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Newton's law of cooling: rates of cooling at two temperatures, find the surrounding temperature

The same question, asked 2 times: 14 May 2024 S2*, 20 Apr 2025 S2. Every wording below, oldest first.

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  1. Question 1

    14 May 2024 S2

    42
    A metal rod cools at the rate of 4°C/min4°C/\text{min} when its temperature is 90°C90°C and the rate of 1°C/min1°C/\text{min} when its temperature is 30°C30°C. The temperature of the surrounding is

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  2. Question 2

    20 Apr 2025 S2

    19
    A metal sphere cools at a rate of 1.5∘C/min1.5^{\circ}C/min when its temperature is 80∘C80^{\circ}C. When the temperature of the sphere is 40∘C40^{\circ}C, its rate of cooling is 0.3∘C/min0.3^{\circ}C/min. The temperature of the surrounding (θ0)\left( \theta_{0} \right) is

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