2.
The reflector of a satellite dish is in the shape of a parabola with a diameter of 4 feet and a depth of 2 feet. To get the maximum reception we need to place the antenna at the focus.

a. Write the equation of the parabola of the cross section of the dish, placing the vertex of the parabola at the origin. Convert the equation into standard form, if necessary. What is the defining feature of the equation that tells us it is a parabola?
b. Describe the graph of the parabola. Find the vertex, directrix, and focus.
c. Use the endpoints of the latus rectum to find the focal width.
d. How far above the vertex should the receiving antenna be placed?

Answers

Answer 1

Answer:

Step-by-step explanation:

Assume the dish opens upwards. The cross-section through the vertex is a parabola. You know three points on the parabola: (0,0), (2,2), and (-2,2). Plug the points into y = ax² + bx + c to get a system of three equations where a=0.5, b=c=0.

Equation of parabola: y = 0.5x²

:::::

Vertex (0,0)

Focal length = 1/(4×0.5) = 0.5

Focus (0,0+0.5) = (0, 0.5)

Directrix y = 0-0.5 = -0.5

:::::

At endpoints of latus rectum, y = 0.5

x = ±√0.5 = ±√2/2

Focal width = 2×√2/2 = √2

:::::

Place antenna at focus, (9,2)


Related Questions

The midpoint of AB is (1.2). The coordinates of A are (-3, 6) Find the coordinates of B.

Answers

Answer: coordinates of B are (5,-2)

Step-by-step explanation:

let B be (x2,y2)

x1 = -3 y1 = 6

x = 1

y = 2

so

x = (x2 + x1)/2

1 = (x2+(-3))/2

or, 2 = x2 - 3

so, x2 = 5

now

y = (y2+y1)/2

or, 2 = (y2 + 6)/2

or, 4 = y2 + 6

so, y2 = -2

As a student, you are able to earn extra money by assisting your neighbors with odd jobs.
If you charged $10.25 an hour for your assistance, about how many hours would you
need to work to earn $8,425? Show your work. (

Answers

9514 1404 393

Answer:

  about 822 hours

Step-by-step explanation:

If h is the number of hours for which you are paid $10.25 per hour, then the number you need is ...

  8425 = 10.25h

Divide by the coefficient of h:

  8425/10.25 = 10.25h/10.25

  821.95121...(5-digit repeating decimal)

You need to work about 822 hours to earn $8425.

_____

Your pay for 822 hours will be $8425.50. If taxes are deducted, you need to work a while longer.

8. Write 3x3 – 21x2 + 36x in factored form.
3x(x - 4)(x - 3)
3x(x - 5)(x - 2)
3x(x + 6)(x + 2)
O
3x(x + 4)(x + 3)

Answers

Answer:

A

Step-by-step explanation:

3x^3 – 21x^2 + 36x=3x(x^2-7x+12)=3x(x - 4)(x - 3)

ba xạ thủ độc lập bắn vào một mục tiêu. xác suất bắn trúng tương ứng là 0,8; 0,7; 0,6. mỗi xạ thủ bắn một viên. gọi X là số viên bắn trúng.
a) lập bảng phân phối xác suất.
b) tính E(X) và VAR(X)

Answers

Answer:

well I don't know

Step-by-step explanation:

your speaking vietnam

Answer:

Step-by-step explanation:

If why varies with the square of x and Y equals 24 when x equals 10 then the constant of proportionality is ____, and the value of y when x equals 20 is ____. Assume x is greater than or equal to 0. Select two answers

Answers

Answer:

Step-by-step explanation:

y varies with the square of x:

y = kx²

y equals 24 when x equals 10

24 = k·10²

constant of proportionality k = 0.24

when x = 20, y = 0.24·20² = 96

"select two answers"  —where are the choices?

look at the image below

Answers

Answer:

4.2 mi²

Step-by-step explanation:

Volume of a cone = (1/3)πr²h, where r = radius and h = height

(1/3)πr²h

= (1/3)×π×1²×4

= 4π/3

= 4.2 mi² (rounded to the nearest tenth)

The perimeter of Tamara's suitcase is 8x - 3 and the perimeter of Anna's suitcase is
3x + 2. Write an algebraic expression that represents
the difference between the perimeter of Tamara's suitcase
and the perimeter of Anna's suitcase?

