The equation of the hyperbola is,
(x/12)² - 4y²/(527) = 1
The standard equation of the hyperbola is
(x/a)² - (y/b)² = 1
Here (a, 0) and (-a, 0) are vertices and asymptotes y = ± √(b/a)x
Foci are (c, 0) & (-c, 0)
Then a² + b² = c²
Here we have to give that.,
2a = 24
a = 12
And 2c = 7
c = 7/2
Therefore a = 12 and c = 3.5
Substituting a and c in Pythagorean identity;
b² = 527/4
Then, the equation of the hyperbola is
(x/12)² - 4y²/(527) = 1
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We have b = 0, which implies that the foci coincide with the vertices, making the hyperbola a degenerate case. In this scenario, the equation of the border would be a vertical line passing through the vertices/foci, given by the equation x = ±a.
To find the equation of the hyperbolic border created by the shadow on the wall, we can start by understanding the properties of a hyperbola. A hyperbola is defined as the set of all points such that the difference of the distances from any point on the hyperbola to two fixed points, called the foci, is constant.
Let's label the vertices of the hyperbola as A and B, and the foci as F1 and F2. The distance between the vertices is given as 2a inches, and the foci are located at a distance c inches from the vertices.
Using the given information, we can find the value of a and c. Since the center of the hyperbola is at the origin, the coordinates of the vertices are (±a, 0), and the coordinates of the foci are (±c, 0).
The distance between the foci is given by the equation:
c = √(a^2 + b^2)
We know that the distance between the foci is given as 2c inches, so:
2c = 2√(a^2 + b^2)
Since c is given as a distance from the vertices, we can substitute c = a - b to simplify the equation:
2(a - b) = 2√(a^2 + b^2)
Squaring both sides to eliminate the square root:
4(a - b)^2 = 4(a^2 + b^2)
Expanding the equation:
4(a^2 - 2ab + b^2) = 4a^2 + 4b^2
Simplifying the equation:
4a^2 - 8ab + 4b^2 = 4a^2 + 4b^2
Canceling out the common terms:
-8ab = 0
Dividing by -8:
ab = 0
This implies that either a = 0 or b = 0. However, since a represents the distance between the vertices and b represents the distance between the foci and vertices, we can rule out a = 0 as it would result in a degenerate hyperbola.
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Not sure how to do this.
Answer:
-4 ≤ x ≤ -2, 4 ≤ x ≤ 7
Step-by-step explanation:
A function shows the relationship between two or more variables. A function is said to be constant over an interval if its output value is same for every input value within that interval.
As seen in the question, the x variable is the input while the y variable is the output. The function is constant from x = -4 to x = -2. Also, the function is constant within the interval from x = 4 to x = 7. Hence, the interval is:
-4 ≤ x ≤ -2, 4 ≤ x ≤ 7
Find all the roots of the equation
[tex] {x}^{6} - 64 = 0[/tex]
Answer:
x = 2
x =-2
x =1 +√3i
x =1 -√3i
x =-1 +√3i
x =-1 -√3i
Step-by-step explanation:
[tex]x^{6} -64 = 0\\(x^{3} -8)(x^{3} + 8) = 0\\ \\( x - 2) (x^{2} + 2x + 4)( x + 2) (x^{2} -2x + 4) = 0\\[/tex]
x = 2
x =-2
x =1 +√3i
x =1 -√3i
x =-1 +√3i
x =-1 -√3i
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Solve the equations for x and match the solutions.
1
r
6
4 = 1
+ 5
-ar
20 = -14
7 + 2ar = 13
Answer:
..
Step-by-step explanation:
[tex]x = - \frac{a}{6} [/tex]
[tex]x = - \frac{6}{a} [/tex]
[tex]x = \frac{3}{a} [/tex]
3 miles in 25 minutes same rate in 20 minutes?
Step-by-step explanation:
25 minutes=3 miles
1 minute = 3/25 miles
20 minutes = 3/25 * 20 miles
= 2.4 miles
Therefore, the answer is 2.4 miles.
