QuestionFor skydivers, it is recommended that the parachute is opened by the time they reach an altitude of 2900 ft . Once a parachute opens, skydivers fall at approximately $22 \mathrm{ft} / \mathrm{sec}^{2}$ .Assuming the chute opens at 2900 ft , the height in feet of a skydiver can be modeled by the function $H(x)=2900-22 x$ , where $x$ is the number of seconds after the chute opens.
Find the $x$ intercept and explain what it means in the context of this problem.
Part: $0 / 2$
Part 1 of 2
The $x$ intercept is $\square$ . Round to the nearest tenth if necessary. (Write your answer as an ordered pair. Select "None if applicable.)

Studdy Solution

STEP 1

1. The function $H(x) = 2900 - 22x$ represents the height of a skydiver after the parachute opens.
2. The $x$ -intercept occurs when the height $H(x)$ is zero, meaning the skydiver has reached the ground.

STEP 2

1. Set the height function equal to zero to find the $x$ -intercept.
2. Solve for $x$ .
3. Interpret the $x$ -intercept in the context of the problem.

STEP 3

Set the height function equal to zero to find the $x$ -intercept:
$H(x) = 2900 - 22x = 0$

STEP 4

Solve for $x$ :
$2900 - 22x = 0$
Add $22x$ to both sides:
$2900 = 22x$
Divide both sides by 22:
$x = \frac{2900}{22}$
Calculate the value:
$x \approx 131.8$

STEP 5

Interpret the $x$ -intercept in the context of the problem:
The $x$ -intercept $(131.8, 0)$ indicates that it takes approximately 131.8 seconds for the skydiver to reach the ground after the parachute opens.
The $x$ -intercept is $(131.8, 0)$ .

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