Answers

Answer:

perimeter: 2

Step-by-step explanation:

8x-3 = 6x

8x – 6x = 3

2x = 3

x = 3/2

The required algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The difference between the perimeter of Tamara's suitcase and Anna's suitcase can be found by subtracting the expression for the perimeter of Anna's suitcase from the expression for the perimeter of Tamara's suitcase:

(8x - 3) - (3x + 2)

Simplifying the expression by removing the parentheses and combining like terms, we get:

8x - 3 - 3x - 2

= 5x - 5

Therefore, the algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

Learn more about models here:
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Use the given conditions to write an equation for each line in point-slope form and slope-intercept form.
Slope= 1/3, passing through the origin.

Answers

Answer:

y = 1/3x        y - 0 = 1/3 (x - 0)

Step-by-step explanation:

slope intercept: y = 1/3x

point slope: y - 0 = 1/3 (x - 0)

A-(buc)=(A-b)u(A-c)

Answers

Step-by-step explanation:

I don't get the question a bit but I hope this makes sense

:)

Hey there, everyone!

I just wanted to shout out to all of those whom have helped me through my tortuous math homework and say thank you very much. XD

I manage to pass my very first year of high school without physically going to school.

It was a lot of twist and turns, I must say. But at least I managed to pass through!

Man, I'm gonna miss 2021 because now I'll have to ACTUALLY go to school. But when that day comes, I do hope you guys will continue helping me on!

In the mean time, stay safe everyone and thanks a lot!

But hold up! I got one more question!

I really want to delete my account so badly but I can't because I forgot my password and I'm using my school email unfortunately. Anyone got a solution to my issue? :(

Answers

Answer:

I don't know the answer please tell me

Assuming that a person going to community college can't afford to go to a four-year college is an example of a) a generalization. b) discrimination. O c) a stereotype. O d) tolerance.

Answers

Answer:

a) generalization

Step-by-step explanation:

The statement is an example of a generalization. This is because the statement is assumming that all individuals who go to community college are poor. Therefore, this is why they cannot go to a four-year college, and instead go to a community college which is far cheaper. This assumption is being applied to all individuals who attend community college, without any further or more-specific information about each individual, therefore generalizing the entire situation.

Find the missing Side of the triangle

Answers

Answer:

2√15

Step-by-step explanation:

Use the Pythagorean theorem.

2² + x² = 8²

x² + 4 = 64

x² = 60

x² = 4 * 15

x = 2√15

Espanol
In the past year Christine watched 24 movies that she thought were very good. She watched 60 movies over the whole year. of the movies she watched, what
percentage did she rate as very good?

Answers

Answer:

40%

Step-by-step explanation:

She thought that 24 movies out of 60 were very good. Put the smaller number over the larger number to create a fraction:

Then convert 24/60 to a proper fraction:

24/60 = 2/5

Then, convert that to percent:

2/5 = 40%

40% because 24/60*100 is equal to 40

solve the following equations

Answers

Answer:

x=0,5/2

Step-by-step explanation:

five sutracted from x is at most -21 translate the sentence into an inequality?​

Answers

First of all, let’s look at the question. 5 subtracted from x. This means that it is 5 - x. Then, we know it is at most -21. That means that 5 - x needs to be less than or equal to -21.

Therefore, our equation is 5 - x < 21. Please note that the inequality sign should have a solid sign beneath.

Determine if the outside temperature is a function of the time of day or if the time of day is a function of temperature and explain why or why not.

Answers

Answer:

Step-by-step explanation:

Temperature is a function of the time of day. There can be only one temperature at any particular time.

In contrast, a particular temperature can occur more than one time in a day, so time is not a function of temperature.

Bà B đến ngân hàng ngày 05/05/2019 để gửi tiết kiệm 250 triệu đồng thời hạn 3 tháng, lãi suất 7%/năm, NH trả lãi định kỳ hàng tháng (kỳ lĩnh lãi đầu tiên là ngày 05/05/2019). Đến ngày 05/08/2019, bà B tất toán sổ tiết kiệm trên. Tính số tiền bà B nhận được vào ngày đáo hạn sổ tiết kiệm là? (Cơ sở công bố lãi suất là 365 ngày)

Answers

Answer:

Ask in English then I can help u

find the surface area of the prism.​

Answers

Answer:

6*8=48km....10*6=60...6*8=48....6*6=36 total =192km

Answer:

s=(2BaseArea) +(Base perimeter/hight

Does anyone know the answer??