2√m^2 if m is greater than or equal to 0
Answer:
[tex] \displaystyle \boxed{|2m| }[/tex]
Step-by-step explanation:
we are given that
[tex] \displaystyle 2 \sqrt{ {m}^{2} } [/tex]
since m is greater than or equal to 0 it's a positive number therefore, the square root of m is defined and recall that √x²=|x| thus
[tex] \displaystyle \boxed{2 |m|}[/tex]
remember that,|a|•|x|=|ax| hence,
[tex] \displaystyle \boxed{ |2m|}[/tex]
and we're done!
Answer:
2m
Step-by-step explanation:
Given :-
2√m² , m is greater than or equal to 0 .By question,
→ 2√m²
→ 2 * m
→ 2m
Ngân hàng rơi vào tình trạng vỡ nợ khi nào
Answer:
.
Step-by-step explanation:
.
As part of a classic experiment on mutations, 10 aliquots of identical size were taken from the same cul-ture of the bacterium E. coli. For each aliquot, the number of bacteria resistant to a certain virus was determined. The results were as follows:
14 15 13 21 15
14 26 16 20 13
Construct a frequency distribution of these days and display it as a histogram.
Determine the mean and the median of the dad and mark their locations on the histogram.
Answer:
a. See the attached excel file for the frequency distribution table, and the attached photo for the histogram.
b. We have:
Mean = 16.7
Median = 15
Note: See the attached photo for the locations of Mean and Median on the histogram.
Step-by-step explanation:
a. Construct a frequency distribution of these days and display it as a histogram.
Note: See the attached excel file for the frequency distribution table, and the attached photo for the histogram.
b. Determine the mean and the median of the dad and mark their locations on the histogram.
From the attached excel file, we have:
Total of F = 10
Total of FX = 167
Therefore, we have:
Mean = 167 / 10 = 16.7
Median is the middle number after arranged the data in ascending or descending order. Using the ascending order, we have:
13 13 14 14 15 15 16 20 21 26
Since 15 and 15 are in the middle, their average are the median which is calculated as follows:
Median = (15 + 15) / 2 = 15
Note: See the attached photo for the locations of Mean and Median on the histogram.
Congruent sides???????????
Answer:
the second option : ST and WX
Step-by-step explanation:
congruent means they would completely cover each other when oriented in the same direction and positioned at the same location.
after dying the two mirroring actions we get
VS correlates to ZW
ST correlates to WX
TU correlates to XY
UV correlates to ZY
Select the correct answer.
What is the domain of y = tan x?
A. (-0,0)
B. (0,7)
c. all stan
D. all x 91
Need Plato help
Answer: d all
Step-by-step explanation: Because The domain of the function y = tan (x)) is all real numbers except the values where cos (x) is equal to 0, that is, the values π 2 + π n for all integers n. The range of the tangent function is all real numbers.
Nuts Galore sells a trail mix containing dried banana chips, roasted almonds, and chocolate chips that sells for $6.52 per pound. The dried banana chips costs $4 per pound, the roasted almonds cost $8 per pound, and the chocolate chips cost $6 per pound. The amount of roasted almonds used is three times the amount of chocolate chips used. If they plan to make 100 pounds of this trail mix, how many pounds of each ingredient should be used
Answer:
[tex]x = 28[/tex] ----- Banana
[tex]y = 54[/tex] ----- Almonds
[tex]z = 18[/tex] ---- Chocolate
Step-by-step explanation:
Let
[tex]x \to[/tex] banana
[tex]y \to[/tex] almonds
[tex]z \to[/tex] chocolate
So, we have:
[tex]x + y + z = 100[/tex] --- total used
[tex]4x + 8y + 6z = 652[/tex] -- i.e. 6.52 * 100 --- total sales from 100 pounds
[tex]y = 3z[/tex]
Required
The number of pounds of each (i.e. x, y and z)
Substitute [tex]y = 3z[/tex] in [tex]x + y + z = 100[/tex]
[tex]x + 3z + z = 100[/tex]
[tex]x + 4z = 100[/tex]
Make x the subject
[tex]x = 100 - 4z[/tex]
Substitute [tex]y = 3z[/tex] in [tex]4x + 8y + 6z = 652[/tex]
[tex]4x + 8 * 3z + 6z = 652[/tex]
[tex]4x + 24z + 6z = 652[/tex]
[tex]4x + 30z = 652[/tex]
Substitute [tex]x = 100 - 4z[/tex]
[tex]4(100 - 4z) + 30z = 652[/tex]
[tex]400 - 16z + 30z = 652[/tex]
Collect like terms
[tex]- 16z + 30z = 652-400[/tex]
[tex]14z = 252[/tex]
Divide by 14
[tex]z = 18[/tex]
Substitute [tex]z = 18[/tex] in [tex]x = 100 - 4z[/tex]
[tex]x = 100 - 4 * 18[/tex]
[tex]x = 100 - 72[/tex]
[tex]x = 28[/tex]
To calculate y, we have:
[tex]y = 3z[/tex]
[tex]y = 3 * 18[/tex]
[tex]y = 54[/tex]
Suppose the random variables X, Y, and Z have the following joint probability distribution. x y z f ( x , y , z ) 1 1 1 0.05 1 1 2 0.10 1 2 1 0.15 1 2 2 0.20 2 1 1 0.20 2 1 2 0.15 2 2 1 0.10 2 2 2 0.05 Determine the conditional probability distribution of X given that Y
Answer:
Determine the conditional probability distribution of X given that Y = 1 and Z = 2. Round your answers to two decimal places (e.g. 98.76).
