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marcelie

  • one year ago

Help Please !!!!!! When temperature is 0 degrees Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the corresponding Fahrenheit temperature is 212. Express the Fahrenheit temperature as a linear function of C, the Celsius temperature, F(C). a. Find the rate of change of Fahrenheit temperature for each unit change temperature of Celsius. b. Find and interpret F(28). c. Find and interpret F(–40).

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  1. anonymous
    • one year ago
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    so you have two data points right?

  2. marcelie
    • one year ago
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    i think so

  3. anonymous
    • one year ago
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    (0,32) and (100,212)

  4. anonymous
    • one year ago
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    since we have two points, we can always create a straight line.

  5. marcelie
    • one year ago
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    so then i use the slope of the line ?

  6. anonymous
    • one year ago
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    you use the general formulae of a line. y=mx+c here F=mC+c where 'c' is the intercept, C is celcius temp and F is farenheit temp

  7. anonymous
    • one year ago
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    |dw:1441355697020:dw|

  8. anonymous
    • one year ago
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    we already know the intercept right? F=32? since C=0

  9. anonymous
    • one year ago
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    hence F=mC+32 what is the other point we know? Substitute that point into the equation to solve for m

  10. marcelie
    • one year ago
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    so my linear equation will be y= 1.8x +32 ?

  11. anonymous
    • one year ago
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    F=mC+32 we know point (100,212) Subt this into first eq. 212=100m+32 100m=180 m=180/100 m=1.8 hence F=1.8C+32

  12. anonymous
    • one year ago
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    well done

  13. anonymous
    • one year ago
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    so now, what is the rate of change of Fahrenheit? it is the differential with respect to time right?

  14. marcelie
    • one year ago
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    so when it says rate of time is there a formula for it ?

  15. marcelie
    • one year ago
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    So this is what i came up with my answers a, ? b. f(28) = 82.4 c. f(-40)=-40

  16. anonymous
    • one year ago
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    b and c ask you to interpret. So this means for b. we say, at 28 degrees Celsius, the temperature is 82.4 Fahrenheit

  17. anonymous
    • one year ago
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    for a. we differentiate that equation with respect to time. \[F=1.8C+32\] \[\frac{ d }{ dt }\left( F \right)=\frac{ d }{ dt }\left( 1.8C+32 \right)\] \[\frac{ dF }{ dt}=1.8\frac{ dC }{ dt }\]

  18. anonymous
    • one year ago
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    the differentiation of a constant is always zero. remember.

  19. marcelie
    • one year ago
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    so is that a formula ?

  20. anonymous
    • one year ago
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    yep

  21. anonymous
    • one year ago
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    that is the rate of change of farenheit temperautre

  22. marcelie
    • one year ago
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    okay. so what do i plug in to it ?

  23. anonymous
    • one year ago
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    hmm. maybe what i did was a bit too complex for you at this level.

  24. marcelie
    • one year ago
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    yes. lol i am taking pre cal. so i thinks its calculus lol

  25. anonymous
    • one year ago
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    ah right.

  26. anonymous
    • one year ago
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    perhaps that is simply the slope they are looking for?

  27. marcelie
    • one year ago
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    so for a its f = 1.8c +32 ? or do i have to solve it more?

  28. anonymous
    • one year ago
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    well 'for each unit change in celcius temp, means we should plug in c=1,2,3,...etc right?

  29. anonymous
    • one year ago
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    thats simple what a unit change means

  30. anonymous
    • one year ago
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    have you learnt what a derivative is or not?

  31. marcelie
    • one year ago
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    okay. so once i plug in those numbers whats the next step is ? I dont think so.

  32. anonymous
    • one year ago
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    i don't know if theres enough information to calculate the rate. we aren't given the time of how long it takes to get from 0 degrees to 100 degrees.. :/

  33. marcelie
    • one year ago
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    hmmm. so should i leave the answer as f= 1.8c+32 ?

  34. anonymous
    • one year ago
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    thats the answer for the questions: 'Express the Fahrenheit temperature as a linear function of C, the Celsius temperature, F(C).'

  35. anonymous
    • one year ago
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    but yea, not 100% sure what a wants us to find out sicne you are doing pre-calc

  36. marcelie
    • one year ago
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    hmmm. how would u solve it ?

  37. anonymous
    • one year ago
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    \[\frac{ dF }{ dt}=1.8\frac{ dC }{ dt }\]

  38. marcelie
    • one year ago
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    okay. so what do i plug in for df /dt = 1.8 dc/dt

  39. anonymous
    • one year ago
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    nothing. that is just a general from on how to write functions with respect to time, i.e rates of change

  40. anonymous
    • one year ago
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    you don't have enough info to find the rate

  41. marcelie
    • one year ago
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    ah okay.

  42. marcelie
    • one year ago
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    for letter b the wording is the same but the number changes right ?

  43. marcelie
    • one year ago
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    i mean for letter c.

  44. anonymous
    • one year ago
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    yep so at -40 degrees celcius, the temperature is equivalent to ... degrees farenheit

  45. anonymous
    • one year ago
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    all good?

  46. marcelie
    • one year ago
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    Okay . Got it !!!!!!!! Thank You. You helped me a lot

  47. anonymous
    • one year ago
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    no problem :) hope all goes well

  48. marcelie
    • one year ago
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    Enjoy ur medal :D

  49. anonymous
    • one year ago
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    ahhaha i will, gladly!

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