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Question

The temperature at $$12$$ noon was $$10^o$$C above zero. If it decreases at the rate of $$2^o$$C per hour until midnight, at what time would the temperature be $$8^o$$C below zero? What would be the temperature at midpoint?


Solution

Given, $$12$$ noon temperature was $${10}^{o}C$$ above zero.

$$T(12pm)={10}^{o}C$$

It decreases at the rate of $${2}^{o}C$$ per hr until $$ 12\ am $$

$$\cfrac{dT}{dt}$$ (12pm to 12am) $$=-{2}^{o}C$$

$$T(t)=-2t+{T}_{0}$$

$${T}_{0}={10}^{o}C$$

$$-{8}^{o}=-2t+{10}^{o}$$

$$2t={18}^{o}$$

$$t=9$$

It means at 9 pm, the temperature is $$-{8}^{o}C$$

Mathematics
NCERT
Standard VII

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