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 inches, 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?
Answers
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 x 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, [tex]x_{max}[/tex], of the maximum point of a parabola given in the form, y = a·x² + b·x + c is found using the following formula;
[tex]x_{max}[/tex] = -b/(2·a)
The x-coordinate, [tex]x_{max}[/tex], of the maximum point of the given equation of the parabola, h(x) = 160·x - 16·x², (a = -16, b = 160) is therefore;
[tex]x_{max}[/tex] = -160/(2 × (-16)) = 5
Therefore, the number of feet along the way, the function will reach maximum height, [tex]x_{max}[/tex] = 5 feet
(3) The function, h(x) = 160·x - 16·x², will reach maximum height, [tex]h_{max}[/tex], at x = 5, therefore;
[tex]h_{max}[/tex] = h(5) = 160 × 5 - 16 × 5² = 400
The maximum height of the spray, [tex]h_{max}[/tex] = 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.
Related Questions
A seat’s position on a Ferris wheel can be modelled by the function y = 18 cos 2.8(x + 1.2) + 21, where y represents the height in feet and x represents the time in minutes. Determine the diameter of the Ferris wheel.
Answers
Step-by-step explanation:
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+320
Problems 5-9, Find the value of the variable to the nearest tenth of each triangle.
Answers
Answer:
35
Step-by-step explanation:
HELP ME WIT THIS QUESTION
Answers
Answer:
I (-4, -3)
J (-4,-2)
K (-2,-2)
L (0,-4)
I need help I don't understand this at all.
Answers
please mark this answer as brainlist
How do you find the diameter of a quarter circle?
Answers
Answer:
um 1/4
Step-by-step explanation:
If p (x) = x4 + 2x2 + 1 and q (x) = x4 – 2x2 + 1, find p (x) -q (x).
Answers
Answer:
the answer is 4x2
Step-by-step explanation:
p(X)-q(X) = x4 + 2x2 + 1 - ( x4 - 2x2 + 1 )
p(X)-q(X) = x4 + 2x2 + 1 - x4 + 2x2 - 1 )
p(X)-q(X) = 2x2 + 2x2
p(X)-q(X) = 4x2
Answer:
p(x) - q(x) = 4x²
Step-by-step explanation:
p(x) - q(x)
= [tex]x^{4}[/tex] + 2x² + 1 - ([tex]x^{4}[/tex] - 2x² + 1) ← distribute parenthesis by - 1
= [tex]x^{4}[/tex] + 2x² + 1 - [tex]x^{4}[/tex] + 2x² - 1 ← collect like terms
= 4x²
n the graph below determine how many real solutions the quadratic function has, and state them, if applicable. List solutions in order from left to right on the graph, or least to greatest. If the function has only one solution, type the solution in both of the boxes. If there are no real solutions type “none” in both boxes.
Answers
Answer:
There are no real solutions.
Step-by-step explanation:
There are 3 options.
2 real solutions: This happens if in the graph, each arm intersects the x-axis, this means that there are two different values of x such that the equation:
a*x^2 + b*x + c
is equal to zero.
Another way to see this, is if the determinant:
b^2 - 4*a*c
is larger than zero.
1 real solution: This happens when the vertex of the graph intersects the x-axis. This means that there is a single value of x such that:
a*x^2 + b*x + c
is equal to zero.
Another way to see this is if the determinant:
b^2 - 4*a*c
is larger equal zero.
No real solution: if in the graph we can not see any intersection of the x-axis, then we do not have real solutions (only complex ones).
Another way to see this is if the determinant:
b^2 - 4*a*c
is smaller than zero.
Now that we know this, let's look at the graph.
We can see that the vertex is below the x-axis, and the arms of the graph go downwards. So the arms will never intersect the x-axis (and neither the vertex).
So the graph does not intersect the x-axis at any point, which means that there are no real solutions for the quadratic equation.
The correct answer would be "none"
HELP ASAP PLEASE!!!!!
what is the factorization of the polynomial below -x^2-2x+48
Answers
I HOPE IT WILL HELP YOU. I DID HOW I KNOW .
find the perimeter of the isosceles trapezoid
Answers
Answer:
A =136 cm^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) *h where b1 and b2 are the lengths of the bases and h is the height
A = 1/2( 22+12) *8
A = 1/2 ( 34)*8
A =136 cm^2
Solve using the Pythagorean theorem
a^2+b^2=c^2 with This you should get 9.43 (rounded) as your values.
Then just add up the side lengths.
2(9.43)+22+12, which gives a perimeter of 52.87 (rounded)
5^2+8^2=c^2
Prachi was 555 kilometers east of her home when she began driving farther east at 707070 kilometers per hour. Let f(n)f(n)f, left parenthesis, n, right parenthesis be Prachi's distance from her home at the beginning of the n^\text{th}n th n, start superscript, start text, t, h, end text, end superscript hour of her drive.
