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In drilling world's deepest hole it was ...

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 le x le 15`. At what depth will the temperature be between ` 155^(@)C and 205^(@)C`?

Text Solution

Verified by Experts

Given that, ` T=30+25(x-3), 3le x le 15`
According to the question,
`155lt T lt 205`
`rArr 155 lt 30+25(x-3) lt205`
`rArr 155-30 lt 25(x-3) lt 205-30` [ subtracting 30 in whole]
`rArr 125 lt 25 (x-3) lt 175`
`rArr (125)/(25) lt x-3 lt (175)/(25)` [ dividing by 25 in whole]
`rArr 5 lt x-3 lt 7`
` rArr 5+3 lt x lt 7+3` [adding 3 in whole]
` rArr 8 lt x lt 10`
Hence, at the depth 8 to 10 km temperature lies between ` 155^(@) to 205^(@)C` .
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