answer:
Given that Y = 1 : 2/5
Given that Z = 2 : 3/5
Step-by-step explanation:
The conditional probability distribution of X F x | yz^( x )
Given that Y = 1
F x | yz . ( x | yz ) = 2/5
Given that z = 2
= 3/5
attached below is the detailed solution
is 7/4 bigger than -4 / 7
Answer:
7/4 is larger than -4/7
Step-by-step explanation:
7/4 is greater than a whole. 4/4 = 1 whole and the fraction is 7/4. -4/7 is smaller than a whole and is a negative number.
Therefore 7/4 is bigger
Hope this helps!
Answer:
yes 7/4 is bigger than -4/7
Step-by-step explanation:
its bigger because its positive!
PLEASE HELP ME BE CORRECT PLEASE
TELL ME WHERE to PUT EACH POINT
Answer:
Point A:
(3, -5)
Point B:
(6, -2)
Point C:
(5, -7)
Step-by-step explanation:
Background:
Moving to the right means adding to the x.
Moving to the left means subtracting from the x.
Moving up means adding to the y.
Moving down means subtracting from the y.
So take each point and add 3 to the x, and subtract 4 from they y.
Point B:
(3, 2) → (6, -2)
Point A:
(0, -1) → (3, -5)
Point C:
(2, -3) → (5, -7)
The cardinal number of {200, 201, 202, 203, ..., 1099}
Answer:
I have not been able to answer it sorry
Place the steps for finding f-1(x)
9514 1404 393
Answer:
B, C, H, D, F, A
Step-by-step explanation:
Starting with y = f(x), swap x and y to get x = f(y), then solve for y. The solution steps "undo" what is done to y, in reverse order. Y is ...
multiplied by 721 subtracted from the productthe square root of the differenceTo "undo" these steps in reverse order, after swapping x and y, you must square both sides, add 21, then divide by 7.
If the left tiles are labeled A to H from top to bottom, the correct sequence of steps is ...
B, C, H, D, F, A
PLEASE HELP
A spinner is divided into eight equal sections numbered 1-8. find the probability of not spinning a 5. write your answer as a fraction, percent and decimal.
Answer:
7/8, 87.5%, 0.875
Step-by-step explanation:
There is only 1 5 on the spinner. And there are 8 equal sections.
The probability of spinning a 5 is 1/8.
So, the probability of not spinning a 5 is 7/8
To find the Percent and Decimal form, divide 7 by 8.
You get 0.875-the decimal form
Move the decimal point 2 places to the right:
87.5
Add the percent symbol, and you're done!
I hope this helps!
Tell me if you need more explaining :)
Tonya wants to estimate what proportion of the students in her dormitory like the dorm food. She interviews a simple random sample of 50 students living in the dormitory. She finds that 14 think the dorm food is good. Find a 90% confidence interval for the true proportion of students that think the dorm food is good.
a. 0.176 to 0.384
b. 28%
c. 0.28 +/- 0.03
d. 0.156 to 0.404
Answer:
Step-by-step explanation:
The solution of the problem has been solved on paper and attached in the attachment section. Kindly refer to that and feel free to ask any doubt.
