Question

20 POINTS!!

M is directly proportional to r squared when r=2, m=14
Workout the value of r when M =224

Answer 1

r = 8

Explanation:

Given that M is directly proportional to r² then the equation relating them is

M = kr² ← k is the constant of proportionality

To find k use the condition when r = 2 , M = 14

k =
`(m)/(r^(2) )` =
`(14)/(4)` =
`(7)/(2)`

M = r² ← equation of proportion

When M = 224, then

224 =
`(7)/(2)`r² ← multiply both sides by 2

7r² = 448 ( divide both sides by 7 )

r² = 64 ( take the square root of both sides )

r =
`√(64)` = 8

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