An archway in front of a school is in the shape of a parabola. The top of the arch is the vertex (0,0). The school seal is at the focus, 2.5 feet below the vertex, and the arch is 18 feet wide at the ground
Answers
Answer:
a) The equation of the arch is [tex]y = -10\cdot x^{2}[/tex].
b) The height of the arch from the ground is 810 feet.
Step-by-step explanation:
Statement is incomplete. Complete statement is:
An archway in front of a school is in the shape of a parabola. The top of the arch is the vertex (0,0). The school seal is at the focus, 2.5 feet below the vertex, and the arch is 18 feet wide at the ground.
Write an equation that represents the arch.
What is the height from the top of the arch to the ground?
a) Write an equation that represents the arch.
According to the statement, the archway is a vertical downward parabola. From Analytical Geometry we know that parabolas are represented by the following equation in standard form:
[tex]y-k = 4\cdot p\cdot (x-h)^{2}[/tex] (Eq. 1)
Where:
[tex]p[/tex] - Distance between vertex and focus, measured in feet.
[tex]x[/tex] - Independent variable, measured in feet.
[tex]y[/tex] - Dependent variable, measured in feet.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, measured in feet.
If we know that [tex]p = -2.5\,ft[/tex], [tex]h = 0\,ft[/tex] and [tex]k = 0\,ft[/tex], then the equation that represents the arch:
[tex]y = -10\cdot x^{2}[/tex]
The equation of the arch is [tex]y = -10\cdot x^{2}[/tex].
b) What is the height from the top of the arch to the ground?
Given that parabola is a symmetrical curve, we determine the vertical position at the base of the arch ([tex]x = 9\,ft[/tex]):
[tex]y_{min} = -10\cdot (9\,ft)^{2}[/tex]
[tex]y_{min} = -810\,ft[/tex]
Then, the height of the arch from the ground is given by this difference:
[tex]h = 0\,ft-(-810\,ft)[/tex]
[tex]h = 810\,ft[/tex]
The height of the arch from the ground is 810 feet.
Related Questions
-3(-2y-4)-5y-2
Please help
Answers
Answer:
y+10
Step-by-step explanation:
6-5y-2
8+5y
PLEASE HELP I NEED TO PASS!
Which table has a constant of proportionality between y and x of 2?
A
B
C
HELP!
Answers
Answer:
Its B
Step-by-step explanation:
Multiply x by 2 to get your answer
Can anyone solve this
Answers
Answer:
the answer is the last one. hope this helped.
Step-by-step explanation:
SOH CAH TOA
Find the missing side.
Round to the nearest tenth.
Answers
Answer:
1- 50
2-49
3-22
Step-by-step explanation:
just add the sides that you have and then subtract the sum by 90 becasue theu are right triangles
i need help with this also. (homework due tomorrow)
Answers
Answer:
Using Pyhagoras theoram,
(H)^2 = (B)^2 + (P)^2
B = 13 in
P = 5 in
[tex](h)^{2} = (13)^{2} + {(5)}^{2} \\ = > (h)^{2} = 169 + 25 \\ = > (h)^{2} = 194 \\ = > h = \sqrt{194} \\ = > h = 13.92[/tex]
Hence, the missing side is 13.92 inhes.
Answer:
13.93
Step-by-step explanation:
[tex]5^{2} + 13^{2} = c^{2}[/tex]
[tex]25 + 169 = 194 = c^{2}[/tex]
[tex]\sqrt{194} = c^{2}[/tex]
[tex]13.92838827718 = c[/tex]
then round up to 13.93
On subtracting 6 from three times of a number, we get 15. Then the number is
Answers
Answer:
Step-by-step explanation:
If we take the number as 7 so 3 times 7 is
3 x 7 = 21
Subtracted by 6 = 21 - 6= 15
So the number is 7
Answer:
7
Step-by-step explanation
Add the subtracted value to the other given value
15+6=21
Since we know it is 3 times the number, divide by 3 to get the number
21/3=7
Check:
21=3x7
21=21
The length of a rectangle is eight centimeters less than twice its width. If the perimeter of
the rectangle is 20 centimeters, find its dimensions.
