Answer:
d = [tex]\sqrt{\frac{216W}{35L} }[/tex]
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 )
[tex]\frac{140}{864}[/tex] = k , that is
k = [tex]\frac{35}{216}[/tex]
W = [tex]\frac{35}{216}[/tex] Ld² ← equation of variation
Multiply both sides by 216
216W = 35Ld² ( divide both sides by 35L )
[tex]\frac{216W}{35L}[/tex] = d² ( take the square root of both sides )
d = [tex]\sqrt{\frac{216W}{35L} }[/tex]
