Question

water boils at different temperatures at different elevations. the boiling temperature of water is 212°f at sea level (0 feet) but drops about 1.72°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°f. determine a formula for the boiling point b, in degrees fahrenheit, at elevation h, in feet. (type an equation. simplify your answer. do not include the degree symbol in your answer.)

Explanation:

Step1: Identify the linear - relationship components

The initial boiling point at sea - level is 212. The rate of change is - 1.72 per 1000 feet of elevation. Let $h$ be the elevation in feet and $b$ be the boiling point. The general form of a linear equation is $y = mx + c$, where $m$ is the slope and $c$ is the y - intercept. Here, $m=-\frac{1.72}{1000}$ and $c = 212$. So the formula for the boiling point $b$ in terms of elevation $h$ is $b=212-\frac{1.72h}{1000}$.

Step2: Solve for $h$ when $b = 190$

First, substitute $b = 190$ into the equation:
$190=212-\frac{1.72h}{1000}$
Then, rearrange the equation to solve for $h$.
Subtract 212 from both sides:
$190 - 212=-\frac{1.72h}{1000}$
$- 22=-\frac{1.72h}{1000}$
Multiply both sides by - 1:
$22=\frac{1.72h}{1000}$
Multiply both sides by 1000:
$22\times1000 = 1.72h$
$22000 = 1.72h$
Divide both sides by 1.72:
$h=\frac{22000}{1.72}\approx12790.7$

Answer:

The formula for the boiling point is $b = 212-\frac{1.72h}{1000}$. The elevation when the boiling point is 190°F is approximately 12790.7 feet.