Question

this question has two parts. first, answer part a. then, answer part b.
part a
in 2012, james cameron descended to the bottom of challenger deep in the marianas trench, the deepest point in the ocean. the vessel he rode in was called deepsea challenger. challenger deep is 35,814 feet deep at its lowest point.
deepsea challenger’s descent was a change in depth of (-4) feet per second. we can use the equation ( y = -4x ) to model this relationship, where ( y ) is the depth and ( x ) is the time in seconds that have passed. how many seconds does this model suggest it would take for deepsea challenger to reach the bottom?
( 8953.5 ) seconds
to end the mission deepsea challenger made a one - hour ascent to the surface. how many seconds is this?
( 3600 ) seconds
part b
the ascent can be modeled by a different proportional relationship ( y = kx ). what is the value of ( k ) in this case?

Explanation:

Part A

Step 1: Understand the equation

The depth \( y \) is modeled by \( y = - 4x \), where \( y \) is the depth (in feet) and \( x \) is the time (in seconds). We know the total depth \( y=- 35814\) (negative because it's a descent).

Step 2: Solve for \( x \)

We set \( y=-35814\) in the equation \( y = - 4x \). So, we have the equation \(-35814=-4x\). To solve for \( x \), we divide both sides of the equation by \(- 4\):
\(x=\frac{-35814}{-4}=\frac{35814}{4} = 8953.5\)

Step 1: Understand the ascent model

The ascent is modeled by \( y = kx \), where \( y \) is the depth (in feet) and \( x \) is the time (in seconds). The total depth to ascend is \( y = 35814\) feet (positive because it's an ascent), and the time for the ascent is 1 hour. First, we convert 1 hour to seconds. Since 1 hour \(=60\) minutes and 1 minute \( = 60\) seconds, 1 hour \(=60\times60 = 3600\) seconds.

Step 2: Solve for \( k \)

We know that when \( x = 3600\) seconds, \( y=35814\) feet. Substitute these values into the equation \( y=kx\):
\(35814=k\times3600\)
To find \( k \), we divide both sides by \( 3600\):
\(k=\frac{35814}{3600}=\frac{35814\div6}{3600\div6}=\frac{5969}{600}\approx9.9483\) (or we can simplify the fraction as \(k = \frac{5969}{600}\))

Answer:

\( 8953.5 \)

Part B