A searchlight is shaped like a paraboloid of revolution. If the light source is located 4 feet from the base along the axis of symmetry and the opening is 20 feet​ across, how deep should the searchlight​ be?

Answers

Answer 1

Answer:

The searchlight should be 6.25ft deep

Step-by-step explanation:

Given

[tex]Across = 20ft[/tex]

[tex]Base = 4ft[/tex]

Required

The depth of the searchlight

[tex]Across = 20ft[/tex] implies that the search light span 10 units to either side of the x-axis

[tex]Base = 4ft[/tex] implies that the search light span 4 units to the y-axis

The attached image illustrates the revolution.

From the attached image, the endpoints of the searchlight is:

[tex](x,y) = \{(-10,4), (10,4)\}[/tex]

The depth (a) of the search light is calculated using:

[tex]x^2 = 4ay[/tex]

Make a the subject

[tex]a = \frac{x^2}{4y}[/tex]

Substitute -10 or 10 for x and 4 for y

[tex]a = \frac{(-10)^2}{4*4}[/tex]

[tex]a = \frac{100}{16}[/tex]

[tex]a = 6.25ft[/tex]

A Searchlight Is Shaped Like A Paraboloid Of Revolution. If The Light Source Is Located 4 Feet From The

Related Questions

A $550 T.V is discounted by 30%. It is then discounted another 10%

Answers

Answer:

$346.5

Step-by-step explanation:

10% of $550 is 55

3*55 = 165

550 - 165 = $385

10% of $385 is 38.5

385 - 38.5 = $346.5

Have a nice day! :-)


What is the average of the integers from 25 to 41?
27
33
36
66

Answers

Answer:

B. 33

Step-by-step explanation:

The average of the terms of a contiguous subsequence of any arithmetic progression is the average of the first and last terms.

To see this, notice that if you remove  25  and  41 from your sequence, then the average of the remaining terms is still given by the average of the extreme terms

Is the point (4,11) a solution to the following system of equations? How do you know?
y=2x+14
y=3x−5

Answers

No because when you plug in the ordered pair to either equation it doesn’t work. Y=2x+14 would go to 11=2(4)+14 and you would get 11=22 which is wrong. Again with y=3x-5 would be 11=3(4)-5; 11=7 which is wrong again.

find the slope(4,9),(1,6)
plz help

Answers

Answer:

slope: m = 1

Step-by-step explanation:

Can somebody recommend me some horror, psychological, yandere, and/or thriller anime?

Anything besides these would be appreciated:

1. Angels of Death
2. Shiki
3. Re:Zero
4. Corpse Party
5. Magical Girl Site
6. Happy Sugar Life
7. SCHOOL-LIVE!
8. Talentless Nana
9. Higurashi
10. Wonder Egg Priority
11. Shadows House
12. Blood C
13. To Your Eternity
14. Puella Magi Madoka Magica
15. Another
16. The Lost Village
17. Serial Experiments Lain
18. Chaos;Head

Answers

Answer:

the future diary  

Step-by-step explanation:

I watched Future Diary on Hulu, its a really good anime, its more of a yandere type of anime, hope you enjoy it!

what is 2+2 4+4 8+8 i need math help

Answers

Answer:

2+2 is 4 4+4 is 8 8+8 is 16

Step-by-step explanation:

if you need them added up here: 4+8 =12 12+16 = 28

KHAN ACADEMY HELP pls

Answers

Answer:

image

Step-by-step explanation:

plzzz give me brainliest

Find the number of degrees in the missing angle of each triangle below

Answers

Answer:

A=44

B=58

C=103

D=118

E=138

F=22

Step-by-step explanation:

Hope this helps

Suppose that 40% of cars in your area are manufactured in the U.S., 30% in Japan, 10% in Germany, and 20% in other
countries. Determine the following probabilities.
a. a car selected at random is made in Germany or Japan
b. a car selected at random is not US-made
c. two cars are selected at random, both are from Japan
Complete your work in the space provided or upload a file that can display math symbols if your work requires it. Include
your calculations in your answer.

Answers

Answer:

A)  The probability that a randomly chosen car is made in Germany or Japan is 40%.

B)  The probability that a car chosen at random is not made in the United States is 60%.

C)  The probability that two randomly chosen cars are both from Japan is 9%.