Answers

Answer:

I think the answer is 39x, 13y

Step-by-step explanation:

point : extra points

1 : 3

y : 39

y= 39÷3

y= 13

Volunteering: The General Social Survey asked 1309 people whether they performed any volunteer work during the past year. A total of 518 people said they did. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the population proportion of people who performed volunteer work in the past year. Round the answer to at least three decimal places. The point estimate for the proportion of people who performed volunteer work in the past year is .

Answers

Answer:

The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.

Step-by-step explanation:

Point estimate of a proportion:

Proportion is the number of desired outcomes divided by the number of total outcomes.

518 out of 1309 people performed volunteer work:

This means that:

[tex]p = \frac{518}{1309} = 0.396[/tex]

The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.

is f(x)=e^-3x an exponential function?

Answers

Yes, because we have the number ‘e’ raised to x, although it is now -3x, it is still a variation of x

The sum of the lengths of any two sides of a triangle must be greater than the third side. if a triangle has one side that is 11 cm and a second side that is 1 cm less than twice the third side, what are the possible lengths for the second and third sides?

Answers

2a+2a-1>11, a>3, b=2a-1

simplify using distributive property
2396 X 78 + 2396 X 22 ​

Answers

Answer:

239600

Step-by-step explanation:

2396 × 78 + 2396 × 22 ​=2396 × (78 + 22) ​=2396 × 100 =239600

[tex]\boxed{\sf a(b+c)=ab+ac}[/tex]

[tex]\\ \sf\longmapsto 2396\times 78 +2396\times 22[/tex]

[tex]\\ \sf\longmapsto 2396(78+22)[/tex]

[tex]\\ \sf\longmapsto 2396(100)[/tex]

[tex]\\ \sf\longmapsto 239600[/tex]


Which line is horizontal?
O y=2
O y = 2x
O y = -2x
o y=x

Answers

Answer:

y=2

Step-by-step explanation:

A horizontal line has a slope of zero so the x term is zero

y = mx+b

y = b

y must equal a constant

help help......................................................................................

Answers

Hey there! Is there more text to this? I would love to help, but there is no question.

How many skirt-blouse outfits can a woman choose from if she has 5 skirts and 6 blouses?

Answers


She can have 30 different outfits/combinations

The prices of paperbacks sold at a used bookstore are approximately Normally distributed, with a mean of $7.85 and a standard deviation of $1.25.


Use the z-table to answer the question.


If the probability that Joel randomly selects a book in the D dollars or less range is 56%, what is the value of D?


$4.46

$7.75

$8.04

$8.10

(C) 8.04

Answers

Answer:

The answer you want is indeed, (C).

8.04

ED2021

Answer:

C) 8.04

Step-by-step explanation:

edge 2023

Which confidence level would produce the widest interval when estimating the mean of a population based on the mean and standard deviation of a sample of that population? A. 60% B. 70% C. 80% D. 90% ​

Answers

Answer:

D. 90%

Step-by-step explanation:

it is within the 90th percentile

The confidence level of D. 90% would produce the widest interval when estimating the mean of a population from the mean and standard deviation of a sample of that population.

What is Confidence Interval?

Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.

From the definition of the confidence interval itself, it is clear that the level with the widest interval will be the highest confidence level.

So if you need a wider interval for estimating the mean of a population from the mean and standard deviation, you need to take higher confidence level.

Here the options are 60%, 70%, 80% and 90%.

Here, the highest level is 90% which is the highest among the given levels.

Hence the confidence level is option D. 90%.

To learn more about Confidence Interval, click here :

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2.
Mr. Champion has 14 fruit trees.
He has 1 apple tree and 1 plum tree, and the rest are divided evenly
among apricot, pear, and peach trees.
Last Thursday, Mr. Champion picked 6 apricots from each apricot
tree, 10 peaches from each peach tree, 3 pears from each pear tree, and 4
apples from the apple tree.
How many pieces of fruit did Mr. Champion pick last Thursday?
(Show your work)

Answers

Answer: 80 pieces of fruit

Explanation:
Let’s find out the amount of trees Mr Champion has.
He has 14 in total. 1 apple tree and 1 plum tree, and the rest are divided evenly among apricot, pear and peach trees. This means:
1 apple tree + 1 plum tree = 2 trees
14 - 2 = 12 trees
12 / 3 (varieties of trees) = 4
In conclusion, he has
1 apple tree, 1 plum tree, 4 apricot, pear and peach trees.

