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Question 1
14. Martha dives into a swimming pool from a diving board that is 15 feet above the water. Her initial upward velocity is 5 feet per second. The function h(t)=−16t2+5t+15
models Marthas height from the waters surface, where t represents time in seconds since she dove.(2 points)
Complete the statements.

The interpretation of h(1) is that at
1 second
, Marthas height is
4 feet
from the waters surface.

Question 2
15. 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
$50

$100
$100

$400

3 answers

Question 1

To complete the statement, we first evaluate the function \( h(t) = -16t^2 + 5t + 15 \) at \( t = 1 \):

\[ h(1) = -16(1)^2 + 5(1) + 15 \] \[ h(1) = -16 + 5 + 15 = 4 \]

So, the completed statement is:

The interpretation of \( h(1) \) is that at 1 second, Martha's height is 4 feet from the water's surface.

Question 2

The cost function for the tuxedo rental company is given by \( t(d) = 50d + 200 \).

The cost starts at $200 (the flat fee) and increases by $50 for each additional day the tuxedo is rented.

Here are some possible costs based on the number of days \( d \):

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

Thus, reasonable scales for the vertical axis considering realistic rental scenarios would be:

  • $200
  • $250
  • $300
  • $350
  • $400

Among the options provided, reasonable scales for the vertical axis that could be selected based on the cost model are:

  • $100
  • $400

While the $100 mark isn't precisely on our calculated values, it is a reasonable scale for visualization, especially in a wider range graph. Thus we could select:

Responses include:

  • $100
  • $400

If only exact multiples of $50 are desired for clearer increments, we might choose:

  • $200
  • $250
  • $300
  • $350
  • $400

If you can pick exact increments based on your model, use those that span the range of values expected based on \( d \). Ultimately, you can select whichever of the options are most relevant to your requirements.

8 of 98 of 9 Items

Question
16. Peter is building a fenced in area for his dog. He has 250 feet (ft.) of fencing to create an area for his dog. He is building it next to his house so he will only need fencing for 3 sides of the rectangular area. The diagram shows the width, d, of the area Peter is building for his dog.

The function A(d)=d(250−2d) represents the area that will be fenced in for Peter's dog, in square feet.

Complete the statements.

(2 points)
A reasonable scale for the horizontal axis of the function A(d)=d(250−2d) is
, A reasonable scale for the vertical axis of the function A(d)=d(250−2d) is

To determine reasonable scales for the horizontal and vertical axes for the function \( A(d) = d(250 - 2d) \), we need to understand the context of the problem.

Horizontal Axis (Width, \( d \))

  1. Understanding \( d \):

    • Since Peter is building a fenced area for his dog where he has 250 feet of fencing for 3 sides, \( d \) represents the width of the fenced area.
    • The length of the fenced area can be represented as \( 250 - 2d \) since he is using fencing for 3 sides (2 widths and 1 length).

  2. Finding Possible Values for \( d \):

    • The width \( d \) must be positive and restricted such that the length \( 250 - 2d \) is also positive.
    • We can set up the inequality: \[ 250 - 2d > 0 \implies d < 125 \]
    • Thus, the reasonable range for \( d \) is \( 0 < d < 125 \).

  3. Choosing a Scale:

    • For the horizontal axis, a reasonable scale might include increments, such as:
      • 0 to 125 feet, with reasonable increments (e.g., 10 ft, 20 ft, etc.).

    A possible answer could be:

    • **A reasonable scale for the horizontal axis of the function \( A(d) = d(250 - 2d) \) is ** 0 to 125 feet.

Vertical Axis (Area, \( A(d) \))

  1. Understanding \( A(d) \):

    • The area \( A(d) = d(250 - 2d) \) is a quadratic function that opens downwards since the leading coefficient of \( d^2 \) will be negative when expanded.
    • To find the maximum area, we can determine it by finding the vertex of the parabola.

  2. Finding the Maximum Area:

    • The vertex \( d \) occurs at: \[ d = -\frac{b}{2a} = -\frac{250}{-4} = 62.5 \]
    • Substituting \( d = 62.5 \) back into the area function to find the maximum area: \[ A(62.5) = 62.5(250 - 2(62.5)) = 62.5(250 - 125) = 62.5 \times 125 = 7812.5 \text{ square feet}. \]

  3. Choosing a Scale:

    • The maximum area is \( 7812.5 \) square feet, so the vertical axis should be at least up to this point.
    • A reasonable scale for the vertical axis might therefore be:
      • 0 to 8000 square feet (or more) with increments like 500 sq ft or 1000 sq ft.

    A possible answer could be:

    • **A reasonable scale for the vertical axis of the function \( A(d) = d(250 - 2d) \) is ** 0 to 8000 square feet.

Complete Statements

So, your completed statements would be:

  • A reasonable scale for the horizontal axis of the function \( A(d) = d(250 - 2d) \) is 0 to 125 feet.
  • A reasonable scale for the vertical axis of the function \( A(d) = d(250 - 2d) \) is 0 to 8000 square feet.