. A soccer player kicks a ball with an initial velocity of 38 feet every second. The function f(x)=−16x2+38x

Question

can be used to model the time the ball is in the air.
What is the meaning of the origin for this situation?(1 point)

Answer 1

In the context of the function \( f(x) = -16x^2 + 38x \), which models the height of the soccer ball over time when kicked with an initial velocity of 38 feet per second, the origin (0, 0) has a specific meaning.

At the origin, \( x = 0 \) and \( f(0) = 0 \). This means that at time \( x = 0 \) seconds (the moment the soccer player kicks the ball), the height (or position) of the ball is 0 feet, which indicates that the ball is at ground level (or at the height of the player's foot before being kicked).

Therefore, the origin represents the initial moment when the ball is kicked and confirms that it is starting from the ground level.

Answer 2

A tuxedo rental company charges a flat fee of $200 plus a $50 per day fee to rent one of their tuxedos. The function that models the cost to rent a tuxedo is t(d)=50d+200, where d represents the number of days in which the tuxedo is rented and t represents the total cost of the rental.
Select all reasonable scales for the vertical axis.(3 points)
Responses

$1
$1

$5
$5

$25
$25

$50

Answer 3

To determine reasonable scales for the vertical axis when modeling the cost to rent a tuxedo using the function \( t(d) = 50d + 200 \), we should consider the possible costs.

1. Flat Fee: The base cost is $200.
2. Daily Fee: The cost increases by $50 for each additional day.

Let's calculate some example costs for a few different values of \( d \) (number of days):

• For \( d = 0 \): \( t(0) = 50(0) + 200 = 200 \)
• For \( d = 1 \): \( t(1) = 50(1) + 200 = 250 \)
• For \( d = 2 \): \( t(2) = 50(2) + 200 = 300 \)
• For \( d = 3 \): \( t(3) = 50(3) + 200 = 350 \)
• For \( d = 4 \): \( t(4) = 50(4) + 200 = 400 \)

Based on this, the total cost for renting a tuxedo can start at $200 and increase in increments of $50 for each additional day.

Now, considering the options provided:

• $1: This scale is too small, as costs start at $200.
• $5: This scale is also too small for the same reason.
• $25: This could be reasonable for small increments, but it still may not align perfectly with the fees (which increase by $50).
• $50: This scale is reasonable as it aligns with the daily increase and provides clear visual increments reflecting the costs.

Based on this analysis, the only reasonable scale for the vertical axis is:

• $50

In practical applications, using increments of $50 will allow for clear visualization of the rental costs as they increase from the starting price.