Keshav observed that the increase in the temperature of a body is given by `T_(1) = 2t^(2)` for the first 5 minutes and `T_(2)` = 3t for the next 5 minutes, where `T_(1)`, `T_(2)` and 't' are temperatures in Fahrenheit, Celsius scales and time in minutes, respectively. If the initial temperature of the body is `20^(@)F` and the relation between the Celsius and Fahrenheit scale is, then find the temperature of the body after 8 minutes in Celsius scale.

Answer

`30^(@)C`

Explanation

For 1st 5 minutes
`T_(1) = 2t^(2)`
`2xx25`
`= 50^(@)F`
Initial temperature = `20^(@)F`
After 5 min = `20^(@) + 50^(@) = 70^(@)F`
`(C)/(5) = (F-32)/(9)`
`C = (70-32)/(9) xx 5`
`=21^(@)C`
Increase in temperature after next 3 minutes
`T_(2) = 3t`
`= 3 xx 3`
`T_(2) = 9`
implies Increase in temperature is `9^(@)C`
Temperature after 8 minutes
= 21 + 9
`=30^(@)C`