A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one sheet. The diameter at the base is 260 m and the minimum diameter, 500 m above the base, is 180 m. Find an equation for the tower. (Assume the position of the hyperboloid is such that the center is at the origin with its axis along the z-axis, and the minimum diameter at the center.)

Answers

Answer 1

Answer:

(x/90)² + (y/90)² - z²/343750

Step-by-step explanation:

we assume that the horizontal cross-sections are circles,

From our equation

a= b

Given the minimum diameter as 180

The trace= ,0

Minimum radius a= 180/2= 90

The base of the tower is the trace in Z = -500

using the equation of hyperbole of one sheet below

(x/a)² + (y/b)² - ( (z/c)²=1

a= 90

+((-500)²/c)²

x² +y²=90²+ 55000²/c²

diameter at base= 260/2=130m

130² + 55000²/c²= 130²

We can find c

c²=55000²/(130²/90²) = 1210000/8800

= 343750

hence, the equation is

(x/90)² + (y/90)² - z²/343750


Related Questions

Leora had some money in her wallet. She spent $18.62 buying groceries and had $43.55 left. How much money did she have in her wallet before she bought the groceries?
$24.93
$35.93
$45.41
$62.17

Answers

Answer:

62.17

Step-by-step explanation:

you add 18.62 to 43.55 and get 62.17.

hope this helps.

Answer:

62.17 boom

Step-by-step explanation:

Solve the inequality. 6x + 14 > 20
???????

Answers

Answer:

x > 1

Step-by-step explanation:

6x + 14 > 20

      -14    -14

6x > 6

/6    /6

x>1

Simplify the expression. (5x^3+4x^2+6x-3)+(-2x^3+3x^2-7x+9)-(5x+3)(4x^2+x-1)

Answers

Answer:

-17x³-10x²+x+9

Step-by-step explanation:

(5x³+4x²+6x-3)+(-2x³+3x²-7x+9)-(5x+3)(4x²+x-1)

(5x³+4x²+6x-3)+(-2x³+3x²-7x+9)-(20x³+5x²-5x+12x²+3x-3)

(3x³+7x²-x+6)-(20x³+17x²-2x-3)

-17x³-10x²+x+9

Factorise Fully x^2 + x

Answers

Answer:

X(x+1)

Step-by-step explanation:

If it is wrong I'm sorry.

An environmental study of a certain community suggests that t years from now, the average level of carbon monoxide in the air will be Q(t)=0.05t^2 + 0.1t + 3.4 parts per million. By approximately how much will the carbon monoxide lvel change during the coming 6 months?

Answers

Answer:

3.4625

Step-by-step explanation:

Given the equation:

Q(t)=0.05t^2 + 0.1t + 3.4 parts per million

Where t = time in years

By approximately how much will the carbon monoxide lvel change during the coming 6 months?

t = 6 months = 6/12 = 0.5 year

Q(0.5) = 0.05(0.5)^2 + 0.1(0.5) + 3.4 parts per million

Q(0.5) = 0.05(0.25) + 0.05 + 3.4

Q(0.5) = 0.0125 + 0.05 + 3.4

Q = 3.4625

Carbon monoxide level will change by approximately 3.4625 parts per million in 6 months

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

Answers

Answer:

4

Step-by-step explanation:

f(g(x)) = 3(x-2) + 10

f(g(0)) = 3x - 6 + 10

f(g(0)) = 3(0) - 6 + 10

f(g(0)) = 0 - 6 + 10

f(g(0)) = 4

Sita Rahim drove due north for 3 hours at 46 miles per hour. From the
same spot, Yasmina Young drove due south for 2 hours at 43 miles per
hour. How far apart were they after their trip?

Answers

Answer:

224 miles

Step-by-step explanation:

What you would do is take the 3 hours times the 46 mph to get 138 miles.

3*46=138

Next, multiply the 2 hours by the 43 mph to get 86 miles.

2*43=86

Lastly, you're going to add the two.

138+86=224 miles.

what is the expression equivalent to 5(6+4)​

Answers

Answer:

2(15+10)

Step-by-step explanation:

when you multiply the integers by 5 you get 30 + 20 so you just divide them by 10.

