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Let a be directly proportional to m and n^2, and inversely proportional to y^3. If a=4 when m=9, n=4, and y=2, find a when m=7, n=3, and y=5.

a=? (Type an integer or a simplified fraction.)

Respuesta :

ShyzaSling

Answer:

4

Step-by-step explanation:

Step 1

Let a be directly proportional to m and n^2

a [tex]\alpha[/tex] m(n)²

a = km(n)²

Step 2

Let a be inversely proportional to y^3

a [tex]\alpha[/tex] [tex]\frac{1}{y^{3} }[/tex]

a = [tex]\frac{k}{y^{3} }[/tex]

Step 3

Plug values in the equation to find k

4 = k (9)(4)²/2³

4 = k 144 / 8

4 = 18k

k = 4/18

k = 2/9

Step 4

find a

a = (2/9)(9)(4)²/2³

  = 32 / 8

  = 4

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