Binomial Theorem

Question
CBSEENMA11014379

In drilling world’s deepest hole, it was found that the temperature T in degree celsius, x km below the surface of the earth, was given by

straight T space equals space 30 plus space 25 left parenthesis straight x minus 3 right parenthesis comma space space space 3 less than straight x less than 15

At what depth will the temperature be between 200 degree straight C and 300 degree straight C?

Solution

We have
                   space space straight T space equals space 30 plus 25 left parenthesis straight x minus 3 right parenthesis comma space 3 less than straight x less than 15
It is given that 200 < T < 300
or                                 200 < 30 + 25(x - 3) < 300
or                                  170 < 25 (x - 3) < 270
or                              170 over 25 less than left parenthesis straight x minus 3 right parenthesis less than 270 over 25
or                          6.8 + 3 < x < 10.8 + 3
or                                 9.8 < x < 13.8
 Hence, the depth will be between 9.8 km and 13.8 km.
              

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