Question

c. it took the trieste 3 hours to ascend back to sea level. this can be modeled by a different relationship ( y = kx ). what is the value of ( k ) in this situation?

1. the design of the trieste was based on the design of a hot air balloon built by auguste piccard, jacques’s father. in 1932, auguste rode in his hot - air balloon up to a record - breaking height.

a. augustes ascent took 7 hours and went up 51,683 feet. write a relationship ( y = kx ) to represent his ascent from his starting location.

b. auguste’s descent took 3 hours and went down 52,940 feet. write another relationship to represent his descent.

c. did auguste piccard end up at a greater or lesser altitude than his starting point? how much higher or lower?

Explanation:

Step1: Solve 2a: Find k for ascent

We know $y = 51683$ (total height), $x = 7$ (hours). Rearrange $y=kx$ to $k=\frac{y}{x}$.
$k = \frac{51683}{7} = 7383$
The relationship is $y = 7383x$.

Step2: Solve 2b: Find k for descent

We know $y = -52940$ (negative for descent), $x = 3$ (hours). Rearrange $y=kx$ to $k=\frac{y}{x}$.
$k = \frac{-52940}{3} \approx -17646.67$
The relationship is $y = -\frac{52940}{3}x$ or $y \approx -17646.67x$.

Step3: Solve 2c: Compare net altitude

Calculate net change: Total ascent + total descent.
$\text{Net change} = 51683 + (-52940) = 51683 - 52940 = -1257$

Answer:

2a. $y = 7383x$
2b. $y = -\frac{52940}{3}x$ (or $y \approx -17646.67x$)
2c. He ended up at a lesser altitude than his starting point, 1257 feet lower.