A radio telescope has a parabolic surface, as shown below.

A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 9 meters and its width from left to right is 12 meters.

If the telescope is 9 m deep and 12 m wide, how far is the focus from the vertex?

Answers

Answer 1
OK, so the graph is a parabola, with points x=0,y=0; x=6,y=-9; and x=12,y=0

Because the roots of the equation are 0 and 12, we know the formula is therefore of the form

y = ax(x - 12), for some a

So put in x = 6

-9 = 6a(-6)

9 = 36a

a = 1/4

So the parabola has a curve y = x(x-12) / 4, which can also be written y = 0.25x² - 3x

The gradient of this is dy/dx = 0.5x - 3

The key property of a parabolic dish is that it focuses radio waves travelling parallel to the y axis to a single point. So we should arrive at the same focal point no matter what point we chose to look at. So we can pick any point we like - e.g. the point x = 4, y = -8

Gradient of the parabolic mirror at x = 4 is -1

So the gradient of the normal to the mirror at x = 4 is therefore 1.

Radio waves initially travelling vertically downwards are reflected about the normal - which has a gradient of 1, so they're reflected so that they are travelling horizontally. So they arrive parallel to the y axis, and leave parallel to the x axis.

So the focal point is at y = -8, i.e. 1 metre above the back of the dish.

Related Questions

Type the correct answer in the box. Round your answer to the nearest hour. A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula , where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number. It takes 15 hours for the number of bacteria to increase to 300.

Answers

Answer:

so 15 hour for the 100 to become 200 and then it will become 400 in another 15 hours. but we need to find the time for 300 so it will take half of 15 hours

+ 15 hours for it to become 300 cells which is: 7 1/2 + 15 = 22 hours and 30 minutes

Step-by-step explanation:

answer from gauth math

Answer:

22 hours and 30 minutes

Step-by-step explanation:

In a well-shuffled, standard 52 card deck, what is the probability that a card is a Queen, given that it is a black card

Answers

There are two black queens in a standard deck, so the probability is 2/52 or 1/26.

If instead you know you pulled a black card from the deck and you’re wondering what the probably is that it’s a queen, then it’s 2/26, since there are still 2 black queens, but only 26 black cards.

Answer:

2/52

Step-by-step explanation:

How do you convert 3.2 (2 repeating) as a fraction?

Answers

Answer:

3+2/9 = 29/9

Step-by-step explanation:

examples:

4/9 = 0.444444

8/9 = 0.888888

3/9 = 0.3333333

7/9 = 0.777777

1/9 = 0.111111111

2/9 = 0.22222222

80/99 = 0.808080

67/99 = 0.6767676767

44/99 = 0.4444444

12/99 = 0.1212121212

345/999 = 0.345345345

i think you get the point.

so we know 2/9 = 0.22222, so now just add a 3:

3+ 2/9 = 27/9 + 2/9 = 29/9

Question is in the picture

Answers

9514 1404 393

Answer:

x = 3y = 9

Step-by-step explanation:

Congruent sides are the same length.

  AB = DF

  3(2x +10) = 12x +12

  6x +30 = 12x +12 . . . . eliminate parentheses

  18 = 6x . . . . . . . . . . . . subtract 6x+12

  3 = x . . . . . . . . . . . . . divide by 6

__

  BC = FG

  2y +12 = 2(2y -3)

  y +6 = 2y -3 . . . . . . . divide by 2

  9 = y . . . . . . . . . . . . subtract y-3

Find three irrational numbers between
0.53 and 0.54

Answers

Answer:

Step-by-step explanation:

You could use anything that does not change the value of 3 in 0.53 or the 4 in 0.54

So for example

0.533

0.536

0.538

all would make the sentence above true.

Answer:

0,533(3); 0,53111(1); 0,53222(2)

Step-by-step explanation:

a is a number to find

0,53<a<0,54

=>a ∈ { 0,53111(1); 0,53122(2);....;0,5399(9)}

can i use a cash counter as a cashier. As in a website on my phone that tells me the exact change to give out to a person

Answers

seems pretty accurate so sure. it’s really hard to count up a lot of change so that’s helpful however if it’s not permitted then Sox

Patrick is a loan officer at a bank. He has
$2,000,000 to lend out and has two loan programs.
His home equity loan is currently priced at 6% per
annum, and his unsecured personal loan is priced
at 14%. The bank president wants Patrick to earn
a rate of return of 12% on the $2,000,000 available.
How much should Patrick lend out at 6%?

