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 1

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.

An Archway In Front Of A School Is In The Shape Of A Parabola. The Top Of The Arch Is The Vertex (0,0).

Related Questions

I want the answer PLZ

Answers

Answer:

3

Step-by-step explanation:

They have the same side length and its shown

please help me with this! thank you so much!

Answers

Answer: Look at the photo

Step-by-step explanation:

[tex](3x + 3) + (4x + 2) = 180\\7x + 5 = 180\\[/tex]

Substract 5 from both sides

[tex]7x = 175[/tex]

Divide by 7 from both sides

x = 25

(3x+3) = (4x+2)
-3x -3x
3=1x+2
-2 -2
1=x
That’s how you get x
3•1 +3 = 6

4•1 + 2 =6
I’m pretty sure that’s right it’s been a minute

values of x and y
to
135°

Answers

Step-by-step explanation:

Answer:

xy/100=135

xy=13500

x=13500/y

Plz help I don’t get what this is

Answers

Answer:

A) 98.94 sq. meters

B) 42 sq. meters

Step-by-step explanation:

A) So first we calculate the area for the square which is 15*20 = 300. Then we calculate the area of the circle which is pi*r^2 and in this case the radius is 4 which is 1/2 of 8. The area is approx. 201.06. Then we subtract that from 300. 300-201.06 = 98.94. The answer for A) is approx. 98.94

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

B)First we calculate the area of the whole square which is 8*6 = 48. Then the area of the garden which is 2*3 = 6. 48-6 = 42. The answer is B) is 42 then.  


Jenni works at a salon and earns a 15% commission on her total sales. How much
must she sell in total in order to earn $90 in one day?

Answers

Answer:

$600

Step-by-step explanation:

90/0.15

Consider a geometric sequence with a first term of 4 and a fourth term of -2.916.
a) Find the common ratio of this sequence.
b) Find the sum to infinity of this sequence.

Answers

Answer:

a) Find the common ratio of this sequence.

Answer: -0.82

b) Find the sum to infinity of this sequence.

Answer: 2.2

Step-by-step explanation:

nth term in geometric series is given by [tex]4\ th \ term = ar^n-1\\-2.196 = 4r^{4-1} \\-2.196/4 = r^{3} \\r = \sqrt[3]{0.549} \\r = 0.82[/tex]

where

a is the first term

r is the common ratio and

n is the nth term

_________________________________

given

a = 4

4th term = -2.196

let

common ratio of this sequence. be r

[tex]4\ th \ term = ar^n-1\\-2.196 = 4r^{4-1} \\-2.196/4 = r^{3} \\r = \sqrt[3]{-0.549} \\r = -0.82[/tex]

a) Find the common ratio of this sequence.

answer: -0.82

sum of infinity of geometric sequence is given by = a/(1-r)

thus,

sum to infinity of this sequence = 4/(1-(-0.82) = 4/1.82 = 2.2

Does anyone know this!? Pick the one the correctly describes it!
If its correct ill mark you as the best answer!

Answers

Answer:

d- the slope is undefined

Step-by-step explanation:

How do you work out 3^2+2^3 indices

Answers

3^2 +2^3

9+2^3

9+8

Answer : 17

x+6y=-36 solve for y​

Answers

Answer:

y=−1/6x−6

Step-by-step explanation:

What is the slope of the line that passes through the points (4, 6) and
(-16, -18)?

Answers

Answer:

-3 / 5

Step-by-step explanation:

18-6 / -16-4

12 / -16-4

12 / -20

-3 / 5

Please help me :( someone anybody just once I won’t ask again

Answers

Answer:

1) 77

2) -11

3) -11

4) 7

5) 29

Step-by-step explanation:

Just sub the x into the equation.

*I recommend checking my answers, but this is what I would put/

Help me please !!!!!!!!

Answers

Answer: Since x is 157 degrees the missing value,m, is 23 degrees because a line is 180 degrees, n is also 23 degrees so it would be the same

Step-by-step explanation:

What is the y-intercept in this problem?

Answers

Answer:

(0, -1) I think

Step-by-step explanation:

I have not done this in a while

Hope this helps, though.

The y-intercept is -1

Please help me find the domain and range

Answers

Answer:

Domain: (-∞,-1) U (-1,∞)

Range: (-∞,1) U (0,∞)

What is the value of x

Answers

Answer:

98 degrees

Step-by-step explanation:

First calculate the entire triangles angles:

180 - 53 - 45 = final angle of triangle

82 = final angle of triangle

Using the straight line rule for angles, x and the inner angle must equal to 180 degrees:

180 - 82 = x

98 = x

Angle x is 98 degrees.

Solve for c.

2c^2 = 338

c = ?
c = ?

Answers

Answer:

C=13, -13

Have a wonderful day!!!

264 equals the sum of 96 and t
Write the sentence as an equation.

