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Question 1041176: in 1970, Russian geologists began drilling a very deep borehole in the Kola Peninsula. Their goal was to reach a depth of 15 Kilometers, but high temperatures in the borehole forced the to stop in 1994 after reaching a depth of 12 kilometers. They found that the approximate temperature x kilometers below the surface of the Earth is given by: T = 30 + 25(x-3), 3<=x<=12
where T is temperature in degrees Celsius. at what depth is the temperature between 150°c and 250°c, inclusive?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x is the depth in kilometers.
T is the temperature in degrees celsius.
the formula is T = 30 + 25 * (x-3).
3 <= x <= 12.
when x = 3, T = 30 + 25 * (3-3) = = 30.
when x = 12, T = 30 + 25 * (12-3) = 255.
to solve for T between 150 and 250, you replace T with those values and you solve for x.
the formula is T = 30 + 25 * (x-3).
solve for x in the formula as follows:
subtract 30 from both sides of the equation to get T - 30 = 25 * (x-3).
divide both sides of the equation by 25 to get (T - 30)/25 = x - 3
add 3 to both sides of the equation to get (T - 30)/25 + 3 = x.
solve for x to get x = (T - 30)/25 + 3.
when T = 150, this formula becomes:
x = (150 - 30)/25 + 3 = 7.8.
when T = 250, this formula becomes:
x = (250 - 30)/25 + 3 = 11.8
the temperature will be at or between 150 and 250 when x is at or between 7.8 and 11.8.
the formula is T = 30 + 25 * (x-3).
when x = 7.8, T = 30 + 25 * (7.8-3) = 150.
when x = 11.8, T = 30 + 25 * (11.8-3) = 250.
everything checks out.
your solution is:
the temperature will be between 150 and 250 degrees celsius inclusive when the depth is between 7.8 and 11.8 kilometers inclusive.
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