Question

20 POINTS!!

Answer 1

Answer:

r = 8

Step-by-step 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 = $\frac{m}{r^{2} }$ =$\frac{14}{4}$  = $\frac{7}{2}$

M = r² ← equation of proportion

When M = 224, then

224 =$\frac{7}{2}$r² ← multiply both sides by 2

7r² = 448 ( divide both sides by 7 )

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

r = $\sqrt{64}$ = 8

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