... 8600 ft, the liquid boils at 196.55 degrees Fahrenheit. At an altitude of 4200 ft, the liquid boils at 203.86 degrees fahrenheit. Write an equation giving the boiling point b of the liquid l, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of liquid at 2600 ft?
The relationship between altitude and the boiling point of a liquid is linear. At an altitude of?
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- 3+ months ago by Jmitchell...
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- liquid, boiling, point, geometry, degrees, write, altitude, linear, quick, relationship, math, degree, mathematics, mathematician, help, algebra, relationships
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Answers (1)
Imagine a Cartesian Coordinate System with altitude A in ft on the x-axis and boiling point B in °F on the y-axis:
B/°F
↑
→ A/ft
There are two points given:
____ A _ | __ B __
P1 (4200 | 203.86)
P2 (8600 | 196.55)
The relationship between altitude and the boiling point of a liquid is linear. Thus we have to build a linear function with the structure:
y = m * x + c
where m is the slope and c signifies the y-intercept.
Firstly, we will calculate the slope of that linear function using the formula:
m = (y2 - y1) / (x1 - x2)
m = (196.55 - 203.86) / (8600 - 4200)
m = -7.31 / 4400 = -0.00166136(36...)
Secondly we'll have to determine the y-intercept c using m and inserting the values (x1|y1) and (x2|y2) respectively:
-c = m * x - y
-c = -0.00166136(36...) * 4200 - 203.86 = -210.837(72...)
or with the values of the other point:
-c = -0.00166136(36...) * 8600 - 196.55 = -210.837(72...)
Thus:
c = 210.837(72...)
Hence, the sought-for equation is:
B = -0.00166136(36...) * A + 210.837(72...)
(I put the repetend in parenthesis. The ellipses indicate the infinite repeat.)
Inserting the 3rd given altitude will yield the corresponding boiling temperature:
B = -0.00166136(36...) * 2600 + 210.837(72...) = 206,51818181818181817(45...)
You should cut the decimals to a reasonable degree of accuracy, though:
At an altitude of 2600 ft the liquid will boil at approx. 206.52°F.
Sorry, some TYPOS have accidentally SNEAKED into my answer. HERE is the
CORRECTED VERSION:
Imagine a Cartesian Coordinate System with altitude A in ft on the x-axis and boiling point B in °F on the y-axis:
B/°F
↑
→ A/ft
There are two points given:
____ A _ | __ B __
P1 (4200 | 203.86)
P2 (8600 | 196.55)
The relationship between altitude and the boiling point of a liquid is linear. Thus we have to build a linear function with the structure:
y = m * x + c
where m is the slope and c signifies the y-intercept.
Firstly, we will calculate the slope of that linear function using the formula:
m = (y2 - y1) / (x2 - x1)
m = (196.55 - 203.86) / (8600 - 4200)
m = -7.31 / 4400 = -0.00166136(36...)
Secondly we'll have to determine the y-intercept c using m and inserting the values (x1|y1) and (x2|y2) respectively:
-c = m * x - y
-c = -0.00166136(36...) * 4200 - 203.86 = -210.837(72...)
or with the values of the other point:
-c = -0.00166136(36...) * 8600 - 196.55 = -210.837(72...)
Thus:
c = 210.837(72...)
Hence, the sought-for equation is:
B = -0.00166136(36...) * A + 210.837(72...)
(I put the repetend in parentheses. The ellipses indicate the infinite repeat.)
Inserting the 3rd given altitude will yield the corresponding boiling temperature:
B = -0.00166136(36...) * 2600 + 210.837(72...) = 206,51818181818181817(45...)
You should cut the decimals to a reasonable degree of accuracy, though:
At an altitude of 2600 ft the liquid will boil at approx. 206.52°F.