kLd² ← k is the constant of variation

To find k use the condition W = 140 when d = 4 and L = 54, thus

140 = k × 54 × 4² = 864k ( divide both sides by 864 )

$\frac{140}{864}$ = k , that is

k = $\frac{35}{216}$

W = $\frac{35}{216}$ Ld² ← equation of variation

Multiply both sides by 216

216W = 35Ld² ( divide both sides by 35L )

$\frac{216W}{35L}$ = d² ( take the square root of both sides )

d = $\sqrt{\frac{216W}{35L} }$