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Nikitich [7]
2 years ago
14

Someone help with this I’m gonna fail !

Mathematics
1 answer:
Dafna1 [17]2 years ago
7 0
The answer is option D
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A radio telescope has a parabolic surface, as shown below.
krek1111 [17]
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.
5 0
2 years ago
A right triangle has side lengths of 0.6 meter and 0.8 meter. What is the length of the hypotenuse? Round to the nearest tenth.
Sonja [21]

Use the Pythagorean theorem since you are working with a right triangle:

a^2+b^2=c^2a2+b2=c2

The legs are a and b and the hypotenuse is c. The hypotenuse is always opposite the 90° angle. Insert the appropriate values:

0.8^2+0.6^2=c^20.82+0.62=c2

Solve for c. Simplify the exponents (x^2=x*xx2=x∗x ):

0.64+0.36=c^20.64+0.36=c2

Add:

1=c^21=c2

Isolate c. Find the square root of both sides:

\begin{gathered}\sqrt{1}=\sqrt{c^2}\\\\\sqrt{1}=c\end{gathered}1=c21=c

Simplify \sqrt{1}1 . Any root of 1 is 1:

c=c= ±11 *

c=1,-1c=1,−1

4 0
2 years ago
PLEASE HELPPP I TOLD MY MOM I WOULD BE DONW ITH THIS CLASS TODAY SO SHE WOULDNT YELL AT ME BUT I HAVE 54 ASSIGNMENTS
Scrat [10]
(x^2+1)(x+2)(x −2)

*ps the ^ means it’s a exponent

Hope I helped <3 sorry if I was wrong :(
8 0
2 years ago
-54 + 108 =<br> Thank you!
julsineya [31]

Answer: 54 and welcome

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Select the correct answer.<br> Which number has a repeating decimal form?
Dmitry_Shevchenko [17]

Answer:

D: 2/6

Step-by-step explanation:

2/6= 0.333333 repeating

8 0
3 years ago
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