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The temperature at 12 noon was 10 degrees C above zero. If it decreases at the rate of 2 degrees C per hour until midnight, at what time would the temperature be 8 degrees C below zero? What would be the temperature at mid-night?

5. The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?

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Given,

Temperature at 12 noon = 10^{\circ}C

Final temperature = -8^{\circ}C

\therefore Decrease in temperature = 10 - (-8) = 18^{\circ}C

Time taken for the temperature  to decrease by 2^{\circ}C1\ hour

\therefore Time taken for the temperature  to decrease by 18^{\circ}C

=\frac{1}{2}\times18\ hour

= 9\ hours

Now,

Time until mignight = 12\ hours

\therefore Decrease in temperature in 12\ hours = 2\times12 = 24^{\circ}C

Therefore, temparature at midnight = (10 - 24)^{\circ}C = -14^{\circ}C

Therefore, temperature at mid-night will be 14^{\circ}C below zero.

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