Question

solve p varies directly as the square of s and inversely as r, when s=6,r=3,and p=48 find the value of p when s =10and r=5​

Answer 1

see explanation

Explanation:

Given that p varies directly as s² and inversely as r then the equation relating them is

p =
`(ks^2)/(r)` ← k is the constant of variation

To find k use the condition when s = 6, r = 3 and p = 48, that is

48 =
`(6^2k)/(3)` ( multiply both sides by 3 to clear the fraction

144 = 36k ( divide both sides by 36 )

4 = k , thus

p =
`(4s^2)/(r)` ← equation of variation

When s = 10 and r = 5 , then

p =
`(4(10)^2)/(5)` =
`(400)/(5)` = 80