1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
maksim [4K]
2 years ago
10

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

Mathematics
1 answer:
krek1111 [17]2 years ago
5 0
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.
You might be interested in
If M = 5x2 + 7x-4 and N = -3x2-4x+5, then M -N equals
Yuki888 [10]

Answer:

M-N=4

Step-by-step explanation:

6 0
3 years ago
The diameter of a circle is 18 in. 4x +5 represents the radius. Write two equations that you can find the value of x. Then find
Firdavs [7]
A and C are the formulas to use
7 0
3 years ago
Divide: 83.5 ÷ 6.25 The first step in solving 83.5 ÷ 6.25 is to multiply the divisor and dividend by . The new division problem
kherson [118]

Answer:

The first step in solving 83.5 ÷ 6.25  is to multiply the divisor and dividend by  

[✔ 100 ]

sorry idk the answer for the second one :(

Step-by-step explanation:

7 0
3 years ago
While cooking a stew, Jim used 2/3 of a shaker of salt and 7/12 of a shaker of pepper. How
Juli2301 [7.4K]

Answer:

he used one 1/12 more of salt.

Step-by-step explanation:

2/3 I know equals 8/12

And

7/12 = 7/12 so

You just do

8/12 - 7/12 = 1/12

8 0
2 years ago
The graph shows how much water is coming out of a faucet over time. How many gallons of water will flow if the faucet runs for 3
zhenek [66]
The answer is 2 gallons
3 0
3 years ago
Read 2 more answers
Other questions:
  • If 8 identical blackboards are to be divided among 4 schools, how many divisions are possible? how many if each school must rece
    10·1 answer
  • Pablo ran a concession stand last Saturday and made $79.80 from selling a total of 53 hot dogs and hamburgers. Each hot dog sold
    12·1 answer
  • Find the quotient of these Complex Numbers. <br><br><br> (5-i) / (3+2i)
    9·1 answer
  • Find the product of 51 and -2.5
    6·2 answers
  • Need help can someone explain this problem<br>please.​
    5·1 answer
  • The triangular banner Inez is
    10·1 answer
  • Will give brainlessst if you answer plsssss
    14·1 answer
  • You need to put a, b, c, d in the right four spots
    10·2 answers
  • A prime number has two factors, itself and 1? *
    9·1 answer
  • Write a linear equation to describe the number pattern that starts with –8 and continues with negative multiples of 8. PLEEEEEEE
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!