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Functions of two variables

  1. Jan 28, 2009 #1
    1. The problem statement, all variables and given/known data
    [​IMG]

    If the wind is blowing at 25 mph, approximately what temperature feels like 0°F?


    2. Relevant equations



    3. The attempt at a solution


    I answered -24 and it's wrong...
    What should it be?
     
  2. jcsd
  3. Jan 28, 2009 #2

    Mark44

    Staff: Mentor

    Yeah, -24 is wrong. Look down the left-most column at the rows for wind speed and find the two numbers in that row that are closest to 0°F perceived temperature. Then look at the top row and find the two actual temperatures the correspond to the two temps you found in the table. You will probably need to do linear interpolation to come up with a single number.

    Here's an example. If the question is "the wind is blowing at 10 mph, approximately what temperature feels like 24°F?"
    I see in the row for 10 mph the perceived temperatures that bracket 24°F, namely 27°F and 21°F. The actual temps that go with these are 35°F and 30°F. Since my perceived temperature is exactly halfway between the two values in the table, the actual temperature will be exactly halfway between 35°F and 30°F, or 32.5°F.

    That's the basic idea. For the linear interpretation I think you'll need to do, you'll have to do a bit more arithmetic than I did, but it ain't "rocket science."
     
  4. Jan 28, 2009 #3
    so I am looking at the -3 and 4 column which corresponds to a value between 15 and 20?
     
  5. Jan 28, 2009 #4

    Mark44

    Staff: Mentor

    Yes. The value you want will be closer to 15 than 20, since 0 is closer to -3 than it is to 4.
     
  6. Jan 28, 2009 #5
    and how would I find that value exactly?
     
  7. Jan 28, 2009 #6

    Mark44

    Staff: Mentor

    Use the equation y = mx + b, where x is the perceived temp and y is the actual temp.

    You have two points on this line: (-3, 15) and (4, 20). Use these points to find the slope m. Use either point to find b.

    When you have the equation of the line, find y when x is 0.

    That's one way to do it; there are other ways as well.
     
  8. Jan 28, 2009 #7
    isn't the point supposed to be (3,15) and (-4,15)
     
  9. Jan 28, 2009 #8

    Mark44

    Staff: Mentor

    They should be (-4, 15) and (3, 20).
     
  10. Jan 28, 2009 #9
    okay and I found the equation to be :


    y = 5/7x + 17.85

    so therefore the answer is 17.85.. correct?
     
  11. Jan 29, 2009 #10

    Mark44

    Staff: Mentor

    Pretty close. 17.86 is closer. The exact value is 17 6/7.
     
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