1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ziro4ka [17]
2 years ago
6

The minimum diameter for a hyperbolic cooling tower is 57 feet...

Mathematics
2 answers:
Verizon [17]2 years ago
4 0

Answer:

Can give you the example then you have to figure out.

Step-by-step explanation:

We are assuming the center of the tower is at the origin, so we can use the standard form of a horizontal hyperbola centered at the origin: \displaystyle \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1

​a

​2

​​  

​

​x

​2

​​  

​​ −

​b

​2

​​  

​

​y

​2

​​  

​​ =1, where the branches of the hyperbola form the sides of the cooling tower. We must find the values of \displaystyle {a}^{2}a

​2

​​  and \displaystyle {b}^{2}b

​2

​​  to complete the model.

First, we find \displaystyle {a}^{2}a

​2

​​ . Recall that the length of the transverse axis of a hyperbola is \displaystyle 2a2a. This length is represented by the distance where the sides are closest, which is given as \displaystyle \text{ }65.3\text{ } 65.3  meters. So, \displaystyle 2a=602a=60. Therefore, \displaystyle a=30a=30 and \displaystyle {a}^{2}=900a

​2

​​ =900.

To solve for \displaystyle {b}^{2}b

​2

​​ , we need to substitute for \displaystyle xx and \displaystyle yy in our equation using a known point. To do this, we can use the dimensions of the tower to find some point \displaystyle \left(x,y\right)(x,y) that lies on the hyperbola. We will use the top right corner of the tower to represent that point. Since the y-axis bisects the tower, our x-value can be represented by the radius of the top, or 36 meters. The y-value is represented by the distance from the origin to the top, which is given as 79.6 meters. Therefore,

x

2

a

2

−

y

2

b

2

=

1

Standard form of horizontal hyperbola

.

 

b

2

=

y

2

x

2

a

2

−

1

Isolate  

b

2

 

=

(

79.6

)

2

(

36

)

2

900

−

1

Substitute for  

a

2

,

x

,

and  

y

 

≈

14400.3636

Round to four decimal places

The sides of the tower can be modeled by the hyperbolic equation

\displaystyle \frac{{x}^{2}}{900}-\frac{{y}^{2}}{14400.3636 }=1,\text{or}\frac{{x}^{2}}{{30}^{2}}-\frac{{y}^{2}}{{120.0015}^{2} }=1

​900

​

​x

​2

​​  

​​ −

​14400.3636

​

​y

​2

​​  

​​ =1,or

​30

​2

​​  

​

​x

​2

​​  

​​ −

​120.0015

​2

​​  

​

​y

​2

​​  

​​ =1

Troyanec [42]2 years ago
3 0

wait what ............

You might be interested in
write two additional sentences where the sum is negative. in each sentence one added should be positive and the other
Goshia [24]
10 + (-5) = 10 - 5 = 5

-11 + 20 = 20 + (-11) = 20 - 11 = 9

102 + (-1) = 102 - 1 = 101

<span>-20 + 60 = 60 + (-20) = 60 - 20 = 40 </span>
6 0
3 years ago
What is four hundred eight thousand,seventeen in standard form and expanded form?
mestny [16]
408,017 is in standard form and
400,000+8,000+10+7=408,017 is expanded form
sixty five thousand and fifty eight is word form
60,000+5,000+50+8=65͵058 is expanded form
6 0
3 years ago
Read 2 more answers
Find the product of 51 and -2.5
Elodia [21]

Answer: -127.5

Hope this helps!

3 0
3 years ago
Read 2 more answers
82. A company spends x hundred dollars on an advertising
crimeas [40]

The company spends $649 on advertising

The sales function after advertising is given as:

S(x) = 5 + 7\ln(x + 1)

When the total sales is $19,100, we have S(x) = 19100

So, the sales function becomes

5 + 7\ln(x + 1) = 19.1

Subtract 5 from both sides

7\ln(x + 1) = 14.1

Divide both sides by 7

\ln(x + 1) = 2.014

Take exponents of both sides

x + 1 = e^{2.014

x + 1 = 7.49

Subtract 1 from both sides

x= 6.49

Hence, the company spends $649 on advertising

Read more about functions at:

brainly.com/question/12940982

5 0
2 years ago
Giving brainly to correct answer
Elena L [17]

Answer:

The answer is the second one

im sorry if this is wrong

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Other questions:
  • The cowboy rode into town on friday stayed there for 3 days and left on friday how can that be
    15·2 answers
  • Dress 40$ and tax 20% how much is dress
    11·1 answer
  • X is greater than or equal to -5 and less than 0
    10·1 answer
  • The graph of f(x)=x^6-2x^4-5x^2+6
    13·1 answer
  • How can you tell if ordered pairs are a function or not
    7·2 answers
  • Expressions equal 1 divided by 16
    5·1 answer
  • The perimeter of a rectangle below is 60 units. Find the length of side PQ
    15·2 answers
  • alex reads 12 pages. jenna reads 15 pages in 12 minutes. they are both reading 60- page magazine who will finish reading first
    5·1 answer
  • You are part of a school and have to report the results of standardized test scores. Which measure of central tendency would you
    15·1 answer
  • (4, 2); slope = 3<br> How do you do this problem and show work
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!