$\"\"$

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Newtons Law of Cooling is $\"\"$ .

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Here $\"\"$ is the temperature of the object and $\"\"$ is the surrondings temperature.

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Change in temperature $\"\"$ .

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At the intital time $\"\"$ .

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$\"\"$ and $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the equation $\"\"$ .

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$\"\"$ .

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The general equation is $\"\"$ .

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Substitute $\"\"$ in the above equation.

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$\"\"$ .

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$\"\"$

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(a).

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After half an hour, the temperature is $\"\"$ then $\"\"$ .

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Hence $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the above equation.

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$\"\"$ .

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Substitute $\"\"$ in the equation $\"\"$ at $\"\"$ .

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$\"\"$

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$\"\"$

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The equation is $\"\"$

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Find the temperature after $\"\"$ minutes.

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The equation is $\"\"$ .

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$\"\"$ .

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Temperature after $\"\"$ minutes :

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in the equation $\"\"$ .

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$\"\"$ .

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Temperature after $\"\"$ minutes is $\"\"$ .

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$\"\"$

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(b).

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Find the time when the temperature is $\"\"$ .

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The equation is $\"\"$ .

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$\"\"$

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After $\"\"$ minutes the temperature is $\"\"$ .

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$\"\"$

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(a) Temperature after $\"\"$ minutes is $\"\"$ .

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(b) After $\"\"$ minutes the temperature is $\"\"$ .