Help!!! Super confusing math question.?

Update:

a. Given that 1°C is 33.8°F (or t1 = 33.8) and d = 1.8, write out the general formula, tn , that

represents the relationship between degrees Fahrenheit and degrees Celsius. Be sure to define the variables

b. Given two points on the graph, the freezing point of water at 0°C or 32°F and the boiling

point of water at 100°C or 212°F, calculate the slope of the line. Explain how this value

relates to the general formula found in part a.

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4 Answers

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  • 3 years ago
    Favorite Answer

    The value d=1.8 is probably intended to be in a formula such as:

    (f - 33.8) = (c - 1.0) * d

    ...where f is a temperature in Fahrenheit units and c is the same temperature in Celsius units. In this form, d represents the change in F temperature corresponding to a 1 degree C change.

    That's a totally weird point to use as a point of origin. The almost universal choice is to define 32F = 0C = freezing/melting point of water at a standard 1 atm pressure.

    Two other good choices are:

    212F = 100C .... boiling point of water at 1atm. pressure

    -40F = -40C .... the temperature at which both scales give the same numerical value

    If you rewrite the formula above, you can get:

    f = dc + (31.8 - d)

    ... so that the graph of f vs. d is a straight line, d is the slope of that line and (31.8 - d) is the intercept.

    It's the melting and boiling point temperatures that are normally used to find both slope and intercept for that line, though. The conversion from C to F is *defined* to be linear (so that temperature differences are proportional) and that line is defined to contain those two (c,f) points: (0, 32) and (100, 212).

    The slope of that line is (212 - 32)/(100 - 0) = 180/100 = 9/5, or 1.8 as a decimal fraction.

  • 3 years ago

    An arithmetic sequence is defined as:

    aₙ = a₁ + (n - 1) d

    Given that t₁ = 33.8 and d = 1.8:

    tₙ = 33.8 + 1.8 (n - 1)

    Here, n is the temperature in Celsius and tₙ is the temperature in Fahrenheit.

    To find the slope between (0, 32) and (100, 212), just use the slope formula:

    m = Δy / Δx

    I think you can take it from there.

  • Amy
    Lv 7
    3 years ago

    You have three points on the line:

    (0, 32)

    (1, 33.8)

    (100, 212)

    Write the equation of the line that goes through these points.

    You only need two points to define a line, so the second question is asking you to solve it again and make sure you get the same answer.

  • Anonymous
    3 years ago

    If you want our help then you're going to need to post a picture with text we can read.

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