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
andrey2020 [161]
2 years ago
13

When a sprinkler is installed in the ground, the spray of water goes up and falls in the pattern of a parabola. The height, in i

nches, of a spray of water is given by the equation h(x)=160x−16x2 where x is the number of feet away from the sprinkler head the spray is. What is the height of the spray 2 feet away from the sprinkler head?

Mathematics
1 answer:
Westkost [7]2 years ago
7 0

Answer:

(1) 256 inches

(2) 5 feet

(3) 400 inches

(4) 10 feet

Step-by-step explanation:

(1) The function that gives the height in inches of the spray of water at a distance <em>x</em> from the sprinkler head is given as follows;

h(x) = 160·x - 16·x²

At x = 2 feet, we have;

h(2) = 160 × 2 - 16 × 2² = 256

Therefore, the height of the spray water at a horizontal distance of 2 feet from the sprinkler head h(2) = 256 inches

(2) The x-coordinate, x_{max}, of the maximum point of a parabola given in the form, y = a·x² + b·x + c is found using the following formula;

x_{max} = -b/(2·a)

The x-coordinate, x_{max}, of the maximum point of the given equation of the parabola, h(x) = 160·x - 16·x², (a = -16, b = 160) is therefore;

x_{max} = -160/(2 × (-16)) = 5

Therefore, the number of feet along the way, the function will reach maximum height, x_{max} = 5 feet

(3) The function, h(x) = 160·x - 16·x², will reach maximum height, h_{max}, at x = 5, therefore;

h_{max} =  h(5) = 160 × 5 - 16 × 5² = 400

The maximum height of the spray, h_{max} = 400 inches

(4) The water is at ground level where h(x) = 0, therefore;

At ground level, h(x) = 0 = 160·x - 16·x²

160·x - 16·x² = 0

∴ 16·x × (10 - x) = 0

By zero product rule, we 16·x = 0, or (10 - x)  = 0, from which we have;

x = 0, or x = 10

The water is at ground level at x = 0 and x = 10 feet, therefore, the water will hit the ground again (the second time after leaving the sprinkler head at x = 0) at x = 10 feet.

You might be interested in
Eleanor deposits 20% of the money that she earns each week in a savings account. If Eleanor earns $85 each week, how much money
RoseWind [281]

Answer:

She will deposit $17.

Step-by-step explanation:

So this is really simple.

20% of $85= 0.20•85= 17=$17

5 0
2 years ago
Read 2 more answers
5+ 3x - 37 = 6x + 23 - 8x what is the value for x
iris [78.8K]

Answer:

The value of X is 11

X=11

Step-by-step explanation:

Isolate the variable by dividing each side by the factors that don't contain the cariable.

4 0
2 years ago
Im only have 10 minutes please. Is math​
alukav5142 [94]
Answer: A
Explanation do Pythagorean theorem and find the third side. Then do adjacent/hypotenuse.
7 0
2 years ago
Read 2 more answers
How many squares make up the surface of a cube?<br>O A. Seven<br>O B. Five<br>O C. Six<br>D. Eight​
Blababa [14]
The answer to the question is C (6)
3 0
2 years ago
Read 2 more answers
What is the value of x in the product of powers below?
sashaice [31]

Mmm, x is equals to -7....

8 0
3 years ago
Other questions:
  • A rectangular greenhouse has an area of 6,480 square meters. Its length is 120 meters.
    9·2 answers
  • 9 more than the product of 51 And a number t
    11·1 answer
  • Frank finished 65% of his math homework before dinner. If this amount represents 26 problems,How many problems will Frank need t
    14·1 answer
  • If sin42 degrees = 2/3 then cos48 degrees = what? <br> If tan20.5= 3/8, the tan69.5= what?
    11·1 answer
  • What is 7/25 in decimal form
    10·1 answer
  • at a basketball game, 6 adults pay $20 each and 4 children pay $10 each. What is the total cost for the adult tickets?​
    12·2 answers
  • In Nancy's class, 11/18 of the girls have brown eyes, 2/9 of the girls have blue eyes, and 1/6 of the girls have hazel eyes. How
    7·1 answer
  • 64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44. (pls show an equation to determine S
    8·1 answer
  • Complete the square to find<br> the vertex of this parabola.<br> x2 + 10x – y + 15 = 0<br> ([?], [])
    6·1 answer
  • 60
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!