M is directly proportional to r^(3) when r = 4, M = 160 a) work out the value of M when r = 2. b) work out the value of r when M = 540.

Question

M is directly proportional to
`r^(3)`

when r = 4, M = 160
a) work out the value of M when r = 2.
b) work out the value of r when M = 540.

Answer 1

a) 20

b) 6

Explanation:

When a relation is a direct proportion, it means there is a constant of proportionality that relates the dependent variable to the quantity it is proportional to. That means we can write the equation as ...

M = kr³ . . . . . for constant of proportionality k

We can find k from the given points:

k = M/r³ = 160/4³ = 2.5

So the relation is ...

M = 2.5r³

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a)

For r = 2, we have ...

M = 2.5(2³) = 20 . . . . the value of M when r=2

__

b)

For M=540, we have ...

540 = 2.5r³

r³ = 540/2.5 = 216

r = ∛216 = 6 . . . . . the value of r when M=540