marcelie
  • marcelie
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).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
so you have two data points right?
marcelie
  • marcelie
i think so
anonymous
  • anonymous
(0,32) and (100,212)

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anonymous
  • anonymous
since we have two points, we can always create a straight line.
marcelie
  • marcelie
so then i use the slope of the line ?
anonymous
  • 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
anonymous
  • anonymous
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anonymous
  • anonymous
we already know the intercept right? F=32? since C=0
anonymous
  • anonymous
hence F=mC+32 what is the other point we know? Substitute that point into the equation to solve for m
marcelie
  • marcelie
so my linear equation will be y= 1.8x +32 ?
anonymous
  • 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
anonymous
  • anonymous
well done
anonymous
  • anonymous
so now, what is the rate of change of Fahrenheit? it is the differential with respect to time right?
marcelie
  • marcelie
so when it says rate of time is there a formula for it ?
marcelie
  • marcelie
So this is what i came up with my answers a, ? b. f(28) = 82.4 c. f(-40)=-40
anonymous
  • 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
anonymous
  • anonymous
for a. we differentiate that equation with respect to time. \[F=1.8C+32\] \[\frac{ d }{ dt }\left( F \right)=\frac{ d }{ dt }\left( 1.8C+32 \right)\] \[\frac{ dF }{ dt}=1.8\frac{ dC }{ dt }\]
anonymous
  • anonymous
the differentiation of a constant is always zero. remember.
marcelie
  • marcelie
so is that a formula ?
anonymous
  • anonymous
yep
anonymous
  • anonymous
that is the rate of change of farenheit temperautre
marcelie
  • marcelie
okay. so what do i plug in to it ?
anonymous
  • anonymous
hmm. maybe what i did was a bit too complex for you at this level.
marcelie
  • marcelie
yes. lol i am taking pre cal. so i thinks its calculus lol
anonymous
  • anonymous
ah right.
anonymous
  • anonymous
perhaps that is simply the slope they are looking for?
marcelie
  • marcelie
so for a its f = 1.8c +32 ? or do i have to solve it more?
anonymous
  • anonymous
well 'for each unit change in celcius temp, means we should plug in c=1,2,3,...etc right?
anonymous
  • anonymous
thats simple what a unit change means
anonymous
  • anonymous
have you learnt what a derivative is or not?
marcelie
  • marcelie
okay. so once i plug in those numbers whats the next step is ? I dont think so.
anonymous
  • 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.. :/
marcelie
  • marcelie
hmmm. so should i leave the answer as f= 1.8c+32 ?
anonymous
  • anonymous
thats the answer for the questions: 'Express the Fahrenheit temperature as a linear function of C, the Celsius temperature, F(C).'
anonymous
  • anonymous
but yea, not 100% sure what a wants us to find out sicne you are doing pre-calc
marcelie
  • marcelie
hmmm. how would u solve it ?
anonymous
  • anonymous
\[\frac{ dF }{ dt}=1.8\frac{ dC }{ dt }\]
marcelie
  • marcelie
okay. so what do i plug in for df /dt = 1.8 dc/dt
anonymous
  • anonymous
nothing. that is just a general from on how to write functions with respect to time, i.e rates of change
anonymous
  • anonymous
you don't have enough info to find the rate
marcelie
  • marcelie
ah okay.
marcelie
  • marcelie
for letter b the wording is the same but the number changes right ?
marcelie
  • marcelie
i mean for letter c.
anonymous
  • anonymous
yep so at -40 degrees celcius, the temperature is equivalent to ... degrees farenheit
anonymous
  • anonymous
all good?
marcelie
  • marcelie
Okay . Got it !!!!!!!! Thank You. You helped me a lot
anonymous
  • anonymous
no problem :) hope all goes well
marcelie
  • marcelie
Enjoy ur medal :D
anonymous
  • anonymous
ahhaha i will, gladly!

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