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Old 08-01-2007   #1
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Default Algebra Question. (involves linear equations)?

Word problem:Geothermal energy is createdwherever water comes into contact with heated underground rocks. The underground temp. of rocks varies with their depth below the surface. The temp. (t) in degrees celsius is estimated by the function:t(d)=35d+20where d is the depth in kilometers of the rocksA- Graph the linear equation [y'all don't have to]B-Find the temp. of the rocks at a depth of 3 kilometers [ I think it's 125 or 375?]C-Is the function discrete or continous? Explain your reasoningD-Find the depth if the temp. of the rocks is 195 degrees Celsius
Old 08-01-2007   #2
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B- correct 35x3=105+20=125 degrees C. i would say discrete since the graph must have an end since the depth of the earth is finite.D 195=35d+20 minus 20 from both sides 175=35d divide both sides by 35 and ill let you do the rest
Old 08-01-2007   #3
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The temperature of the rocks at 3 km is found by substituting "3" for "d" in the equation:35(3) + 20 = 105 + 20 = 125 degrees CelsiusThe function is CONTINUOUS because distance is continuous. You can also find the temperature at 3.02756km or at any other distance. The function is, however, finite at both ends. It starts at the earth's surface and would end either at the earth's center if you measure distance from the starting point at the surface, or else you would get a mirror image of your line up to the center as you proceed to the surface on the other side of the world. That would be obvious since your true depth would now be measured from the other side.If the rock temperature is 195 C, we would work the equation backwards to find the depth.195 = 35d + 20Subtract 20 from both sides to get:175 = 35ddivide both sides by 35:5 = dYou would be at a depth of 5 km

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