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svlad2 [7]
3 years ago
14

Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be model

ed by (x-2)^2=10(y-3), where x and y are measured in inches. Where is the focus of the flashlight?
Mathematics
2 answers:
Pepsi [2]3 years ago
7 0

Answer:

C is the answer

Step-by-step explanation:

I'm never wrong.

Tomtit [17]3 years ago
6 0

Answer:

F(2, 11/2)

Step-by-step explanation:

The expression:

(x-2)² = 10(y - 3)

can be rewritten in the vertex form as follows:

(x-2)² = 10y - 30

(x-2)² + 30 = 10y

1/10(x-2)² + 3 = y

General vertex form is:

y = a(x-h)² + k

then, the vertex is locate at (h, k). In this case the vertes is (2, 3), and <em>a </em>= 1/10

The focus of a parabola is located ar F(h, k+p), where <em>p</em> = 1/(4a). Replacing into these equations:

p = 1/(4*1/10) = 5/2

F(2, 3+5/2) = F(2, 11/2)

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I need to find the perimeter and area of the regular polygon.
mezya [45]
The area of a polygon is given by the formula Area = ap/2 where a is the length of the apothem and p is the perimeter. The apothem is a line from the center of the polygon perpendicular to a side.

Depending on the formula you know, you can find the length of a side in 1 of 2 ways. 

The first way uses a triangle. Using the radius of the polygon you can create 8 congruent triangles. The center angle will be 360 / 8 = 45 and two side lengths of 20. You can find the length of the base using the law of cosines.

c^2 = 20^2 + 20^2 - 2(20)(20)(cos 45)
c^2 = 400 + 400 - 800(cos 45)
c^2 = 800 - 800(cos 45)
c = sqrt(800 - 800(cos 45)
c = 15.31

The second way is to use this formula:
r = s / (2 sin(180 / n))
20 = s / (2 sin(180/8)
(20)(2)sin(22.5) = s
(40)sin(22.5) = s
s = 15.31

We need to calculate the perimeter. As there are 8 sides (8)(15.31) = 122.48
Now we need to calculate the apothem using

a = S / (2 tan (180 / n)
a = 15.31 / (2 tan (180 / 8))
a = 18.48

Now solve for the area

Area = ap/2
Area = (18.48)(122.48)/2
Area = 1131.72

perimeter = 122.48
area = 1131.72
7 0
3 years ago
Convert the angle theta=7/4pi radians to degrees
bagirrra123 [75]
7/4pi multiplied by 180/pi give you about 97 degrees when you calculate it.
7 0
3 years ago
If f (x) = 4x - 11 , What is the value of f(5)<br> a. 20x - 55<br> b. 34<br> c. 9<br> d. 4
kramer

Answer:C

Step-by-step explanation:

C

5 0
3 years ago
Rationalization<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B6%7D%7B%20%5Csqrt%7B3%7D%20%7D%20" id="TexFormula1" title=" \f
rosijanka [135]

Answer:

2√3

Step-by-step explanation:

To rationalize, we multiply the denominator and numerator by the surd at the base

We have it that;

6/√3 * 1

= 6/√3 * √3/√3

= 6 √3/3 = 2√(3

7 0
3 years ago
Solve<br> Log(x-1)+log(2)=7
Rudiy27

Answer:

x is 6 i believeee if you're solving for x!!

Step-by-step explanation:

5 0
3 years ago
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