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The function V(r)=10πr2

represents the volume of a cylinder that is 10 inches high with a radius of r. Which is the correct interpretation for the function notation V(3)=90π
?(1 point)
Responses

The volume of the cylinder is 3 when the radius is 90π
.
The volume of the cylinder is 3 when the radius is 90 pi .

The volume of the cylinder is 90π
when the radius is 3.
The volume of the cylinder is 90 pi when the radius is 3.

A radius of 3 gives the value 90.
A radius of 3 gives the value 90.

A cylinder of 90π
is produced from a radius of 3.

7 answers

The correct interpretation of the function notation \( V(3) = 90\pi \) is:

The volume of the cylinder is \( 90\pi \) when the radius is 3.

This response directly relates to the function \( V(r) = 10\pi r^2 \), where substituting \( r = 3 \) gives the volume of the cylinder when the radius is 3 inches.

Monique is punting a football and the height the ball travels is a function of time. The function h(s)=−s2+10s+3
gives the height of the ball, h(s)
, given the number of seconds, s
, that the ball has been in the air. After flying through the air for 7.5 seconds, what is the height of the ball? Find h(7.5)
.(1 point)
Responses

134.25
134.25

24
24

21.5
21.5

21.75

To find the height of the ball after 7.5 seconds, we need to evaluate the function \( h(s) = -s^2 + 10s + 3 \) at \( s = 7.5 \).

Substituting \( s = 7.5 \) into the function:

\[ h(7.5) = -(7.5)^2 + 10(7.5) + 3 \]

Calculating \( (7.5)^2 \):

\[ (7.5)^2 = 56.25 \]

Now plugging that into the equation:

\[ h(7.5) = -56.25 + 75 + 3 \]

Calculating further:

\[ h(7.5) = -56.25 + 75 + 3 = -56.25 + 78 = 21.75 \]

The height of the ball after 7.5 seconds is \( \boxed{21.75} \).

Use the table to answer the question.

Years, x Value of Car, f(x)
1 29, 750.00
2 25, 287.50
3 21, 494.38
4 18, 270.22
5 ?
A car decreases in value after a given number of years. The following function represents the value of the car in dollars with respect to its age, x, in years: f(x)=35,000(.85)x
. Use the input-output table to determine the value of the car after 5 years. Round your answer to the nearest cent.

(1 point)
Rounded to the nearest cent, after 5 years, the value of the car will equal $
.
Remaining Attempts : 3

To find the value of the car after 5 years using the function \( f(x) = 35,000(0.85)^x \), we need to substitute \( x = 5 \) into the function.

Calculating \( f(5) \):

\[ f(5) = 35,000(0.85)^5 \]

First, calculate \( (0.85)^5 \):

\[ (0.85)^5 \approx 0.4437053125 \]

Now substitute this back into the equation:

\[ f(5) = 35,000 \times 0.4437053125 \]

Calculating that gives:

\[ f(5) \approx 35,000 \times 0.4437053125 \approx 15,029.64 \]

Therefore, rounded to the nearest cent, the value of the car after 5 years will equal $15,029.64.

Use the image to answer the question.

A line graph is shown, starting at the origin and continues off the graph. The x axis is labeled Minutes, and ranges from 0 to 25 in increments of 5. The y axis is labeled Miles, and ranges from 0 to 10 in increments of 5.

Based on the graph of the function, what value will correctly complete the sentence?

(1 point)
Josie can run two miles in
minutes.

To answer the question, I would need to see the line graph you are referring to, specifically the point where Josie's running distance reaches two miles.

However, I can guide you on how to identify this value:

  1. Look at the y-axis, which represents the distance in miles. Find the point that corresponds to 2 miles on that axis.
  2. Move horizontally from that point to the line graph.
  3. From the intersection of the line graph and your horizontal line, drop straight down to the x-axis, which represents the time in minutes.
  4. Read off the value on the x-axis directly below the intersection.

Once you find the minute value at the point where Josie's distance is 2 miles, you can fill in the sentence accordingly.

If you are able to describe the graph or provide the coordinates for the point where she reaches two miles, I would be able to assist further!