Answer
50
How to get it
So start to add in the parenthesis 6+4 is 10
Then erase the parentheses since we got the answer but turn it into an multiplication sign
5 times 10 is 50
Hope this helped :)

Find the distance between the points (-3,-6) and (-3,-2)

Answers

Answer:

The answer is

4 units

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3,-6) and (-3,-2)

The distance is

[tex]d = \sqrt{( { - 3 + 3})^{2} + ({ - 6 + 2})^{2} } \\ = \sqrt{ {0}^{2} + ({ - 4})^{2} } \\ = \sqrt{16} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

We have the final answer as

4 units

Hope this helps you

Answer: the answer is 4 units

Explanation: it is 4 units because since they are both on the x axis and 6 - 2 is equal to 4. It’s four units.

What is the quotient?
5^-6
5^3

Answers

Step-by-step explanation:

1/5^(3+6)= 1/5^9

the solution

Step-by-step explanation:

1/5^(3+6)=1/5^9

the solution

Brian saw 106 birds and half as many squirrels. Which of the following is a good estimation of how many more birds he saw than squirrels?

Answers

Answer:

53

Step-by-step explanation:

PLEASE HELP
Twice a number n is at least 30

Answers

Answer: n = 15

Step-by-step explanation: 2x15 = 30

Answer:

15

Step-by-step explanation:

15 times 2 is 30. Therefore, 15 can be the correct answer!

Please mark me brainliest if I helped you! Thank you so much!

:)

What is 3/8-2 what does it equal

Answers

Answer:

the answer would be -1 5/8 in fraction form and -1.625 in decimal form

Answer:

-13/8

Step-by-step explanation:

2 = 16/8

3/8-16/8 = -13/8

Which line is perpendicular to y=7x-3 if the perpendicular line passes through the point (7, 7)? a) y=-7x-1 b) y=-7x+8 c) y=-1/7x+8 d) y=-1/7x+1

Answers

Perpendicular lines have an opposite reciprocal slope, therefore, the slope of the perpendicular line is:

-1/7

So far, y = -1/7x + b. Now we need to plug in (7, 7) into x and y for our equation.

7 = -1/7(7) + b

Simplify the right side

7 = -1 + b

Add 1 to both sides

8 = b

The equation of the perpendicular line is:

y = -1/7x + 8

Lupe has 500 Mexican pesos. If 1 U.S. dollar equals 12.87333 pesos, about how many dollars can Lupe buy for her pesos?

Answers

Answer:

the answer is C. $38.84

Step-by-step explanation:

What is the solution of 3x + y = 9 and 3x - 5y = 15?
OA 1 = 10 y = -1
B.
r = g y = 1
10
C. I = -1. y = 5
OD. x = 1, y = 2
COICO

Answers

Step-by-step explanation:

3x + y = 9

3x − 5y = 15

Solve with elimination.  Subtract the second equation from the first.

6y = -6

y = -1

Plug into either equation to find x.

3x + -1 = 9

3x = 10

x = 10/3

HELP!!! Need help with my home work!

Answers

Answer:

xy - y^2/x

Step by step explanation:

what is 3/5 as a percent

Answers

Answer:60%

Step-by-step explanation:

3 divided by 5 ten times by 100 and you get 60%

Quick I need help, it states what polygon is shown by the street sign

Answers

I’m pretty sure it’s just asking what shape each sign is.

One way is a rectangle
I can’t tell if the do not enter is a circle or square... maybe you can see it better
Stop is an octagon
etc...

Solve for x.
-2 (x + 1/4)+1=5
Enter your answer as a fraction in simplest form in the box.
X = ​

Answers

Answer:

[tex]x=-\frac{9}{4} \\ or \:\\x = -2\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]-2 (x + 1/4)+1=5\\\\-2\left(x+\frac{1}{4}\right)+1=5\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\\\-2\left(x+\frac{1}{4}\right)+1-1=5-1\\\\Simplify\\-2\left(x+\frac{1}{4}\right)=4\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(x+\frac{1}{4}\right)}{-2}=\frac{4}{-2}\\\\Simplify\\x+\frac{1}{4}=-2\\\\\mathrm{Subtract\:}\frac{1}{4}\mathrm{\:from\:both\:sides}\\\\x+\frac{1}{4}-\frac{1}{4}=-2-\frac{1}{4}\\\\Simplify\\x=-\frac{9}{4}\\\\x = -2\frac{1}{4}[/tex]

PLEASE HELP!! Need help with my homework!

