1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sergio [31]
3 years ago
11

Kendra dives off of a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation

: h(x) = x^2 - 7x + 6, where h is the height in feet and x is the horizontal distance in feet from the diving board.
1) How high is the diving board?
2) How deep does the diver dive into the water?
3) At what horizontal distance from the board does the diver enter the water?
4) At what horizontal distance from the board does the diver come to the surface of the water after the dive?
Mathematics
2 answers:
il63 [147K]3 years ago
7 0

Answer:

<em />

  • <em>1) How high is the diving board?:</em> <u>    6 feet above the water surface</u>

  • <em>2) How deep does the diver dive into the water?:</em>   <u>   6.5feet into the water</u>

<em />

  • <em>3) At what horizontal distance from the board does the diver enter the water?</em> <u>        1 feet from the board</u>

  • <em>4) At what horizontal distance from the board does the diver come to the surface of the water after the dive?</em> <u>      6 feet from the board</u>

Explanation:

The dive is modeled by the equation<em> h(x) = x² - 7x + 6.</em>

Two important features that you must notice quickly are:

  • That is a quadratic function, which is a parabola.

  • Since the leading term, x², is positive, the parabola open upwards, and the vertex is a minimum.

As for the questions:

<em>1) How high is the diving board?</em>

The diving board is the place from which Kendra dives off. At this point, the horizontal distance, x, from the diving board is 0.

Then, the height will be given by h(x) with x = 0. Substitute into the equation and compute:

  • h(0) = 0² - 7(0) + 6
  • h(0) = 0 - 0 + 6
  • h(0) = 6

Therefore, the diving board is 6 feet above the water surface.

<em><u>2) How deep does the diver dive into the water?</u></em>

This is the minimum heigth given by the function h(x).

As explained above, this is the vertex of the parabola.

You can find the x-coordinate of the vertex with the equation:

  • x-coordinate of the vertex = -b/(2a)

Where b and a are the coefficients of the linear term and the quadratic terms in the equation for h(x), respetively:

  • a = 1
  • b = -7

  • x-coordinate = - (-7) / (2 × 1) = 7/2 = 3.5

Now you can find h(x) for x = 3.5

  • h(3.5) = (3.5)² - 7(3.5) + 6 = 12.25 - 24.5 + 6 = - 6.25

That is 6.25 feet below the water surface.

<u><em>3) At what horizontal distance from the board does the diver enter the water?</em></u>

That is the x-intercept of the function. This is, the value of x when h(x) = 0.

Thus, solve the equation 0 = x² - 7x + 6.

You can factor the equation:

  • Find two numbers that add up -7  and their product is +6. Those are - 6 and -1:

  • 0 = (x - 1) (x - 6)

Using the zero product property:

  • (x - 1) = 0 or (x - 6) = 0
  • x = 1 or x = 6

Thus, you have two solutions, which are the two x-intercepts of the funtion.

  • x = 1 represents the horizontal distance from the board where the diver enters the water.

The other solution is the answer to the next question.

<u><em>4) At what horizontal distance from the board does the diver come to the surface of the water after the dive?</em></u>

<u><em></em></u>

As explained above, the equation has two x-intercepts. They both are the points where the parabola crosses the x-axis, which is when the height, h(x) is 0. That height is the surface of the water level.

The first x-intercept is the point (horizontal distant from the board) where the diver enters the water, such as asserted above.

The other x-intercept is where the diver comes to the surface of water after the dive and after being submerged in the water: the diver enters the water, dives 6.5feet into the water, and returns to the surface.

Thus, this is the solution x = 6 for h(x) = 0.

Hence, Kendra comes to the surface of water  at 6 feet from the board.

klemol [59]3 years ago
4 0

Answer:

Answers Below!

Step-by-step explanation:

1) How high is the diving board?:    6 feet above the water surface

2) How deep does the diver dive into the water?:     6.5feet into the water

3) At what horizontal distance from the board does the diver enter the water?        1 feet from the board

4) At what horizontal distance from the board does the diver come to the surface of the water after the dive?      6 feet from the board

<u>I got them right on my test for my seconds semester.</u>

You might be interested in
I need help with geometry
Ad libitum [116K]
Same, i need help with geometry too :(
8 0
3 years ago
Find the volume of the cylinder.
Aneli [31]

Answer:

144π or 452.16 units³

Step-by-step explanation:

The formula for volume of a cylinder is \pi r^2 h. We can use the given values for radius and height to find the volume of the cylinder.

<h3>Finding the Volume</h3>

V=\pi r^2 h\\V=\pi6^2(4)\\V=\pi36(4)\\V=144\pi \ OR\ 452.16

The volume of the cylinder is 144π or 452.16 units³.

4 0
2 years ago
Can someone help last one :((
vovangra [49]

Answer:

40.49cm²

Step-by-step explanation:

I hope it helps

8 0
2 years ago
Elena is making greeting cards, which she will sell by the box at an arts fair. She paid $54 for
TiliK225 [7]

Answer:

Elena's sales and expenses will both be $

396

if she sells

36

boxes of cards.

Step-by-step explanation:

7 0
3 years ago
F(x) = x2 + 2x - 2<br> Show graph
Alexandra [31]

Answer:

Step-by-step explanation:

f(x) = x2 + 2x - 2  should be rewritten using " ^ " to indicate exponentiation:

f(x) = x^2 + 2x - 2.

We find a couple of key points and use the fact that this parabola is symmetric about the line

          -2

x = ----------- = -1.  When x = -1, y = f(-1) = (-1)^2 + 2(-1) - 2, or 1 - 2 -2, or -3.

        2(1)

Thus the vertex is at (-1, -3).  The y-intercept is found by letting x = 0:  y = -2.  The axis of symmetry is x = -1.

Graph x = -1 and then reflect this y-intercept (0, -2) about the line x = -1, obtaining (-2, -2).  If necessary, find 1 or two more points (such as the x-intercepts).

To find the roots (x-intercepts), set f(x) = x^2 + 2x - 2 = 0 and solve for x.

Completing the square, we obtain x^2 + 2x + 1 - 2 = + 1, or (x + 1)^2 = 3.

Taking the square root of both sides yields x + 1 = ±√3.  One of the two roots is x = 1.732 - 1, or 0.732, so one of the two x-intercepts is (0.732, 0).

6 0
3 years ago
Other questions:
  • A person flipped a coin 100 times and obtained 73 heads. Can the person conclude that the coin was unbalanced?
    15·2 answers
  • F(x) = x2 + 3x<br> g(x) = 2x – 5<br><br> Find f (x) + g(x)
    12·1 answer
  • Which three-dimensional figure will this net make?
    5·1 answer
  • 2 Ella, James, and Ray's grandmother gave them $24 to divide equally. They spent the
    6·1 answer
  • Ava is 23 cm Taller than olivia, and olivia is half the height of lucas. if Lukas is 1.78 meters tall how tall are ava and Olivi
    14·1 answer
  • Please help this is due tuesday
    7·1 answer
  • Solve: y+8=2=?<br><br> Please explain or put how did you get the answer. Ty
    15·2 answers
  • Last year the robotics club had 30 members. This year the club has 24 members. Find the percent change in the number of members.
    7·2 answers
  • an area of a rectangle city park is 1556 square miles the width of the park is 3/7 miles what is the length in miles of the park
    6·1 answer
  • What is the value of 80-5(x^2-y)+y when x=4 and y=6
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!