Answers

Answer:

96+t=264

Step-by-step explanation:

ANSWER: t+96=264
No explanation needed!

the population of China is about 1.4 x 10 ^ 9 people. Julie grew up in a town with a population of about 7,000 people. How many times greater is the population of China than Julies town? Please answer this in scientific notation​

Answers

Answer:

200000

Step-by-step explanation:

I believe that 200000x7000 = 1400000000 (The answer to the China population equation), therefore should be correct. Hope this helped.

Solve by substitution

Answers

Answer:

(1,4)

Step-by-step explanation:

Answer: x = 1, y = 4

Steps: 3y + 4x = 16,  -2x + y = 2

Isolate y for 3y + 4x = 16:   y = (16 - 4x ÷ 3)

Substitute y into the other equation (-2x + y = 2):   -2x + (16 - 4x ÷ 3) = 2

Simplify: 16 - 10x ÷ 3 = 2

Isolate x for 16 - 10x ÷ 3 = 2:   x = 1

Substitute x = 1 into  y = (16 - 4x ÷ 3):  y = 16 - 4x · 1 ÷ 3

y = 4, x = 1

Plz mark brainliest:)

find x

3x
2x+40
x+50
4x

Answers

Answer:

27

Step-by-step explanation:

The sum of all exterior angles of any quadrilateral= 360°

3x+2x+40+x+50+4x = 360°

11x + 90 = 360°

11x = 360 - 90

10x = 270

x = 270/10

x = 27

I WILL BRAINLEIST PLEASEMegan earned $4 an hour for babysitting. She earned $16 on Saturday. How many hours did she babysit?

Answers

Answer:

4 hours  

Step-by-step explanation:

16/4= 4

A scale drawing of an office space uses a scale of 1 in. : 4 yd. The scale drawing has an area of 12 square inches. What is the area of the actual office space?

Answers

Answer: 48 yards

Step-by-step explanation:

From the question, we are informed that a scale drawing of an office space uses a scale of 1 in. : 4 yd.

When the scale drawing has an area of 12 square inches, to get the area of the actual office space, we multiply the given number by 4 since the actual office space is 4× the scale drawing. This will be:

= 12 × 4 yards

= 48 yards

What is x equal to? And what is the scale factor?

Answers

Answer:

1. 225 km

2. 95 km

3. 412.5 km

Step-by-step explanation:

For this one, it is saying that for every 2 cm, that is 50 km. So if you look at 9 cm, you can divide that by 2 cm to get 4.5 cm, this is what you can multiply by 50 km to get 225. Or you can look at it this way, for every 1 cm, the actual distance is 25 km. Then you can multiply each value by 25 to get your answer. Whichever one works for you.

please help 8(10+8)​

Answers

Answer:

its 180.... that's the answer

Answer:

it is 80 + 64

Step-by-step explanation:

All you have to do is multiply 8 by the numbers inside the parenthesis

which posture or theorem proves that these two triangles are congruent

ASA Congruence
AAS Congruence Theorem
HL Congruence Theorem
SAS Congruence postulate ​

Answers

Answer:

AAS Congruence Theorem

Simplify (1/2)^4.......................................................................

Answers

Answer:

[tex]-1/16[/tex]

Step-by-step explanation:

Answer:

1/16

Step-by-step explanation:

(1/2 × 1/2 × 1/2 × 1×2)

(1/4 × 1/4)

(1/16)

Simplify 4/9 - 5/12 + 1/4

Answers

Answer:

5/18

Step-by-step explanation:

The simplified answer is 5/18

Step-by-step explanation:

the answer is

0.27777777777

Solve the system of equations using substitution.
- 4x + 4y= 8
y= -2x – 10
-
O (4, -18)
O (12, -34)
o(-4,-2)
O (-2,-6)

Answers

The answer is (-4,-2) .

You substitute the value of Y
solve the equation then substitute
the value of X, then again Slove

Answer:

(- 4, - 2 )

Step-by-step explanation:

Given the 2 equations

- 4x + 4y = 8 → (1)

y = - 2x - 10 → (2)

Substitute y = - 2x - 10 into (1)

- 4x + 4(- 2x - 10) = 8 ← distribute and simplify left side

- 4x - 8x - 40 = 8

- 12x - 40 = 8 ( add 40 to both sides )

- 12x = 48 ( divide both sides by - 12 )

x = - 4

Substitute x = - 4 into (2) for corresponding value of y

y = - 2(- 4) - 10 = 8 - 10 = - 2

Solution is (- 4, - 2 )

brainliest and 60 points ;)

8 * 65 * 7 * 321 * 0 * 1=??

Answers

Answer: 0

Step-by-step explanation:

Any expression multiplied by 0 = 0

5.6 divided by 7

A:8
B:7
C.8
D.7
Other:

Answers

Answer:

C

Step-by-step explanation:

Dude, just look it up.

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