Help!!! Super confusing math question.?
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.
- husoskiLv 73 years agoFavorite 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.
- Some BodyLv 73 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.
- AmyLv 73 years ago
You have three points on the line:
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.
- Anonymous3 years ago
If you want our help then you're going to need to post a picture with text we can read.