The path of the water in a pond fountain can be modeled by y=-0.1x^2+2.8x , where x and y are measured in feet. The x -axis represents the surface of the pond. Find the width of the path at the surface of the pond and the height of the path.Width: ___ ft
Height: ___ ft
Answers
Answer:
the width of the path at the surface of the pond is 14 feet, and the height of the path above the surface of the pond is 19.6 feet.
Step-by-step explanation:
To find the width of the path at the surface of the pond, we need to find the x-coordinate of the vertex of the parabola y = -0.1x^2 + 2.8x. The x-coordinate of the vertex can be found using the formula:
x = -b/2a
where a = -0.1 and b = 2.8. Substituting these values, we get:
x = -2.8 / 2(-0.1) = 14
So the width of the path at the surface of the pond is 14 feet.
To find the height of the path, we need to find the y-coordinate of the vertex of the parabola y = -0.1x^2 + 2.8x. The y-coordinate of the vertex is given by:
y = f(x) = -0.1(x - h)^2 + k
where (h,k) is the vertex of the parabola. To find the vertex, we can use the formula:
h = -b/2a and k = f(h)
Substituting a = -0.1 and b = 2.8, we get:
h = -2.8 / 2(-0.1) = 14
k = f(14) = -0.1(14)^2 + 2.8(14) = 19.6
So the vertex of the parabola is (14, 19.6), which means the maximum height of the path above the surface of the pond is 19.6 feet.
Therefore, the width of the path at the surface of the pond is 14 feet, and the height of the path above the surface of the pond is 19.6 feet.
Related Questions
Please help me im stuck
Help pleaseeee my sister needs help and i dnt get this
Combine the like terms to create an equivalent expression: −4p+(−2)+2p+3
Problem 8-19 Because of high tuition costs at state and private universities, enrollments at community colleges have increased dramatically in recent years. The following data show the enrollment (in thousands) for Jefferson Community College for the nine most recent years. Click on the datafile logo to reference the data. Year Period (t) Enrollment (1,000s) 1 1 6.5 2 2 8.1 3 3 8.4 4 4 10.2 5 5 12.5 6 6 13.3 7 7 13.7 8 8 17.2 9 9 18.1 Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.If required, round your answers to two decimal places.y-intercept, b0 = 4.7.17Slope, b1 = 1.46MSE = ???????? NEED THISWhat is the forecast for year 10? 19.283Round your interim computations and final answer to two decimal places.
Answers
Answer:
b is the answer very sure
Step-by-step explanation:
Answer:
Betsy
Step-by-step explanation:
UwU
Answers
The measure of side SQ from the given similar triangles is 40.9 units.
What are similar triangles?
Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, triangle NOP is similar to triangle QRS.
Since the triangles are similar,
NP/SQ = NQ/QR
10/SQ = 13/53.2
13SQ=532
SQ=532/13
SQ=40.9 units
Therefore, the measure of side SQ is 40.9 units.
To learn more about the similar triangles visit:
brainly.com/question/25882965.
#SPJ2
Answer:
Step-by-step explanation:
Answers
Answer:
0.7385 = 73.85% probability that it is indeed a sample of copied work.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Identified as a copy
Event B: Is a copy
Probability of being identified as a copy:
80% of 15%(copy)
100 - 95 = 5% of 100 - 15 = 85%(not a copy). So
Probability of being identified as a copy and being a copy.
80% of 15%. So
What is the probability that it is indeed a sample of copied work?
0.7385 = 73.85% probability that it is indeed a sample of copied work.
Answers
Answer:
6 and 7
Step-by-step explanation:
I think you mean 'the sq rt of 48 lies between what 2 integers.'
The answer is 6 and 7.
Answers
Answer:
10.506
Step-by-step explanation:
its just adding and math lol- if u dont trust it look it at a calculator- hope this helped!!<3
Answers
Complete Question:
A total of 442 tickets were sold for the school play. They were either adult tickets or student tickets. There were 58 fewer
There were 58 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
250 adults tickets
Step-by-step explanation:
Given
Represent Adult with A and Children with C
Required
Find A
Since the ticket were either bought by A or C; then
This gives:
Substitute C + 58 for A
Collect Like Terms
Divide through by 2
Recall that:
Hence, 250 adults bought the ticket
There were 192 adult tickets and 250 student tickets sold for the school play, totaling 442 tickets.
- Let's denote the number of adult tickets sold as "A" and the number of student tickets sold as "S." According to the information provided, we have two equations:
- A + S = 442 (since a total of 442 tickets were sold).
- A = S - 58 (since there were 58 fewer adult tickets than student tickets).
- Now, we can use a system of equations to solve for A and S. We can substitute the value of A from the second equation into the first equation:
- (S - 58) + S = 442
- Combine like terms:
- 2S - 58 = 442
- Add 58 to both sides:
- 2S = 442 + 58
- 2S = 500
- Now, divide by 2 to solve for S:
- S = 500 / 2
- S = 250
- So, there were 250 student tickets sold.
- Now, we can find the number of adult tickets (A) using the second equation:
- A = S - 58
- A = 250 - 58
- A = 192
- Therefore, 192 adult tickets and 250 student tickets were sold for the school play.
Complete question should be:
How many adult tickets and student tickets were sold for the school play if a total of 442 tickets were sold, and there were 58 fewer adult tickets than student tickets?
For more questions on tickets -
#SPJ3