Answered

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M is directly proportional to [tex]r^{3}[/tex]
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.

Sagot :

sqdancefan

Answer:

  a) 20

  b) 6

Step-by-step 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

__

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

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