Q12 of 32 Page 107

In drilling world’s deepest hole it was found that the temperature T in degree Celsius, x km below the earth’s surface was given by T = 30 + 25 (x – 3), 3 ≤ x ≤ 15. At what depth will the temperature be between 155°C and 205°C?

Given,


T = 30 + 25(x – 3), 3 ≤ x ≤ 15


Where, T = temperature and


x = depth inside the earth


Now, Temperature should be between 155°C and 205°C


⇒ 155 < T < 205


⇒ 155 < 30 + 25(x – 3) < 205


⇒ 155 < 30 + 25x – 75 < 205


⇒ 155 < 25x – 45 < 205


Adding 45, we get


⇒ 200 < 25x < 250


Dividing by 25, we get


⇒ 8 < x < 10


Hence, between 8 to 10 cm depth, temperature varies from 155° C to 205° C.


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