Answers
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
The shape of hyperbolic cooling tower is a conic section that can be described with a formula equation.
a = 28.5, b ≈ 52.65
[tex]Equation \ of \ hyperbola;\ \dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]
Reasons:
The parameters of the hyperbolic cooling tower are;
Minimum diameter = 57 feet
The height at which the diameter occurs = 155 ft.
The diameter of the tower = 175 feet
Total height of the tower = 200 feet
Height at which the center of the hyperbola occurs = 155 feet
Solution:
The equation of a hyperbola is; [tex]\dfrac{(x - h)^2}{a^2} - \dfrac{(y- k)^2}{b^2} = 1[/tex]
The center of the hyperbola = (0, 155)
[tex]a = \dfrac{57}{2} = 28.5[/tex]
At y = 155,
Therefore;
[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y -155)^2}{b^2} = 1[/tex]
At y = 200 feet [tex]x = \dfrac{75 \ feet}{2} = 37.5 \ feet[/tex]
Therefore;
[tex]\dfrac{37.5^2}{28.5^2} - \dfrac{(200 -155)^2}{b^2} = 1[/tex]
b² = 2769.0340909
b ≈ 52.62
The equation of the hyperbola is therefore;
[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]
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Related Questions
The sum of two numbers is −36. Their difference is 68. Find the numbers.
Answers
The two numbers from the equations are 16 and -52
The first number is 16
The second number is -52
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first number be = x
Let the second number be = y
So , the equation will be
Let the sum of two numbers be = -36
And the equation will be
x + y = -36 be equation (1)
Let the difference of two numbers be = 68
And the equation will be
x - y = 68 be equation (2)
Subtracting equation (1) from equation (2) , we get
On simplifying the equation
2x = 32
Divide by 2 on both sides of the equation , we get
x = 16
The equation will be
Substituting the value of x in the equation , we get
x + y = -36
16 + y = -36
Subtracting 16 on both sides , we get
y = -52
Hence , the two numbers are 16 and -52
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PPLLEEAASSEE HHEELLPP
Answers
Answer:
Step-by-step explanation:
4
Answer:
[tex]\boxed{4}[/tex]
Step-by-step explanation:
→ Remember when dividing fractions, the second fraction 'flips'
[tex]6/\frac{3}{2} =6*\frac{2}{3}[/tex]
→ Simplify
[tex]6*\frac{2}{3} =\frac{12}{3} =4[/tex]
Jermaine Samson earns 6 1/2% commission
on sales of $5,600 selling flat screen TVs.
What is his commission?
$36,400
$3,640
$364
Answers
Answer:
364
Step-by-step explanation:
0.065 x 5,600
Answer:
$364
Step-by-step explanation:
multiply 0.065 by 5,600
A 2-column table with 6 rows. Column 1 is labeled Tables with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Chairs with entries 6, 12, 18, 24, 30, 36.
Rachel needs two tables for her birthday party. How many chairs will she need?
Answers
Answer:
The answer is 12
Step-by-step explanation:
i got it right
Answer:
the answer is 12
Step-by-step explanation:
Use substitution to solve the system.
4x + 3y = 8
y = 3x - 19
Please helppp
Answers
Answer:
x=5
y=-4
hope it helps
:)
A statistics class has 50 students and among those students, 42 are business majors and 8 like grilled cheese. Of the business majors, 3 like grilled cheese. Find the probability that a randomly selected statistics student is a business major or likes grilled cheese.
Answers
The answer is 0.94 !!!
The probability that a randomly selected statistics student is a business major or likes grilled cheese is 0.94.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that the statistics class has 50 students and among those students, 42 are business majors, and 8 like grilled cheese. Of the business majors, 3 like grilled cheese.
The probability will be calculated as:-
P(AUB) = P(A) + P(B) - P(A[tex]\cap[/tex]B)
[tex]P(AUB)=\dfrac{42}{50}+\dfrac{8}{50}-\dfrac{3}{50}[/tex]
[tex]P(AUB) = \dfrac{50-3}{50}[/tex]
[tex]P(AUB)=\dfrac{47}{50}[/tex]
P(AUB) = 0.94
Therefore the probability that a randomly selected statistics student is a business major or likes grilled cheese is 0.94.
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what number gives a result of -4 when 10 is subtracted from the quotient of the number and 5
Answers
Answer:
35
Step-by-step explanation:
35/5 =
6
6-10 =
-4
The dimensions of a box are 3 cm × 5 cm × 7 cm. The width, length, and height of the box must be increased by the same amount x in order for the box to have a volume of 693 cm cubed. Determine the value of x that will produce a box with a volume of 693 cm3
Answers
Answer:
its 6.6 (I think???)
