The temperature at which water starts to boil is called its boiling point and is

Question

The temperature at which water starts to boil is called its boiling point and is linearly related to the altitude. Water boils at 212 degree F at sea level and at I93.6 degree F at an altitude of 10.000 feet. Find a relationship of the form T = mx + b where T is degrees Fahrenheit and x is altitude in thousands of feet. Find the boiling point at an altitude of 3,600 feet. Find the altitude if the boiling point is 195.5 degree F. Graph T and illustrate the answers to (b) and (c) on the graph. Choose the correct relationship below. T = -1.84x + 212 T = 1.84x - 212 T = 1.84x + 212 T = - 1.84x - 212 The boiling point at an altitude of 3,600 feet is degree F. (Round to two decimal places as needed.) The altitude at which the boiling point isl95.5 degree F is feet. (Round to the nearest whole number as needed.) Graph T. Choose the correct graph below.

Explanation / Answer

Here we have two related points in ordered pair form (x,T) are (0,212)) and (10000,193.6). Now here as with the decrease in temperature, altitude is increaseing that means such line a negative slope and thus the required line will be of form T= -1.84x + b where b is y intercept,

Now as it passes from point (212,0) so on plug in x=0 and T= 212

212= -1.84(0)+b

or b= 212

so required line is T= -1.84x+ 212

so answer of part a) is option A.

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Now for part b), for 3600, x = 3.6, then

T = -1.84(3.6) + 212 = - 6.624 +212 = 205.38

so required temperature is 205.38 degree F. This is the answer of part b)

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Now for part C) when T= 195.5

so 195.5= -1.84x + 212

on subtracting 212 each side,

-1.84x = 195.5 - 212= - 16.5

or x= 16.5/1.84= 8.9674

so required altitude = 8.9674 x 1000 = 8967 feet

This is the answer of part C)

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And two points stated above (0,212) and (10,193.6) are clearly shown in graph, shown in option B only.

So correct graph is in option B. This is the answer of part d)

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