Mathematics

Mathematics

Problem

Let T(r)=5r3−2rT(r)=5r^{3}-2r denote the temperature, in degrees Celsius, on the surface of an expanding metal sphere whose radius rr is measured in centimeters. When r=2 cmr=2\text{ cm} the radius is increasing at a rate of 0.1 cm/min0.1\text{ cm/min}. What is dTdt\dfrac{dT}{dt}, in degrees Celsius per minute, at that instant? a) 5858 b) 5.85.8 c) 4.14.1 d) −5.8-5.8

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