Answers

Answer:

1,500,000 at 14% and 500,000 at 6%

Step-by-step explanation:

x + y = 2,000,000

.14x + .06y = 240,000

[tex]0.14x+0.06\left(2000000-x\right)=240000\quad :\quad x=1500000[/tex]

When g ( t ) = 3 t 2 + 2 t + 1 , evaluate g ( − 4 )

Answers

Answer:

Just substitue every 't' with -4

Step-by-step explanation:

g(-4) = 3*(-4)*(-4) + 2*(-4) + 1

g(-4) = 64-8+1

g(-4) = 57

Answer:

g(-4) is 41

Step-by-step explanation:

[tex]g(t) = 3 {t}^{2} + 2t + 1[/tex]

when t is -4, substitute -4 in place of t:

[tex]g( - 4) = 3 {( - 4)}^{2} + 2( - 4) + 1 \\ g( - 4) = 48 - 8 + 1 \\ g( - 4) = 41[/tex]

Ryan, a consumer electronics​ salesperson, earns a base salary of ​$1100 per month and a commission of 8​% on the amount of sales he makes. One month Ryan received a $1492 paycheck. Find the amount of his sales for the month.

Answers

1100 times 1492, I’m not sure but I hope it helped!

The points A(− 7,-8) and B(18,-8) are the two vertices of an isosceles triangle ABC, where AB=BC. The equation of the perpendicular from B to AC is 4x+3y= 48, try to find the coordinates of point C

Really need some help with this, thank you very much.​

Answers

Answer:

HOPE THIS ANSWER WILL HELP YOU

Been stuck on this one. Sos

Answers

Answer:

B. 50%

Step-by-step explanation:

7/20 = 35%

35% + 15% = 50%

100% - 50% = 50%

what is the standard deviation for city A and city B

Answers

Answer:

$0.8426

Step-by-step explanation:

steps are in the picture above.

Note:if you need to ask any question please let me know.

Find the 50th term of the following
arithmetic sequence 5, 9, 13, 17?

Answers

Answer:

201

Step-by-step explanation:

First you need to know the position to term rule and to find this you use a formula which is:

tn = an + b

Where tn is the term number,  a is the difference between the other terms.

So the tposition to term rule here is 4n+1.

Then we substitute n for the value 50 making it 4(50) + 1 = 201.

201 is the 50th term

Use a commutative property to write an equivalent expression.
7x + y

Answers

9514 1404 393

Answer:

  y +7x

Step-by-step explanation:

The commutative property of addition lets you swap the order of the two terms:

  7x +y = y +7x

The commutative property of multiplication lets you swap the order of the factors.

  7x +y = x·7 +y

i need help answering the question in the picture provided

Answers

answer:

(a).

Equation of circle is x² + y² - 25 = 0

(b).

(-5, 0) » yes

(√7, 1) » no

(-3, √21) » no

(0, 7) » no

Step-by-step explanation:

(a).

If centred at origin, centre is (0, 0)

General equation of circle:

[tex]{ \boxed{ \bf{ {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0}}}[/tex]

but g and f are 0:

[tex] {x}^{2} + {y}^{2} + c = 0 \\ but : \\ c = {g}^{2} + {f}^{2} - {r}^{2} \\ c = { - 25} [/tex]

A statement that consistently and correctly describes a natural phenomenon is a scientific.

A. Control

B. Theory

C. Hypothesis

D. Observation

Answers

B. Theory
hope this helps

When 59,527 is divided by 23, the quotient is 2,588 R ___.

Answers

Answer:

3

Step-by-step explanation:

When 59,527 is divided by 23, the quotient is 2,588 R3.

Hope this helps! :)

How many cubes of side 2cm can be fitted into a box 12 cm long, 8cm wide and 4cm high?

Answers

Answer:

there are 48cubes fetted into a box

The answer is 48.
You find the volume of the box - 12 X 8 X 4 = 384
Find the volume of the Cube with side 2 cm - 2 X 2 X 2 = 8
344 divided by 8 = 48
Therefore, 48 cubes would fit into the box

write 0.8 as a fraction in simplest form.

Answers

The answer would be 8/10, but the simplified answer would be 4/5. I hope this helped answer your question for you. Enjoy your day, and take care!

4/5. Hope this helps!

Use the number line to find a fraction that equals to 1/2

Answers

2/4 is equivalent to 1/2.
2/4, 3/6, 4/8, 6/12, etc

E is the mid point of DF. If DE= 7x. What is the length of DE

Answers

Answer:

I think you're missing information and don't you mean "what's the length of DF?"

Help please ASAP!!!!!

Answers

Answer:

answer is c because you gota tranlate it left

Step-by-step explanation:

Please help will give brainliest

Solve the equation.
-(x + 2) – 2x = -2(x + 1)
x = [?]

