The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8100 ft, the liquid boils at 20

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The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8100 ft, the liquid boils at 20

1.28°F. At an altitude of 4300 ft, the liquid boils at 205.84°F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2200 ft?
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Mathematics

1 answer:

Zinaida [17] · Answer 1 · 2022-10-01T17:19:44+03:00

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Answer:

b = -0.0012a +211

208.36 °F at 2200 ft

Step-by-step explanation:

We are given two points:

(a, b) = (8100, 201.28) and (4300, 205.84)

The slope of the desired line can be found using the slope formula:

m = (y2 -y1)/(x2 -x1)

m = (205.84 -201.28)/(4300 -8100) = 4.56/-3800 = -0.0012

The "y-intercept" of the function can be found from ...

y-intercept = b -ma

y-intercept = 201.28 -(-0.0012)(8100) = 211.00

So, the function of interest is ...

b = -0.0012a +211

__

At 2200 ft, the boiling point is ...

b = -0.0012×2200 +211 = -2.64 +211 = 208.36

The boiling point of the liquid at 2200 ft is 208.36 °F.