## 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).

1. anonymous

so you have two data points right?

2. marcelie

i think so

3. anonymous

(0,32) and (100,212)

4. anonymous

since we have two points, we can always create a straight line.

5. marcelie

so then i use the slope of the line ?

6. anonymous

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

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8. anonymous

we already know the intercept right? F=32? since C=0

9. anonymous

hence F=mC+32 what is the other point we know? Substitute that point into the equation to solve for m

10. marcelie

so my linear equation will be y= 1.8x +32 ?

11. anonymous

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

well done

13. anonymous

so now, what is the rate of change of Fahrenheit? it is the differential with respect to time right?

14. marcelie

so when it says rate of time is there a formula for it ?

15. marcelie

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

16. anonymous

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

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

the differentiation of a constant is always zero. remember.

19. marcelie

so is that a formula ?

20. anonymous

yep

21. anonymous

that is the rate of change of farenheit temperautre

22. marcelie

okay. so what do i plug in to it ?

23. anonymous

hmm. maybe what i did was a bit too complex for you at this level.

24. marcelie

yes. lol i am taking pre cal. so i thinks its calculus lol

25. anonymous

ah right.

26. anonymous

perhaps that is simply the slope they are looking for?

27. marcelie

so for a its f = 1.8c +32 ? or do i have to solve it more?

28. anonymous

well 'for each unit change in celcius temp, means we should plug in c=1,2,3,...etc right?

29. anonymous

thats simple what a unit change means

30. anonymous

have you learnt what a derivative is or not?

31. marcelie

okay. so once i plug in those numbers whats the next step is ? I dont think so.

32. anonymous

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

hmmm. so should i leave the answer as f= 1.8c+32 ?

34. anonymous

thats the answer for the questions: 'Express the Fahrenheit temperature as a linear function of C, the Celsius temperature, F(C).'

35. anonymous

but yea, not 100% sure what a wants us to find out sicne you are doing pre-calc

36. marcelie

hmmm. how would u solve it ?

37. anonymous

$\frac{ dF }{ dt}=1.8\frac{ dC }{ dt }$

38. marcelie

okay. so what do i plug in for df /dt = 1.8 dc/dt

39. anonymous

nothing. that is just a general from on how to write functions with respect to time, i.e rates of change

40. anonymous

you don't have enough info to find the rate

41. marcelie

ah okay.

42. marcelie

for letter b the wording is the same but the number changes right ?

43. marcelie

i mean for letter c.

44. anonymous

yep so at -40 degrees celcius, the temperature is equivalent to ... degrees farenheit

45. anonymous

all good?

46. marcelie

Okay . Got it !!!!!!!! Thank You. You helped me a lot

47. anonymous

no problem :) hope all goes well

48. marcelie

Enjoy ur medal :D

49. anonymous