Step-by-step explanation:
the volume of that box is 105 and 105 x 6.6 is 693. please forgive me if I'm wrong i havent learned this yet.
The dimensions of the new box are 7 cm, 9 cm, and 11 cm.
How to solveThe original volume of the box is 357 = 105 cm3. After the dimensions are increased by x, the new volume is (3+x)(5+x)(7+x) = 693 cm3.
Expanding the product gives [tex]x^3+15x^2+71x-588 = 0.[/tex]
This cubic equation can be solved for x, and the only real solution is x = 4.
Therefore, the value of x that will produce a box with a volume of 693 cm3 is 4. This means that the dimensions of the new box are 7 cm, 9 cm, and 11 cm.
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I WILL GIVE BRAINLIEST AND POINTS PLEASE I NEED TO PASS !!!!!!
Answers
A negative number divided by a positive number is:
Answers
Answer:
When you divide a negative number by a positive number then the quotient is negative.
Step-by-step explanation:
hope this helped
the value of x for the exponential function f(x) = e^x is a set of real numbers?true or false
Answers
Answer:
a) f(x) = x^2
b) f(x) = x
c) any pair of numbers
Step-by-step explanation:
The value of the exponential function f ( x ) = eˣ has the domain as the set of all real numbers
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential function be represented as A
Now , the value of A is
f ( x ) = eˣ be equation (1)
And , exponential functions have a positive base, and a variable for an exponent.
The scope of an exponential function encompasses all real numbers since all powers of a positive base are defined. All the values of the function will be positive since we begin with a positive base and powers of a positive base are always positive.
The function never accepts the value 0 or any negative number, as indicated by that. An exponential function can only be applied to positive values. Other than that, their activities are varied.
And , the domain is all real numbers and the range is all positive real numbers
Hence , the value of the exponential function is a set of real numbers
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What is the slope? Help please
Answers
Answer:
2 or 2/1 either one works
Step-by-step explanation:
otra forma de representar 42/9
Answers
Answer:
42/9=14/3
Step-by-step explanation:
Simplificación de Fracciones
Una fracción de la forma x/y puede ser representada de infinitas maneras, siempre y cuando produzcan el mismo resultado.
Por ejemplo, las fracciones 5/3 y 10/6 son equivalentes porque producen el mismo resultado. Obsérvese que tanto el numerador como el denominador en la segunda están multiplicados por 2.
Igualmente si tenemos 10/6, podemos obtener 5/3 dividiendo a ambos por 2.
La fracción 42/9 puede convertirse a una fracción equivalente dividiendo ambos términos por 3 para obtener 14/3
A washing machine marked for $320 was sold at $280. What was the percentage of discount for the washing machine?
Answers
Answer:
the person who bought it saved 40 dollars and the percentage saved was 12.50 i just used a discount calculator on google
Step-by-step explanation:
Answer:
12.5%
Step-by-step explanation:
Does anyone know the answer please help!!!!
Answers
Explanation
Let p be "Today is Friday" and let q be "Today is Wednesday."
Write in words the disjunction of the two statements. (Select all that apply.)
A. Today is Friday or Wednesday.
B. Today is not Friday or Wednesday.
C. Today is Friday or today is Wednesday.
D. Today is neither Friday nor Wednesday.
E. is not Friday or today is not Wednesday.
Answers
Answer:
Today is neither Friday nor Wednesday.A and C
I think this is correct
: )
Autumn buys 9 bottles of orange juice at the corner store for a total cost of $10.71. If each bottle costs the same amount, how much is each bottle of juice?
Answers
Answer:
1.19$ each
Step-by-step explanation:
10.71/9= 1.19
Which expression is equivalent to?
Answers
PLEASE HELP
Graph the following equation:
y=1/4x-2
Answers
Answer:
see explanation
Step-by-step explanation:
-2 is your y-intercept so one point on your plot is (0,-2)
your slope is 1/4, rise/run
so from the y-int go up 1 and right 4, so another point is (-1,4)
and you can keep going up 1 and right 4 for as many points as you need.
Complete the definition.
A relation/function is a relation/function where there is exactly one unique output/input for each output/input
Answers
Answer:
A relation has an input value which corresponds to an output value. When each input value has one and only one output value, that relation is a function. Functions can be written as ordered pairs, tables, or graphs. The set of input values is called the domain, and the set of output values is called the range.
Step-by-step explanation:
56:43 Theo found the driving distance from Glacier National Park to Yellowstone Park to be 448 miles. Theo used a map that had a ratio of StartFraction 5 centimeters over 320 miles EndFraction. How many centimeters is the distance on the map? Round to the nearest unit if necessary. 4 centimeters 7 centimeters 64 centimeters 90 centimeters
Answers
Answer:
7 cm
Step-by-step explanation:
Convert 448 miles to the equivalent in cm on the map:
448 mi 5 cm 2240 cm
--------------- * --------------- = --------------- = 7 cm (which matches the 2nd ans.)
