A body cools from `70^@C` to `60^@C` in 10 minutes. Calculate the temperature of body after further 7 minutes if temperature of surroundings is `12^@C` .

Explanation

To solve the problem of a body cooling from \(70^\circ C\) to \(60^\circ C\) in 10 minutes and then finding its temperature after a further 7 minutes with surroundings at \(12^\circ C\), we will apply Newton's Law of Cooling.

### Step-by-Step Solution:

1. **Understanding Newton's Law of Cooling**:
Newton's Law of Cooling states that the rate of change of temperature of an object is proportional to the difference between its own temperature and the ambient temperature. The formula can be expressed as:
\[
\frac{dT}{dt} = -k(T - T_s)
...