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.)
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
Find the midpoint of the segment with the given endpoints. (8, 0) and (- 10, 4)
Answer:
(-1, 2)
Step-by-step explanation:
The midpoint coordinates are the average of the end point coordinates:
M = (A +B)/2
M = ((8, 0) +(-10, 4))/2 = (8-10, 0+4)/2 = (-1, 2)
The midpoint is (-1, 2).
what is the solution to 8t+5= 6t+1 ?
(variables on both sides
Answer:
8t+5=6t+1
2t+5=1
2t=-4
t=-2
Step-by-step explanation:
Shawn is starting a woodworking project for which he needs a large number of 2x4s. He plans to buy 2x4s that are 6 feet in length and cut them into the following sizes: eight pieces that are 12.5 inches long • six pieces that are 8.75 inches long • nine pieces that are 6.25 inches long Note: A 2x4 ("two by four") is a rectangular piece of wood that is two Inches high and four inches wide, as shown in the picture. It can have varying lengths. The 2x4s that Shawn is buying have a length of 6 feet, or 72 inches. 6' or 72" 2" 4" Find the most efficient way for Shawn to cut these pieces. In other words, what is the fewest number of boards he can cut from? Describe for Shawn the most efficient way to cut his boards. You may include a diagram if you wish.
Answer:
The fewest amount number of boards Shawn can cut from is 3.... Im not very sure... Ive been stuck on this answer, too
A rule of thumb for estimating the size of a crowd is that 2 people take up
5 square feet. If a club has a dance floor that is 30 x 20 feet, how many
people could crowd onto the floor?
Answer:
120 people
Step-by-step explanation:
Length of dance floor = 30 ft
Width of dance floor = 20 ft
Given that 2 people will occupy 5 ft² of space, the number of people that will crowd the floor of the dance floor is calculated as follows:
= Area of dance floor ÷ 5 ft²
= (30*20) ÷ 5
= 600 ÷ 5
= 120.
120 people will crowd the dance floor.
if x=3 and y= 2 cm what is the perimeter of the plygon
Answer:
where is the image then i will comment the ansewr thanks
Step-by-step explanation:
Answer:
99
Hope this helps you guys!
30 points!!!
To convert measurements in the metric system, you can move the decimal point left or right. Why does this work? The metric system only uses decimal numbers. Converting in the metric system does not involve multiplication or division. The metric system is based on powers of 10. The metric system does not have conversion factors.
Answer:
Because it could be negitive or positive that chooses where the decimal goes it can either go left or right
hope this helps :)
Answer:
its c trust me :)
Step-by-step explanation:
What is the vertex of the graph of y = 1/4 (x - 2)^2+ 6?
(0,7)
(4,7)
(2,6)
(-2,-6)
Answer:
focus | (2, 7)
vertex | (2, 6)
semi-axis length | 1
focal parameter | 2
eccentricity | 1
directrix | y = 5
Step-by-step explanation:
A scuba diver returning to the surface swims to move up quickly, then waits a few meters below the surface to avoid pressure issues. They complete the ascent more slowly. The function f represents the diver's distance from sea level over time, in seconds. Which of the following is true for f? f(x)= { 3x+1, if −9 < x ≤ −2 f(x)= {−5, if. −2 < x ≤ 1 f(x)= { x−6, if 1 < x < 7 Group of answer choices The domain is the depth interval (−26, 1). The domain is the depth interval (−9, 1]. The domain is the set of times −9 < x < −2, −2 < x < 1, and 1 < x < 7. The domain is the time interval (−9, 7). Group of answer choices domain: (–3, 3] negative: (–3, –2), (2, 5] range: (–3, 4] decreasing: (–1, 4) increasing: (–3, –1) positive: (–2, 2)
Answer:
See below
Step-by-step explanation:
Given:
f(x)= { 3x+1, if −9 < x ≤ −2 f(x)= {−5, if. −2 < x ≤ 1 f(x)= { x−6, if 1 < x < 7Combination of domain for the function is the following union:
(-9, 2]∪ (-2, 1]∪(1, 7) = (-9, 7)Group of answer choices:
The domain is the depth interval (−26, 1).
incorrect as (-26, -9) interval is not covered in given functionThe domain is the depth interval (−9, 1].
incomplete rangeThe domain is the set of times −9 < x < −2, −2 < x < 1, and 1 < x < 7.
incorrect as doesn't include x = -2 and x = 1The domain is the time interval (−9, 7).
This is correct as it is same with the domain set we got above.3x 40° to Sum of angle measures: 180°
Answer:
yes
Step-by-step explanation:
This table displays the height of water as a pool is being Use the table to interpret the rate of change.
filled.
What is the change for each consecutive input?
Time (min)
Height
(in.)
What is the change for each consecutive output?
10
3.75
What is the rate of change for the relationship?
11
4.1
VVU
ለለለ
12
4.45
13
4.8
Answer: the first one is 1 the second and third is 0.35
Step-by-step explanation:
I jus guessed and got it right someone else has to explain sorry
Answer: 1.) 1
2.) 0.35
3.) 0.35
Step-by-step explanation:
I am an odd number.my digits add up to 7. i am bigger than 50 and smaller than 100.who am i?
Answer:
61
Step-by-step explanation:
i hope this is correct lol
HELP What is the perimeter of this rectangle?
Answer:
7×2=14 (for the long side)5×2=10 (for the short sides) the you add up the two answers 14+10=24
Ten less than 3 times a number is the same as the number plus 4.