Step-by-step explanation:

Supposing that 40% of cars in my area are manufactured in the US, 30% in Japan, 10% in Germany, and 20% in other countries, to determine the probabilities that a car selected at random is made in Germany or Japan, a car selected at random is not US-made and two cars are selected at random, both are from Japan, the following calculations must be performed:

A)

(30 + 10) / 100 = X

40/100 = X

0.4 = X

Therefore, the probability that a randomly chosen car is made in Germany or Japan is 40%.

B)

(30 + 10 + 20) / 100 = X

60/100 = X

0.6 = X

Therefore, the probability that a car chosen at random is not made in the United States is 60%.

C)

10/30 x 10/30 = X

0.3 x 0.3 = X

0.09 = X

Therefore, the probability that two randomly chosen cars are both from Japan is 9%.

Somebody Please help!!!

Answers

Answer:

176

Step-by-step explanation:

8+8+64+64+16+16

Drag numbers into the blanks to rewrite the square roots.
square root -5 (it doesnt let me put the symbol. whats the answer?

Answers

Answer:

Step-by-step explanation:

for a lot of math classes they just tell you  "don't take the square root of a negative number"   Then when you see this   [tex]\sqrt{-5}[/tex]  it looks all wrong.  But,  just think of the two things under the radical as

[tex]\sqrt{-1*5}[/tex]

now, take the  -1 out of the square root as   "  i  "

i[tex]\sqrt{5}[/tex]

and if you want to put it into correct complex form

0 + i[tex]\sqrt{5}[/tex]

Please help me with this:

A teacher decorated her classroom with 3 times as many balloons as paper fans. She used 12 fewer streamers than twice the number of paper fans. If the teacher had a total of 120 balloons, paper fans, and streamers, how many of each kind of decoration did she use?

Answers

Answer:

She used 22 paper fans, 66 balloons, and 32 streamers.

Step-by-step explanation:

In order to solve this problem, we need to find out the value of the paper fans. Because we need to find out the balloon amount, which is 3 times as much. The amount of streamers is 12 fewer than two times. We can't find it out just yet since we don't know the value of the paper fans. To find it out:

First, let's call the amount of paper fan as "x".

Then, we need to find out the amount of balloons. It is 3 times x. Which is the same as 3x.

The equation is now x + 3x + (?) = 120

We need to find out the amount of the (?).

So, to do that, it says the value is 12 fewer than 2 times the value of x. (x, because it is the amount of paper fans.)

It should be 2x-12.

Now, the equation is x+3x+2x-12=120.

Once we solve it, we know "x" is 22.

Now, we can multiply 3 by 22. Which is 66.

Then we can multiply 22 by 2, which is 44, and subtract 12, which is 32.

To double check, 22 + 44 + 32 = 120.

That's your answer!

Answer:

Step-by-step explanation:

its 22, and 66, and 32

Mr. Thompson is buying rulers for his class.
Which option gives Mr. Thompson the best price per ruler?
A. 4 rulers for $1.00
B. 50 rulers for $15.00
C. 100 rulers for $20.00
D. 200 rulers for $30.00

Answers

Answer:

D: 200 rulers for $30.00. You have quite a few choices! You may need to find out the percentage [%] of each first.

Step-by-step explanation:

A: 1 Ruler for $0.25

B: $0.30

C: $0.20

D: $0.15

Find the volume of the cube below

Answers

the answer to this question is 27

What voltage is required to force 4.5 amperes of current through an electric iron having a resistance of 25.5 ohms

Answers

Answer:

V = 114.75 Volts

Step-by-step explanation:

Ohm's Law   V = IR

I = 4.5 A

R = 25.5 Ω

V = (4.5)(25.5)

V = [4×25.5] + [0.5×25.5]

V =  102 + 12.75

V = 114.75 Volts

What is the probability that I will roll a 4 on a standard number cube?

Answers

Answer:

the probability of rolling any single digit on a 6-sided fair cube is 1/6

To roll a 4 on a standard number cube is 1/6

Select the ratio equivalent to tan(A).


A. 5/13
B. 5/12
C. 13/12
D. 12/5

Answers

The answer is a or c

Find the volume of the cylinder. Round your answer to the nearest tenth.

Answers

Answer: 125.6 inches cubed.

