Subjects calculus

Temperature Rate 358746

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1. **State the problem:** Find the rate of change of temperature $T(h) = \frac{60}{h+2}$ with respect to height $h$ at $h=3$ km. 2. **Formula and rules:** The rate of change of a function is its derivative. For a function $T(h) = \frac{60}{h+2}$, rewrite as $T(h) = 60(h+2)^{-1}$. 3. **Differentiate:** $$\frac{dT}{dh} = 60 \times (-1)(h+2)^{-2} = -\frac{60}{(h+2)^2}$$ 4. **Evaluate at $h=3$:** $$\frac{dT}{dh}\bigg|_{h=3} = -\frac{60}{(3+2)^2} = -\frac{60}{25} = -2.4$$ 5. **Interpretation:** The temperature decreases at a rate of 2.4 degrees Celsius per kilometre at 3 km height.