Step-by-step explanation:
10 - 3x = x-4
Collect like terms
10 +4 = x + 3x
14 = 4x
Divide both sides by 4
X = 14
4
= 7
2
= 6 1
2
Or
= 6.5
Which describes an atom that has fewer neutrons and protons and more electrons than protons
Answer:
Negative charged ion :)
Answer:
Negative charged ion
Step-by-step explanation:
graph y minus 3 equal one half (x+2)
Heidi Muir, a sporting goods wholesaler, purchased goods from a supplier for $3,400. The
supplier offers a 3% discount if the invoice is paid within 10 days; if not paid within 10 days, the
full amount must be paid within 30 days of the invoice date. Use the formula to find the annual
rate Heidi, in effect, is paying the supplier if she fails to pay the invoice at the end of the discount
period
Answer:
56.44%
Step-by-step explanation:
From the question, we have the following values
% Discount = 3%
Full allowed payment days = 30 days
Discount days = 10 days
1 year = 365 days
The formula for Effective Annual rate or Annual rate in effect =
Discount %/(1-Discount %) x (365 days/(Full allowed payment days - Discount days))
= 3%/(1 - 3%) × (365 days/30 days - 10 days)
= 0.03/(1 - 0.03) × (365/20)
= 0.03/0.97 × (365/20)
= 0.5644329897
Converting to percentage
0.5644329897 × 100
= 56.44329897%
Approximately = 56.44%
Therefore, the annual rate Heidi, in effect, is paying the supplier if she fails to pay the invoice at the end of the discount period is 56.44%
An object is translated by (x - 2; y- 6). If one point in the pre-image has the coordinates (-3, 7), what would be the
coordinates of its image?
(-5,1)
(-1, 13)
(-1,7)
(-9,5)
Answer:
(-5,1) would be the coordinates of its image
Answer:
(5,1)
Step-by-step explanation:
hope this helps
Compare -9 and square root -9
Answer:
-9 < 3i
Step-by-step explanation:
3i is bigger than -9 because 3i² is equal to -9
i means imaginary number
Hope this helps!
HELLLP!!!!!!!!!!! PLS
Answer:
3 * 4/4 = 12/4
12/4 + 1/4 = 13/4
One fraction: 13/4
Mixed number [tex]3 \frac{1}{4}[/tex]
Solve the equation for y in terms of x
12x + 3y = 12
Answer:
y = 4 - 4x
Step-by-step explanation:
Step 1: Write equation
12x + 3y = 12
Step 2: Subtract 12x on both sides
3y = 12 - 12x
Step 3: Divide both sides by 3
y = 4 - 4x
Answer:
12x + 3y = 12
3y=12-12x
y=(12-12x)/3=3(4-4x)/3=4-4x
Perpendicular lines AB and CD intersect at point E. If m ZAED = x+ 20, what is the value of ?
160
110
90
70
Answer: the value would be 90
Step-by-step explanation:
2(x + 3) – 10 = 4x
Can you also explain please. Thanks
Answer:
x=-2
Step-by-step explanation:
2(x+3)-10=4x
2x+6-10=4x
6-10=2x
-4=2x
-2=x
Answer:
x = -2
Step-by-step explanation:
First distribute the 2 with x and 3
Equation should look like... 2x + 6 - 10 = 4x
Second combine like terms, 6 and -10
Equation should look like... 2x - 4 = 4x
Third bring 2x to the other side making it -2x and subtract it from 4x
Equation should look like... -4 = 2x
Last divide -4 and 2.
Equation should look like... x = -2
The price for video game A is $15 more than the price for video game B. If the total of these two prices is $39, find the price of each game.
and the cost for video game B is $
The cost for video game A is $
(Type integers or decimals.)
Answer:
Video Game A: $27
Video Game B: $12
Step-by-step explanation:
First, I divide the total in approximately half ($20 and $19). Since the difference between these two numbers is already $1, I only have to make the difference $14. I do this by dividing $14 in half ($7 and $7) and subtracting $7 from $19 and adding $7 to $20. So, video game A costs $27 and video game B costs $12. Also, to check the answer: $27 is $15 more than $12 and $27 + $12 is $39.
matt and craig run into each other at the batting cages they wonder why they didn't see each other more often since they have practices there regularly matts coach takes him there every 7 days and craigs teacher takes him there every 4 when will they see each other again
A car rental agency advertised renting a car for $26.95 per day and $0.24 per mile. If Kevin rents this car for 3 days, how many whole miles can he drive on a $250 budget?
miles (Round down to the nearest whole mile.)
Answer: 26.95 * 3 = 80.85
250/0.24 = 60
∠CAT and ∠TAD is a linear pair. If m∠CAT = 14 and m∠TAD = x+10, find x.
(show work please)
Answer:
156
Step-by-step explanation:
Since, ∠CAT and ∠TAD is a linear pair.
Therefore,
∠CAT + ∠TAD = 180°
14° + (x + 10)° = 180°
(x + 24)° = 180°
x + 24 = 180
x = 180 - 24
x = 156
Find the surface area of a square pyramid if the area of the base is 324 cm squared and the height is 40 cm.
Answer:
height h = 324 cm
slant height s = 324.61669704438 cm
side length a = 40 cm
lateral edge length e = 325.23222472566 cm
1/2 side length r = 20 cm
volume V = 172800 cm^3
lateral surface area L = 25969.33576355 cm^2
base surface area B = 1600 cm^2
total surface area A = 27569.33576355 cm^2
Step-by-step explanation:
Total Surface Area of a square pyramid:
A = L + B = a^2 + a√(a^2 + 4h^2))
A = a(a + √(a^2 + 4h^2))
Agenda:
h = height
s = slant height
a = side length
e = lateral edge length
r = a/2
V = volume
L = lateral surface area
B = base surface area
A = total surface area
Please help I'm stuck
Answer:
I'm stuck to.
Step-by-step explanation:
is there suppose to be an angle or a triangle?
d= V(x2 – x1)2 + (y2 – yy)2
Answer:
y = 2
Step-by-step explanation: divided both from each side