Step-by-step explanation:

Formula for cylinder volume: Volume=(pi times radius cubed) times height

3.14 x 4(radius)=12.56

12.56 x 10 (height) = 125.6

Hope this helps

Katy put $3000 into his bank account.  If the account pays 6% interest compounded continuously, when will it be worth $6000?   Round to 3 decimal places.​

Answers

Answer:

11.55 years

Step-by-step explanation:

Given data

Principal= $3000

Rate= 6%

Final Amount= $6000

expression for the time is given as

t = ln(A/P) / r

Substitute

t= ln(6000/3000)/0.06

t= ln(2)/0.06

t= 0.693/0.06

t= 11.55 years

Hence the time is 11.55 years

Simplify the expression:
9f2 - 10 - 1 + 2/2 + -772​

Answers

Answer:

4f^2-11

Step-by-step explanation:

3360832553 ____ pass___ wZE2XQ​

Answers

Answer:

what is this?

Step-by-step explanation:

if you elaborate I am more then happy to help

Answer:

.

Step-by-step explanation:

-12+2(-4)-7= help me understand how to figure out how to get this answer

Answers

Answer:

- 27

Step-by-step explanation:

- 12 + 2( - 4) - 7

- 12 - 8 - 7

-20 - 7

- 27

geometry help pleaseeee

Answers

Answer: 11

Step-by-step explanation:

[tex]48=4x+4[/tex] (angles opposite congruent sides in a triangle are congruent)

This gives that x = 11

In APQR, T, U and S are points of tangency. PR = 12 units. Find TR.

Answers

Answer:

TR = 3 units

Step-by-step explanation:

PR = 12 units

PS = 9 units

PU = PS = 9 units (tangents drawn from an external point are congruent)

RU = PR - PU

RU = 12 - 9

RU = 3 units

TR = RU = 3 units (tangents drawn form an external point of a circle)

TR = 3 units

Write the equation in standard form of the circle whose diameter has endpoints of (-2, 4) and (8,-6).

Answers

Answer:

(x - 3)^2 + (y + 1)^2 = 50.

Step-by-step explanation:

The center of the circle is the midpoint of the diameter

= (-2+8)/2 , (4 - 6)/2

= (3, -1).

The radius^2  can be calculated from one point on the circle ( -2, 4) and the center (3, -1).

The radius^2 =  (-2-3)^2 + (4- -1)^2

= 25 + 25 = 50.

So the equation of the circle

is (x - a)^2 + (y - b)^ = r^2   where (a, b) is center and radius = r.

= (x - 3)^2 + (y + 1)^2 = 50

The base of the sandbox is shaped like a parallelogram. He parallelogram base has an area of 9 square feet and the sand box gas a volume of 13.5 cubic feet. What is the height of the sandbox?

Answers

Answer:

1.5 feet

Step-by-step explanation:

V = base area x height

divide the two members by the base area

height = V/ base area

height = 13.5 / 9 = 1.5 feet

19 students were surveyed on the number of hours of Netflix they watched last week.

The data from the survey is below:

{0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 10, 11}

What is the range in hours spent watching Netflix?

Show your work for full points!

Answers

Answer:

Solution given:

lowest =0

highest=11

the range in hours spent watching Netflix=

highest-lowest =11-0=

Range is 11.

Answer:

Solution : here ,

lowest = 0

Highest = 11

the range in hours spent watching Netflix

=highest — lowest

= 11 —0

= 11

the range = 11

hope it is helpful to you

If the graph of y = - x ^ 2 translated horizontally 7 units to the right and translated vertically 6 units upwards, what’s the new equation?

Answers

9514 1404 393

Answer:

  y = -(x -7)² +6

Step-by-step explanation:

Replacing x with (x-h) translates the graph h units to the right. You want h=7.

Replacing f(x) with f(x)+k translates the graph k units upward. You want k=6.

These transformations make the new equation be ...

  y = -(x -7)² +6

Plz help this is urgent

Answers

Answer:

D

Step-by-step explanation:

The table represents some points on the graph of a linear function.

What is the slope of the graph of the linear function?

Answers

Answer:

1 over 2

Step-by-step explanation:

9-(-7)=-2

-8-(-4)-4

-6-(-3)=-3

-2-4=-6

When you simplify both of the fractions -2 over -4 and -3 over -6

You get 1 over 2 as the slope for both. 1/2

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