Answers
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Whenever she began to drive farther east, at 70 km per hour, Prachi was 5 km east of her home.
Let f(n) at the beginning of her nth hour drive be Prachi's distance to her home.
f is a sequence of arithmetic.
Write a series explicit form.
[tex]\to f(n) = 70n + 5[/tex]
Answer:
Arithmetic Sequence, f(n)=5+70(n-1)
Step-by-step explanation:
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3/4 + 1/2 + 1/3 + 2/9 + ...... = 9/4
Answers
Answer
The missing value is 4/9
what is the radius of the semicircle
Answers
20
Step-by-step explanation:
Hint: Use the Pythagorean Theorem
———————————————————
We’ll just listen to what the hint says
Pythagorean theorem: a^2 + b^2 = c^2
where a = 16 b = 12 and c = radius
16^2 + 12^2 = c^2
256 + 144 = c^2
c^2 = 400
square root 400
sqrt rt 400 = 20
The radius of the semicircle is 20
Amy has four more 20c coins than 5c coins. The total value of all her 20c and 5c is $3.80. How many 5c coins does Amy have?
Answers
Answer: 12
Step-by-step explanation:
16 X 20c = 3.20
12 x 5c = 0.60
total is 3.80
Amy has 12 five c coins.
The teacher's helper was putting cookies onto plates. He put 1 cookie on the first plate, 4 cookies on the second plate, 16 cookies on the third plate, and 64 cookies on the fourth plate. What kind of sequence is this?
Answers
Answer:
Geometric sequence
Step-by-step explanation:
A geometric sequence involves each number after the first one being multiplied by a specific number, called the common ratio.
This situation is a geometric sequence, where the common ratio is 4.
For example, there are 4 cookies on the second plate, 16 on the third, and 64 on the fourth. To get each number, the previous number is multiplied by 4.
So, this is a geometric sequence.
If he placed one cookie on the first dish, four on the second, sixteen on the third, and sixty-four on the fourth. A geometric sequence is a type of sequence.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,
It is given that the educator placed one cookie on the first dish, four cookies on the second, sixteen cookies on the third, and sixty-four cookies on the fourth.
Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio. The common ratio in this situation, which is a geometric sequence, is 4.
The second dish, for instance, has four cookies, the third, sixteen, and the fourth, sixty-four. Each number is obtained by multiplying the preceding number by four.
Thus, if he placed one cookie on the first dish, four on the second, sixteen on the third, and sixty-four on the fourth. A geometric sequence is a type of sequence.
Learn more about the sequence here:
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Multiply: (2x+y) (n2-3xy+y2)
Answers
Answer:
[tex]{ \tt{(2x + y)( {n}^{2} - 3xy + {y}^{2} )}} \\ = { \tt{(2x {n}^{2} - 3 {x}^{2}y + 2x {y}^{2} + {n}^{2}y - 3x {y}^{2} + {y}^{3} )}} \\ = { \tt{ {y}^{3} - xy(y + 3x) + {n}^{2} y }}[/tex]
Hello!
(2x+y) (n2-3xy+y2)
2x* n²= 2xn²
2x* -3xy = -6x²y
2x* y² = 2xy²
y*n² = yn²
y*-3xy = -3xy²
y* y² = y³
=>
2xn²- 6x²y + 2xy² +yn²- 3xy² +y³
Could I get the answer don’t understand
Answers
Answer:
DE = 21.4
Step-by-step explanation:
The parallel lines divide the transversals proportionally, that is
[tex]\frac{DE}{EB}[/tex] = [tex]\frac{DF}{FC}[/tex] , substitute values
[tex]\frac{DE}{10.7}[/tex] = [tex]\frac{32}{16}[/tex] = 2 ( multiply both sides by 10.7 )
DE = 21.4
Suppose we have 12 books.
How many ways are there to put four of them on a shelf?
PLS HELP ME
Answers
Answer:
1) first book can be at any of 4 places
2) Second book can be on any of leftover 3 places
3) Similarly third book on 2 and forth on 1 place
total : 4 * 3*2 * 1 = 24 ways .
other way we have formula 4!/1! =24 , here ordering is important
It is called arrangement or permutations, while if you need to group some objects it is called combination and there we need to consider unique groups only.
example if you need to choose 2 friends for a party out of 4 friends ,
answer will be 4!/2!*2! = 6 groups. (Ordering doesn’t matter hence division)
hope it hleps
PLEASE MARK BRAINLIEST
Find the measure of one exterior angle for the following regular polygon.