Answers
Answer:
width of given rectangle = 6 cm
length of given rectangle = 4 cm
Step-by-step explanation:
Let the breadth be x cm
given that
The length of a rectangle is eight centimeters less than twice its width
length of rectangle in terms of x = 2(breadth ) - 8 = 2x - 8
we know perimeter of rectangle is given = 2(l + b)
thus, perimeter of given rectangle is = 2 ( x + 2x - 8) = 6x - 16
also given perimeter of the rectangle is 20 centimeters
thus,
6x - 16 = 20
6x = 20 + 16 = 36
x = 36/6 = 6
Thus,
width of given rectangle = 6 cm
length of given rectangle = 2*6 - 8 = 4 cm
8s+15-4s=7s +6 solve for s
Answers
[tex]\bold{Hello!}\\\bold{Your~Answer~Is~Below!}[/tex]
______________________________
[tex]\bold{Solution~Steps:}[/tex]
[tex]1.)~Combine~8s~and~-4s:[/tex]
[tex]\bold{8s+(-4s)=4s}[/tex][tex]2.)~Subtract~7s~from~both~sides:[/tex]
[tex]\bold{7s-7s=Cancels~out}[/tex][tex]\bold{4s-7s=-3s}[/tex][tex]3.)~Subtract~15~from~both~sides:[/tex]
[tex]\bold{15-15=Cancels~out}[/tex][tex]\bold{6-15=-9}[/tex][tex]4.)~Divide~both~sides~by~-3:[/tex]
[tex]\bold{-3s}[/tex] ÷ [tex]\bold{-3s=Cancels~out}[/tex][tex]\bold{-9}[/tex] ÷ [tex]\bold{-3=3}[/tex][tex]\bold{When~there~is~2~negatives~being~divided,~the~quotient~is~always~positive.}[/tex]______________________________
[tex]\bold{Answer:}[/tex]
[tex]\boxed{s=3.}[/tex]______________________________
[tex]\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~~~-TotallyNotTrillex}[/tex]
If a stock falls from $14.89 to $6.47, then what is its percentage of change?
Answers
Answer:
2.30139104 US dollar
i think
Step-by-step explanation:
Ben and Sam are driving in a lake.at 14 feet below the surface, ben spots sam 9 feet directly below him.find smash deprh
Answers
Sam's depth is 25 feet as 14 + 9 = 25
Is the function f(x) = x even, odd or neither?
Answers
Answer:
odd
Step-by-step explanation:
One store was selling a box of baseball cards for $20. You have to pay 9% sales tax on the item.
1. How much would the tax be?
2. What would be the total cost of the baseball cards?
Answers
Answer: 1. $1.80
2. $21.80
Step-by-step explanation:
You apply sales tax to 20 which is 9% or 0.09 so you p multiply 20 by 0.09 which is 1.8. That’s the tax then add that to 20 and get 21.80
Mark the brainliest it would be aprreciated
anelle subtracts –4 from a number. The result is 2. What is the number?
–6
–2
2
6
Answers
Answer:
the answer is 2. so it is 2
Step-by-step explanation:
2 ➕ 2 is 4
Answer:
Option D (6)
Step-by-step explanation:
6-4 is equal to 2
Mr. Carter is building a circular fire pit in his backyard. The diameter of the fire pit is 6 feet and he will fill the interior with gravel covering 5/6 of the area. How much gravel will he need?
A. 23.55 sq. ft.
B. 28.26 sq. ft.
C. 94.2 sq. ft.
D. 113.04 sq. ft.
Answers
Answer:
23.55
Step-by-step explanation:
To calculate the area I did the following equation
area = 3.14 (r) (r)
area = 3.14 (3) (3)
area = 28.26
The area is 28.26 but the question is asking how much gravel would be needed to fill 5/6 of the area.
The equation for 5/6 out of 28.26 is
28.26 (5/6) = 23.55
So the final answer is (a.) 23.55 sq. ft.
(5x - 5)
(6y - 4)
(4x + 10)
Find the value of the variables in the figure.
x =
y =
Answers
Answer:
what are they equal to I can solve if that info is not given
Write the income equation for a small business that
begins with $150 and grows by 20% each year. When
will the company's income be $300?
Answers
Answer:
in 4 years
Step-by-step explanation:
because you should find the 20% of 150
150×20=3000
3000÷100= 30
so 20% of 150 is 30
then you keep adding 30 to the results till you reach 300
The equation is 150+30x=300 and it takes 3 years for the company to earn $300.
Given that, a small business begins with $150 and grows by 20% each year.
We need to find when will the company's income by $300.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, 20% of 150=30
Let x be the number of years.
So, f(x)=150+30x
⇒150+30x=300
⇒30x=150
⇒x=3
The equation is 150+30x=300 and it takes 3 years for the company to earn $300.
To learn more about the equations visit:
https://brainly.com/question/10413253.
#SPJ2
The given table of values represents a linear equation. What is the slope?
A. 4
B. 5
C. 3
D. 6
Answers
Answer:
C. 3
Step-by-step explanation:
Formula for slope is given as [tex] m = {y_2 - y_1}{x_2 - x_1} [/tex]
The coordinates of any two points can be used in this formula. Let's use, (1, 5) and (2, 8).
