Answer:
option B
[tex]\frac{280}{\sqrt{L}\sqrt[3]{P}}[/tex]
Step-by-step explanation:
Step 1
S varies inversely of the cube root of P
s [tex]\alpha[/tex][tex]\frac{1}{\sqrt[3]{P} }[/tex]
s = [tex]\frac{k}{\sqrt[3]{P} }[/tex]
Step 2
S varies inversely with square root of L
s[tex]\alpha\frac{1}{\sqrt{L} }[/tex]
s = [tex]\frac{k}{\sqrt{L} }[/tex]
Step 3
Jointly
s = [tex]\frac{k}{\sqrt{L} \sqrt[3]{P} }[/tex]
Step 4
Plug values given in the question to find constant of proportionality
7 = [tex]\frac{k}{\sqrt{100}\sqrt[3]{64}}[/tex]
7 = k /(10)(4)
7 = k/40
k = 280
Step 5
General formula will be
s = [tex]\frac{280}{\sqrt{L}\sqrt[3]{P}}[/tex]