Now let’s go to the section where he picks the fruit.
6 apricots from 4 trees
10 peaches from 4 trees
3 pears from 4 trees
4 apples from 1 tree

This means:
(6 x 4) + (10 x 4) + (3 x 4) + (4 x 1) = total pieces of fruit picked

24 + 40 + 12 + 4 = total pieces of fruit picked

Now, you add up those four numbers, and you have your answer, 80.



Hope this helps!

What is the mapping for a reflection in the line y=-1

Answers

Answer:

0

Step-by-step explanation:

the key mapping for a reflection in the line y=-1 is 0

Other Questions
5. A body falls freely from rest. It covers as much distance in the last second of itsmotion as covered in the first three seconds. The body has fallen for a time of:B) 5sC) 7sD) 9sA) 35 Please help explanation if possible 1. El gnero dramtico en lengua castellana surge al final del siglo XIII. 2. Las primeras manifestaciones del gnero dramtico eran piezas que se representaban en las plazas y sitios pblicos.3. La nica obra teatral de esta poca que se conserva de forma fragmentada es La Celestina. 4. La Tragicomedia de Calisto y Melibea no es una obra representable, debido a que est escrita en forma dialogada. 5. El gnero literario y tpicamente medieval al que pertenece la obra La Celestina, es la tragicomedia. 6. Dante Alighieri fue el creador de la comedia humanstica.7. Las primeras obras teatrales en castellano que se conservan son de carcter profano.8. El teatro deja los atrios de la iglesia y se traslada a las plazas de las ciudades, como elemento de diversin del pblico.9. Una de las razones por la que La Celestina se considera una novela es por la extensin de la obra.10. El autor de La Celestina es Jorge Manrique. What should be subtracted from 13/(-56) to get 11/28 Yiyi's favorite kind of comedy is the kind that wasn't supposed to be funny in the first place. What kind of film does Yiyi love mostA. slapstick comedyB. campy comedyC. situation comedyD. physical comedy What effect will replacing x with (x - 4) have on the graph of the equation y = (x - 3) ^ 2A. Slides the graph 4 units upB. Slides the graph 7 units down C. Slides the graph 4 units right D. Slides the graph 1 units A sales associate listed a condo for $205,000. A sales associate from a competing office called the listing associate to inform him of a verbal offer of $190,000 on the property. The listing associate did not present the verbal offer. Which statement applies to this situation Help mee whats the answerr :( Q: The midpoint of the line segment with the coordinates (9, -8) and (-2, 1) is _ (f^3-5f+25)-(4f^2-12f+9) What is the inverse of the function ? f(x)=x+1 over x?plato pls help me due tomorrow Co fluence fedur state? What is the responsibility of the United States as the inventor of the atomic bomb, and as a world nuclear power? How did elements get to earth? Devin volunteers at Big Pup Rescue. He is mixing up shampoo solution for the dog washing station. He needs 2 cups of shampoo concentrate for every 9 cups of water. Devin will use 36 cups of water.How much shampoo concentrate should Devin add to the water to make the shampoo solution? Last year, you purchased a stock at a price of $64.00 a share. Over the course of the year, you received $2.20 per share in dividends and inflation averaged 2.7 percent. Today, you sold your shares for $69.00 a share. What is your approximate real rate of return on this investment 4. Develop the following outlines into a beautiful story and supply a suitable title.A poor boy in a village..........walk door to door for job...........finds no job.........one day find a wallet with a large amount of money ..........find an identity card in the wallet with phone number..........a business company's owner's wallet............ decides to return it...........phones the man..........the man comes.........pleased with the boy..............gives him Rs. 1000/- as reward........... man praise his honesty... ....the man offer him a good job in his company............ works hard with honesty promoted to the post of manager...............handles the company..... becomes a co-owner of the company after the man's death........ lives a successful life.......... Jamie kept track of the total hours and minutes she worked this week at the local health food store.Monday - 3 hoursThursday - 5 hours 30 minutesSaturday - 3 hours 30 minutesSunday - 6 hours 45 minutesHow many decimal hours did Jamie work this week? (2 points)17.1118.0518.75 Need help with this last problem. Not sure what is the answer The speed of a horse is 134 meters per second how long does it takes to travel a distance of 19,311?