Fine the constant of variation and the variation equation if y varies jointly as x and w, and inversely as the cube of z, and y=14 when x=1/3, w=27, and z=3 what will k= and y=    

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We are given that y varies jointly with x and w and inversely with `z^3` ; also y=14 when x=1/3,w=27, and z=3.

If a variable varies jointly with two other variables then it varies directly with each of them. So we can write y varies jointly with x and w as `y=kxw` where k is the constant of proportionality. (You only need one, as the two individual contants will have a constant product.)

If y varies inversely with `z^3` we write `y=k/z^3` .

So the equation is `y=(kxw)/z^3`

Substituting the known values we get:

`14=(k(1/3)(27))/(3^3)`

`14*27=9k`

`k=42`

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The equation is `y=(42xw)/z^3` and k=42 is the constant of proportionality.

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