Water boils at different temperatures at different elevations. The boiling temperature of water is 212 degrees * F sea level (0 feet ) but drops about 1.72 degrees * F for every 1,000 feet of elevation. Write a formula for the boiling point at a given elevation. Then solve the formula for the elevation when the boiling point for water is 190 degrees F.

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Abdulazeez10 Abdulazeez10 · Answer 1 · 2020-08-26T03:29:09+02:00

Answer:

The elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex] is 12790.70 feet

Step-by-step explanation:

Let every 1,000 feet of elevation be [tex]x[/tex]. Hence, we can write

[tex]T = 212[/tex] [tex]- 1.72x[/tex]

Where [tex]T[/tex] is the boiling temperature of water at different elevations

Now, to the determine the elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex].

We will determine [tex]x[/tex] by putting [tex]T = 190[/tex] °[tex]F[/tex].

Hence,

[tex]T = 212[/tex] [tex]- 1.72x[/tex]

[tex]190[/tex] [tex]= 212[/tex] [tex]- 1.72x[/tex]

[tex]190 - 212[/tex] [tex]= - 1.72x[/tex]

[tex]- 22[/tex] [tex]= - 1.72x[/tex]

[tex]22 = 1.72x\\x = \frac{22}{1.72} \\x = 12.79070[/tex]

Since [tex]x[/tex] represents every 1,000 feet of elevation, then the elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex]

[tex]12.79070[/tex] × [tex]1000\\[/tex] [tex]= 12790.70[/tex] feet

Hence, the elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex] is 12790.70 feet