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W varies jointly as X and Y and inversely as the square of Z. If W=280 when X=30, Y=12, and Z=3, find W when X=20, Y=10, and Z=2.​

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dommalb

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Answer:

The answer is 350.

Step-by-step explanation:

The joint variation of W with x, y and z may be expressed as follow,                                    W = kxy / z²where k is the constant of variation. Substituting the first set of values for the variables,                                   280 = k(30)(12) / 3²The value of k from the equation is 7. Substituting to the same equation the values of the next set of variables,                                      w = (7)(20)(10) / 2² = 350

Answer:

W = 350

Step-by-step explanation:

W varies jointly as X and Y and inversely as the square of Z.

That means W ∝ [tex]\frac{XY}{Z^{2} }[/tex]

Or W = [tex]\frac{kXY}{Z^{2} }[/tex]

Where k is the proportionality constant.

Now as per statement we will plug in the values

W = 280, X = 30, Y = 12 and Z = 3 to find the value of constant k

280 = [tex]\frac{k(30)(12)}{3^{2} }[/tex]

k = [tex]\frac{280\times 9}{360}[/tex]

k = 7

Now we plug in the values

X = 20, Y = 10, Z = 2 and K = 7 to find the value of W.

W = [tex]\frac{7\times 20\times 10}{2^{2} }[/tex]

   = [tex]\frac{1400}{4}[/tex]

   = 350

Therefore, W = 350 is the answer.

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