Answers
Answer:
40 degrees
Step-by-step explanation:
The formula for calculating the sum of interior angles is ( n − 2 ) × 180 (n = Number of sides)
in this scenario you have 9 sides so put it in the equation.
(9 - 2) ×180 = 1260
1260 is the sum of all the interior angles so we must divide this number by the number of sides to get the angle of one individual interior angle.
1260/9 = 140
180-140 = 40 degrees
Arrange in descending order.
10,-5,-1, 12, 0, -13
Answers
Answer:
12, 10, 0, -1, -5, -13
Step-by-step explanation:
7)On subtracting 8 from x, the result is 2 . Form a linear
equation for the statement.
Answers
Answer:
8-x=2
-x=2-8
-x=-6
x=6
if 8 is subtract from 6answer is 2
Select the correct answer.
Which statement best describes the solution to this system of equations?
3x + y= 17
x + 2y = 49
Ο Α.
It has no solution.
B.
It has infinite solutions.
O c.
It has a single solution: x = 15, y= 17.
OD.
It has a single solution: x = -3, y = 26.
Answers
What value of x is in the solution set of -2(3x + 2) >-8x + 6
Answers
Answer:
x >5
Step-by-step explanation:
-2(3x + 2) >-8x + 6
Distribute
-6x-4 > -8x+6
Add 8x to each side
-6x-4+8x > -8x+8x+6
2x-4 > 6
Add 4 to each side
2x-4+4 > 6+4
2x> 10
Divide by 2
2x/2 >10/2
x >5
Step-by-step:
-2(3x+2)>-8x+6. divided by 2,-3x-2>-4x+3. the solution set of -2(3x+3)>-8x+6 is {x/x>5}
Answer:
6
7.
Which kind of function best models the data in the table? Graph the data and write an equation to model the data.
A. exponential; y = 3x – 1
B. linear; y = x – 1
C. quadratic; y = x2 – 1
D. linear; y = –x – 1
Answers
Answer:
D. linear; y = –x – 1
Step-by-step explanation:
Linear; y=-x - 1
The slope is negative since it’s decreasing. So it’s not the first equation. It’s not a quadratic equation because there is no forming U shape for this data. It’s not a exponential function because the slope is not 3 and a exponential function is in the form y=a(b)^x
...............................................................................................................................................
Answer:
The correct answer is D) linear; y = –x – 1
Step-by-step explanation:
To find this, use any values in the table and it will produce a true statement. This is how we check to see if a model is correct. See the two examples below for proof.
(4, 5)
y = -x - 1
-5 = -4 - 1
- 5 = -5 (TRUE)
(0, -1)
y = -x - 1
-1 = 0 - 1
-1 = -1 (TRUE)
Setting y = 0 allows you to determine the what
of a graph
Answers
[tex]y=0[/tex] allows you to determine the x-intercept of a graph.
x-intercept and y-intercept:The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept. Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.When y is 0, the x-intercept is reached. The graph's intersection with the y-axis, or (0, b), is known as the y-intercept. When x is 0, the y-intercept is reached. When y is 0, the x-intercept is reached.Therefore, [tex]y=0[/tex] allows you to determine the x-intercept of a graph.
Know more about x-intercept and y-intercept here:
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23. Insert the missing number.
4
6
9
14
23
40
?
138
266
Answers
Answer:
hey mate !!!
The pattern followed is
4x2-2= 8-2=6
6 x 2-3= 9
9 x 2- 4= 14
14 x 2-5 = 23
23 x 2-6= 40
40 x 2-7= 73
So, the next number will be 73.
0.25(4f-3)=0.005(10f-9)
Simplify the following
Answers
Answer:
apoco la propiedad asociativa en los siguiente ejercicio 25x11x18=
Intuitively, does it make sense that all circles are similar? Why or why not?
Answers
Answer with explanation:
Yes, each point on a circle is a fixed distance from the center of the circle. This is called the radius of the circle. By definition, all radii of a circle are equal.
Similar polygons have corresponding sides in similar proportion. Regardless of how large a circle is, each point on the circle will still be a fixed distance away from center of the circle. Therefore, the radii are in a constant proportional and all circles are similar.
What is the answer to the question 3x+5x
Answers
Answer:
8x
Step-by-step explanation:
=3x+5x
=8x
Rebecca can paint a room in 12 hours Guadalupe can paint the same room in 16 hours how long does it take for both Rebecca and Guadalupe to paint the room if they are working together
Answers
Guadalupe can paint in 16hrs (and Guadalupe G)
How long ? = (RxG) x 24 divided by 2
(12x16)24/2
2304/60
38.4hrs.
use the formula v=u+at to find the velocity when the initial velocity is 3m/s2 the time is 7 seconds
Answers
Answer:
Step-by-step explanation:
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