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    mattimeo_boyd's Avatar
    mattimeo_boyd Posts: 31, Reputation: 1
    Junior Member
     
    #1

    Apr 29, 2010, 07:09 PM
    Fahrenheit temperature as a function of Celsius temperature
    Given that the relationship between the two temperature scales is linear, use the facts that water freezes at 0 degrees C and 32 degrees F and boils at 100 degrees C and 212 degrees F to DERIVE a formula to express Fahrenheit temperature as a function of Celsius temperature. Show the derivation of the formula.

    1. 40 degrees C=____________

    2. -5 degrees C=____________

    3. 15 degrees C=____________
    ROLCAM's Avatar
    ROLCAM Posts: 1,420, Reputation: 23
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    #2

    Apr 29, 2010, 10:31 PM

    Celsius 100 degrees= fahrentite 180degrees.
    Or C 5 degrees = F 9 degrees.

    One starts at 0 and the other starts at 32. We need to adjust for this.

    1. 40 degrees C= 40* 9/5 = 72+32 = 104 F

    2. -5 degrees C= -5*9/5 = -9 +32
    =23 F

    3. 15 degrees C= 15*9/5 =27 +32
    = 59 F
    mattimeo_boyd's Avatar
    mattimeo_boyd Posts: 31, Reputation: 1
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    #3

    Apr 29, 2010, 10:37 PM

    f(c) = 5
    and
    f(c) = y

    ??
    ebaines's Avatar
    ebaines Posts: 12,132, Reputation: 1307
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    #4

    Apr 30, 2010, 06:50 AM

    You should approach this by deriving a linear equation that expresses Degrees F as a function of Degrees C. Since you are told that this is a linear equation, the general form is like this:

    F = mC + b

    where "m" is the slope of the line and "b" is the "F" intercept (the value of F when C = 0). You are told that C = 0 when F = 32, and C = 100 when F = 212, so you have two equations in two unknowns:

    (1) 212 = m x 100 + b
    (2) 32 = m x 0 + b

    You must now solve for the values of m and b. Can you take it from here?
    mattimeo_boyd's Avatar
    mattimeo_boyd Posts: 31, Reputation: 1
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    #5

    May 2, 2010, 12:30 AM

    Thanks guys I think I figured it out now.

    212-100m=b
    32=b

    212-100m=32
    -100m=-180

    m=9/5
    husenbekele's Avatar
    husenbekele Posts: 1, Reputation: 1
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    #6

    Jan 4, 2012, 12:59 AM
    Using by function degree fahreneit to degree celsius
    ebaines's Avatar
    ebaines Posts: 12,132, Reputation: 1307
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    #7

    Jan 4, 2012, 06:48 AM
    C = (5/9) x (F-32)
    Mikhail2202's Avatar
    Mikhail2202 Posts: 1, Reputation: 0
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    #8

    Mar 27, 2012, 08:03 AM
    F = A + BxC
    to find constants A and B.
    compose two equetions for boilt point and freezed point:
    220 = A + Bx100
    32 = A + Bx0
    Decision of this two equestion system:
    A = 32
    220 = 32 + Bx100
    220 -32 = Bx100
    B = (220 - 32)/100 = 1.88
    Then
    F = 32 + 1.88xC
    C = (F - 32)/1.88
    ebaines's Avatar
    ebaines Posts: 12,132, Reputation: 1307
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    #9

    Mar 27, 2012, 08:16 AM
    Mikhail2202: If you use the correct value for boiling point of water (212 degrees Fahrenheit) you will find that:

    F = 32 + 1.8C
    C = (F-32)/1.8
    Pain_11's Avatar
    Pain_11 Posts: 2, Reputation: 1
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    #10

    Jul 8, 2012, 02:40 PM
    Transform the function so that Celsius is expressed in terms of fahrenheit

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