Let,
[tex] (1, 5) = (x_1, y_1) [/tex]
[tex] (2, 8) = (x_2, y_2) [/tex]
Plug the values into the formula:
[tex] m = {8 - 5}{2 - 1} [/tex]
[tex] m = {3}{1} [/tex]
[tex] m = 3 [/tex]
QRS contains the points: Q(4, 2) R(5, 1) S(3, 7). If the triangle is reflected across the y-axis, what will S' be? ANDWER ASAP WILL GIVE BRAINLEST!!
Answers
Answer:
S'(-3, 7)
Step-by-step explanation:
The coordinate of point S' will be (-5, 1).
What is reflection?A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection.
What is the rule to find the reflection of a point in y-axis?The rules for finding the reflection of a point in y-axis are:
(i) Change the sign of abscissa, i.e. x-coordinate.
(ii) Retain the ordinate i.e., y-coordinate.
Therefore, when a point is reflected in the y-axis, the sign of its abscissa changes.
According to the given question.
We have a triangle QRS.
The coordinates of points Q, R, and S are (4, 2), (5, 1) and (3, 7) respectively.
Since, the triangle QRS is reflected across the y-axis .
Therefore, the coordinate of S' is given by
The sign of abscissa or x-coordinate of (5, 1) changes so, 5 changes to -5.
And the ordinate i.e. 1 will remain same.
Therefore, the coordinate of point S' will be (-5, 1).
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Find the M_ABC in the diagram below.
A
B
(16y-12)
(12y + 8)
E
Answers
Answer:
where is the diagram
Step-by-step explanation:
4 (x +3 ) = 24 need help!!!!
Answers
Because 4*3=12 and 12*2 = 24
Answer:
X=0
Step-by-step explanation:
X=0 because 4(x+3) 4×3 is already 24
Gina's family goes to a theme park. The family pays a $12 fee to park their car and buys admission tickets for all 5 family members. Her family pays a total of $132 . Which equation can be used to solve for t , the price of one admission ticket?
A.
5(12+t)=132
B.
5t+12=132
C.
5(12)+t=132
D.
5+12+t=132
Answers
Answer:
B
Step-by-step explanation:
5t + 12 = 132
We know the price of parking and we know what they paid in total. There are 5 members with the unknown price.
Answer:
B
Step-by-step explanation:
You're trying to find how much a ticket, which is t. you need 5 tickets for the family, plus the twelve dollar fee which is there anyways for the car, and it add up to 132. subtract 12 from 132 and you get 120. 120 divided by 5 is 24. so 24 dollars for a ticket, but the equation you would need is 5t+12=132
How are the key features of a linear function identified and interpreted from a description?
Help I’m dying with math lol
Answers
Answer:
Key features of a linear function from a table are the ordered pairs which are points on a line.In the equation,the slope of the function which is the rate of change and the y-intercept value are indicated.
Step-by-step explanation:
21 2/3 divided 3 1/4
Answers
Answer:
256/39 or 6 22/39
Explain how to find the sum −8.46+5.31.
Answers
Answer:
-3.15
Step-by-step explanation:First you must line them up
- 8 . 4 6
+ 5 . 3 1
-------------------
Then you add
- 8 . 4 6
+ 5 . 3 1
-------------------
3 . 1 5
You get three becuase -8 + 5 is 3.
Hope this helps :)
slope=-2 y intercept=0
Answers
Answer:
Step-by-step explanation:
I am assuming you want an equation
y=mx + b
m is the slope, and b is the y intercept, so just fill in the info
y=-2x + 0
because it is just + 0, you can simply write:
y=-2x
Note: I'm not completely sure of what you're asking, but I hope this helps in some way, shape, or form!! If not, feel free to tell me what you need, and I will edit my response.
I NEED HELP PLZ HELP MEEEEEE!!!!!!!!
Answers
Answer:
54 people were originally in the room.
Step-by-step explanation:
18=2/3 of the half not dancing
(18/2)(3)=27
27 is the 1/2 population or 27=1/2
(27/1)(2)=54
54 people were originally in the room.
Step-by-step explanation:
18=2/3 of the half not dancing
(18/2)(3)=27
27 is the 1/2 population or 27=1/2
(27/1)(2)=54
express 52/9 as a decimial
Answers
Hey there!
In order for you to convert/ express a fraction as a decimal you SHOULD:
DIVIDE the numerator (the TOP number) from the denominator (the BOTTOM number)
Now that we have that guide/side note we can answer your question, shall we?
52/ 9 = 5.777778
If you’re rounding to your Answer, then it’ll be: 5.78
Overall answer is: 5.777778 ✅
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
X^2+(2)b+(-35) then the factored form is?
Answers
Answer:
2b+2x-35
Step-by-step explanation:
let me know if wrong
294 is equal to the quotient of f and 373
Write the sentence as an equation
Answers
Answer:
f/373 = 294
Step-by-step explanation:
Find the fifth term in the sequence: 9, 13, 17,...