1 320 mi 320
3/8 of {38/5-1/3{5/4+10/3}×12/5
Answers
Answer:
1863/275=6.7745recurring
Step-by-step explanation:
Dont u have a calculator
sorry for asking to much but thank u so much for the answers!!!!!
Answers
Answer:
x = 67°
Step-by-step explanation:
there are 180 degrees in a triangle and we know that the two corners equal the same amount. so we can set up an equation like this:
180 = 46 + 2x
so now lets subtract 46 from both sides to simplify the equation.
134 = 2x
now we can divide both sides by 2 to get our final answer.
67 = x
we can check our answer by solving this expression:
67 + 67 + 46 = ?
after adding these together, we get 180 so we know our answer is correct.
hope this helped!
12 % of 140 = with explanation
Answers
Answer: 16.8
Step-by-step explanation: 12% of 140 = 16.8. (I’m not sure what I say for the explanation! Really sorry! But I hope I helped!)
Answer:
16.8
Step-by-step explanation:
12 % of 140
12/100×140
12×140/100
1680/100
16.8
So 16.8 is the answer
A zoo maintains a small patch of bamboo, which it grows as a food supply for its pandas. Four weeks ago, the bamboo was 10 ft 7 in tall. Since then, the bamboo has grown 5ft 12 in. How tall is the bamboo now ?
bamboo has grown 5 ft 12 in. How tall is the bamboo now?
Answers
Answer:
16 feet and 7 inches
Step-by-step explanation:
To find how tall the bamboo is now, first add the number of feet together:
10 + 5
= 15
Then, add the inches:
7 + 12
= 19
This can be converted to 1 foot and 7 inches.
Then, add 15 to this:
= 16 feet and 7 inches
So, the bamboo is now 16 feet and 7 inches tall
The current height of the bamboo is given as 16 feet 7 inches tall.
Given that,
A zoo maintains a small patch of bamboo, which it grows as a food supply for its pandas. Four weeks ago, the bamboo was 10 ft 7 in tall. Since then, the bamboo has grown 5ft 12 in.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
4 weeks ago the height of the bamboo = 10 ft 7 in
It increase by 5 ft 12 or 6 ft since then
Current height = 10.7 + 6 = 16.7 or 16 ft 7 in
Thus, the current height of the bamboo is given as 16 feet 7 inches tall.
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What is the value of B? Thanks!
Answers
Answer:
Vertical change = 4
Horizontal change = 1
Slope = 4
b (y-intercept) = 2
Step-by-step explanation:
From the graph (notice it as also marked with an arrow) you can get the value of "b" (also called the -intercept) is "2"
Please notice that you have entered wrong values for the slope.
By using the points (0, 2), and (1, 6) which are marked on the graph, you estimate the slope doing:
slope = vertical_change / horizontal_change = (y2 - y1) / (x2 - x1)
in our case, the vertical change (y2 - y1) is : 6 - 2 = 4
The horizontal change is (x2 - x1) = (1 - 0) = 1
Then the slope is: 4 / 1 = 4
slope = 4
and "b" (or y-intercept) is 2
At Choo Choo Mike's toy store, there are 100 toys that are randomly selected. Out of those 100, 12 of them are defective. What is the probability if you randomly choose three toys that two of them are defective?
Answers
Answer:
12/100 is the defective rate
so 12/100*12/100*(1-12/100
Step-by-step explanation:
PLEASE HELP ITS A BENCHMARK TEST ILL GIVE BRAINIEST Four points, D. V. Q, and M, are all positive rational numbers that are not equal to one another.
Each point can be marked on a number line.
Use the following information to determine whether each statement about the locations of those points is true. Mark True or False for each statement.
Point D< Point V
• Point Q> Point V
• Point D > Point M
True
False
Statement
Point Q is farthest to the right on the number line.
Point D is farthest to the left on the number line.
Point Mis to the left of Point V.
Point V is to the left of Point D
Answers
Answer:
TRUE
FALSE
TRUE
FALSE
The larger of two numbers is 9 less than four times the smaller number if the sum of
the two numbers is 26. What is the smaller number?
Answers
Answer:
7
Step-by-step explanation:
l = larger number
s = smaller number
l = 4s - 9
l + s = 26
so 4s - 9 + (s) = 26
simplify--> 5s - 9 = 26
--> 5s = 35
---> s = 7
substitute 7 for s to find l
l + 7 = 26
l = 19
Help help help help help
Answers
Answer:
4.5 = 13.5
11/2 = 16 1/2
36 = 12
46.5 = 15.5
Step-by-step explanation:
hope this helped!