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Suppose the rate of melting, M grams per second, of a sphere of ice is inversely proportional to the square of the radius, r cm. When r=20,M=0.6.Find the radius when the rate of melting is 1 gram per second; give the answer correct to 2 decimal places

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Solution

The statement " y varies inversely as x means that when x increases, y decreases by the same factor. In other words, the expression xy is constant:

xy=k

where k is the constant of variation.

Here, it is given that the rate of melting M=0.6 g/sec of a sphere of ice is inversely proportional to the square of radius r=20 cm, therefore,

Mr2=k0.6×(20)2=kk=0.6×400k=0.6×400k=240

Thus, the general equation is Mr2=240.

Since M=1 gm, therefore,

Mr2=2401×r2=240r2=240r=240=15.49

Hence, when the rate of melting is 1 gm/sec, the radius is 15.49 cm.

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