Answers

Answer:

Line segment: AD (without arrow)

Ray: BA (with one sided arrow)

Rays with common endpoint: AC and AD (with one sided arrow)

Intersection: AE (double sided arrow)

Collinear points: B, A, C

PLEASE MARK AS BRAINLIEST




horizontal translation


reflection over the x-axis



reflection over the y-axis

Answers

Answer:

The correct option is;

Reflection over the y-axis

Step-by-step explanation:

An even function is a function that satisfies the following function equation;

f(x) = f(-x)

Therefore, for an even function, we have;

f(x) - f(-x) = 0

Which gives that the values of f(x) of the even function is the same upon reflection about the y-axis whereby the values of x changes from x to -x

Therefore, the symmetry of an even function is about the y-axis

However, an odd function is a function that satisfies the following function equation;

f(-x) = -f(x)

Therefore, reflection across the y-axis will result in an inversion of the odd function such that the odd function is not symmetrical about the y-axis as we have;

f(-x) = -f(x) ≠ f(x) which simplifies to f(x) ≠ f(-x).

9(x +3) = 4x -3 cant figure it out

Answers

Answer:

[tex]x=-6[/tex]

Step-by-step explanation:

[tex]9\left(x+3\right)=4x-3[/tex]

Expand:

[tex]9x+9\times3=4x-3[/tex]

[tex]9x+27=4x-3[/tex]

Subtract 27 from both sides:

[tex]9x+27-27=4x-3-27[/tex]

[tex]9x=4x-30[/tex]

Subtract 4x from both sides:

[tex]9x-4x=4x-30-4x[/tex]

[tex]5x=-30[/tex]

Divide both sides by 5:

[tex]\frac{5x}{5}=\frac{-30}{5}[/tex]

[tex]x=-6[/tex]

10. Use Structure What could be a first step to
solving the equation 3x + -0.5(x + 3) + 4 = 14?
Explain.

Answers

First distribute -0.5 to x and 3 giving you the new equation 3x + -0.5x-1.5

MY NOTES
ASK YOU
A table of solutions for a linear equation is given below. From the table, determine the x-intercept and the y-intercept of the graph of the equation
x-intercept
(x, y) =(
y-intercept
(x, y) =
х
y
-6
0
(x, y)
(-6, 0)
(-3, 4)
(0,8)
-3
4
0
8

Answers

Yes x y 1.24 b to the point of a game that is a little hard to get x y to the point

11-3(a-2)=27 I NEED TO SHOW WORK HELP

Answers

Answer:

3.3 recurring

Step-by-step explanation:

1) expand bracket

11-3a+6=27

2)rearrange equation

11+6=27+3a

11+6-27=3a

17-27=3a

-10=3a

-10/3=a

a=3.3 recurring

Answer:

a= - [tex]\frac{10}{3}[/tex] or -3.33

Step-by-step explanation:

[tex]11-3(a-2)=27[/tex]

subtract 11 on both sides; 27-11=16

[tex]-3(a-2)=16[/tex]

divide both sides by -3

[tex](a-2)=-\frac{16}{3}[/tex]

add 2 on both sides

[tex]a=-\frac{16}{3} +2[/tex]

a=[tex]-\frac{10}{3}[/tex]

Ivan sold 51 boxes of oranges on Friday and 29 boxes on Saturday during a citrus sale. There were 10 oranges in each box. How many oranges did he sell in all??

Answers

Answer:

800 oranges

Step-by-step explanation:

51 x 10 = 510

29 x 10 = 290

510 + 290 = 800

h(x)= -x^2+3x for h(-3)

Answers

i believe the answer is -18.

You have 2.5 pounds of egg whites
You need 37 ounces to make one serving of consommé
How many servings can you make?

Answers

You can only make 1 serving, because 2.5 pounds equals 40 ounces and you need 37 ounces to make 1 serving.

If B is between A and C, and AB = x and BC = 12, and AC = 25, then find the value of AB.
AB = ?

Answers


AB=12 because it is half of it
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