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?
According to the question,
T = 30 + 25(x – 3), 3 ≤ x ≤ 15; where, T = temperature and x = depth inside the earth
The Temperature should be between 155°C and 205°C,
So, we get,
⇒ 155 < T < 205
⇒ 155 < 30 + 25(x – 3) < 205
⇒ 155 < 30 + 25x – 75 < 205
⇒ 155 < 25x – 45 < 205
Adding 45 to each term, we get
⇒ 200 < 25x < 250
Dividing each term by 25, we get
⇒ 8 < x < 10
Hence, temperature varies from 155° C to 205° C at a depth of 8 km to 10 km.
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