Answers

Answer:

x = 0

Step-by-step explanation:

-(x + 2) – 2x = -2(x + 1)

-x-2-2x = -2x-2

-3x-2 = -2x-2

-3x+2x = -2+2

x = 0

Answer:

x = 0

Step-by-step explanation:

-(x + 2) – 2x = -2(x + 1)

=> - x - 2 - 2x = -2x - 2

=> - 2 + 2 = - 2x + 2x + x

=> 0 = x or x = 0 (Ans)

Which of the following is the smallest number?
O 7.8* 102
O 2.36 * 10-3
O 1.94 * 105
04.19* 109

Answers

here’s your answer :the second one is smallest number,
the answer is the second option!!

i need to know whether it is the minimum or maximum function and what that number is as well as where x axis intercepts the quadratic graph . i need to know if there are any roots in the quadratic graph, and i need to know when y=1 , the value of x could be x= or x=

Answers

Answer:

The minimum value of this quadratic function is -4.

At the point (-4, 0), the x-axis intercepts with the quadratic graph.

There is 1 root of this quadratic equation.

Approximately, when y=1, the x value could be -5 or -3.

I don't exactly remember how to do this

Answers

Answer:

29 or D

Step-by-step explanation:

You square both sides to get

7 + y = 36

You then subtract 7 from both sides to get

y = 36 - 7

y = 29

pls help..

10 Round off 843 426 to the nearest thousand.

Answers

Answer:

843,000

Step-by-step explanation:

Go to the thousandth’s place and look to the right and determine wether to round up or down depending if the number is greater than 4 or less than 5

What is the cube of the cube root of 27?​

Answers

Answer:

[tex] { \sqrt[3]{27} }^{3} \\ we \: can \: solve \: this \: in \: two \: ways \\ 1)cube \: root \: means \: power \frac{1}{3} \\ so \: { \sqrt[3]{27} }^{3} = { {27}^{ \frac{1}{3} } }^{3} = {27}^{ \frac{3}{3} } = 27 \\ 2) { \sqrt[3]{27} }^{3} \\ \sqrt[3]{27} = 3 \\ so \: {3}^{3} = 27 \\ thank \: you[/tex]

Write an absolute value equation with-1 and 5 as the solution.

Answers

Answer:

it is detailed solution. please mark brainlest.

Thank you have a nice day

The equation of the absolute function that has the solutions of -1 and 5 will be |x - 2| = 3.

What is an absolute function?

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The absolute function is given as

f(x) = | x |

The solutions of the absolute function are -1 and 5. Then the equation of the absolute function will be

x = -1, 5

Subtract -2 from both sides, then we have

x - 2 = -3, 3

Then apply Mode on both sides, then the equation will be

|x - 2| = 3

The equation of the absolute function that has the solutions of -1 and 5 will be |x - 2| = 3.

More about the absolute function link is given below.

https://brainly.com/question/10664936

#SPJ2

Ms. Drew wants to build a square sand box with an area of 225 sq ft what is the lenght of woods she needs

Answers

15 ft because a square all four sides are the same and 15 x 15 equals 225
Other Questions
True or False? Wireless connections that use a higher frequency are faster but have a shorter range.TrueFalse what is the chemical formula of ( Rust ) ?? How is climate change effecting landformspls help Please Help Asap!! I will mark brainliest for the best answer!!Explain 3 major demographic changes caused by the industrial revolution. A cell can form beads on a string chromatin, but not solenoid fibers. Which molecule has likely been removed or mutated in this cell?a. 1 b. non-histone proteins c. H2A d. topoisomerase Help anyone can help me do this question,I will mark brainlest.The question (g) is P(p,4p),Q(-2p,8p)(h) is R(-2m,5m),S(-4m,-2m) Why are marketers putting so much emphasis on developing strong brands? Q: Predict the final masses of the following dialysis tubes. Find the length of the segment AB. Plz help!!! Ill give you brainliest. 5 thousand is - times as many as 5 hundred 3. A ball is dropped initially from a height of 1.2 m. The rebound from the floor is 3/5 of the previous height. (a) Find the height to which the ball rises at the 2nd bounce. (b) Find the total distance that the ball has travelled when it hits the floor for the tenth time. (c) Assuming that the ball continues to bounce in the same way indefinitely, find the total distance that the ball travels. What is 33.83 x 99.21 Explain how increasing the temperature increases the rate of the reaction Select all that apply please! Given f(x) = 2x+1 and g(x) = 7/4x + 1 what is the value of f(1)-g(-4)A) -3 B) 3 C) 9 D) -9 He sent me a trailer load of wishes what figure of speech is used plz help me I need help How to solve with logarithms?See image please Electrons could be swiped off of theoutermost shell of the electronTrueFalse Find the vertex of the graph of the function. f(x) = (x - 10)2 - 8 (2 points) A. (10, -8)B. (-8, 0) C. (0, 10)D. (-8, 10)