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M is a directly proportional to r cubed when r=4 M=160

1) work out the value of M when r=2
2) work out the value of r when M=540

User Dirk
by
8.5k points

1 Answer

6 votes

Answer:

1) When r = 2, M = 20.

2) When M = 540, r = 6.

Explanation:

M is a directly proportional to r cubed

This means that the equation for M has the following format:


M = ar^3

In which a is a multiplier.

When r=4 M=160.

We use this to find a. So


M = ar^3


160 = a(4^3)


64a = 160


a = (160)/(64)


a = 2.5

So


M = 2.5r^3

1) work out the value of M when r=2


M = 2.5*2^3 = 2.5*8 = 20

When r = 2, M = 20.

2) work out the value of r when M=540


M = 2.5r^3


540 = 2.5r^3


r^3 = (540)/(2.5)


r^3 = 216


r = \sqrt[3]{216}


r = 6

When M = 540, r = 6.

User Dmitry Samoylov
by
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