Sam works at a shoe store. He earns $300 every week plus $15 for every pair of shoes that he sells. How many pairs of shoes would he need to sell to make $500 in a week?
Answer:
300 + 15x = 500
15x = 200
x = 200/15
x=13.333
14 pair of shoes
Step-by-step explanation:
how to solve for
LN and what are the variables
Answer:
v See below. v
Step-by-step explanation:
LM = MN
11x - 21 = 8x + 15
[tex]3x-21=15\\3x=36\\[/tex]
x = 12
LM = 11(12) - 21 = 132 - 21 = 111
MN = 8(12) + 15 = 96 + 15 = 111
LN = 111 + 111 = 222
What is the range of g?
y
--
.
9
7.
6+
5+
4+
3+
2+
1+
.
3
{4}}
-7 -6 -5 -4 -3 -2
+++
2 3 4 5 6 7
-2
-3
-4+
-5
-6+
7
7
Answer:
y 9 5 473648
Step-by-step explanation:
suppose y varies inversely with X, and y = 48 when x = 3. What is the value of x when y = 24?
NO LINKS OR ANSWERING YOU DON'T KNOW.
a. 3
b. 12
c. 6
d. 24
Answer:
C. 6
Step-by-step explanation:
Recall that inverse variation is given by:
[tex]\displaystyle y=\frac{k}{x}[/tex]
Where k is the constant of variation.
We know that y = 48 when x = 3. Substitute:
[tex]\displaystyle (48)=\frac{k}{(3)}[/tex]
Solve for k:
[tex]k=3(48)=144[/tex]
Hence, our equation is:
[tex]\displaystyle y=\frac{144}{x}[/tex]
We want to find x when y = 24. Substitute:
[tex]\displaystyle \frac{24}{1}=\frac{144}{x}[/tex]
Cross-multiply:
[tex]24x=144[/tex]
Divide both sides by 24. Hence:
[tex]x=6[/tex]
Our answer is C.
Which statement about the net is true?
The net can be folded to form a pyramid because at least one of the faces is a triangle.
The net can be folded to form a pyramid because more than one of the faces is a triangle.
The net cannot be folded to form a pyramid because one of the faces is a rectangle.
The net cannot be folded to form a pyramid because the faces that are not a base are not all triangles.
Answer:
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Step-by-step explanation:
What is the domain of D(t) as it applies in this situation?
Answer:
t could be all real numbers.
Step-by-step explanation:
The function D(t) is given by:
[tex]D(t)=-1.5t+12[/tex]
The domain is all the posible x-values for which the function is defined.
In our case, t could be all real numbers.
The answer is the first option.
I hope it helps you!
g A two-factor study with 3 levels of factor A and 3 levels of factor B uses a separate sample of 10 participants in each treatment condition. How many participants are needed for the entire study
Answer:
the total number of participants required is 90
Step-by-step explanation:
Given the data in the question;
Factor A has three levels
Factor B has three levels
sample size n; ten participants
we have two Way ANOVA involving Factor A and Factor B.
Now,
{ Total # Participants Required } = { #Levels factor A } × { #Levels factor B } × { Sample size of each level }
we substitute
{ Total # Participants Required } = 3 × 3 × 10
{ Total # Participants Required } = 9 × 10
{ Total # Participants Required } = 90
Therefore, the total number of participants required is 90
A 4-pound bag of flour costs $10.24. What is the price per ounce if there are 16 ounces in a pound?
Answer:
The price per ounce is $0.16
Step-by-step explanation:
We have:
Price of a 4-pound bag = $10.24
1 pound = 16 ounces
Price per ounce =?
Hence the price per ounce is:
[tex] \frac{\$ 10.24}{4 pound}*\frac{1 pound}{16 ounces} = \frac{\$ 0.16}{ounce} [/tex]
Therefore, the price per ounce is $0.16
I hope it helps you!
What is the inequality shown?
Answer:
2<X ,this is because opened and facing towards x
and
–3≤X this is because the circle is closed and also facing towards x
Stuck on this question
Answer:
the answer of this question is b
2. H = 5 cm
W= 4 cm
L= 8 cm
V= L×W×H
=___×___×___
=______cm3
Answer:
160cm^3
Step-by-step explanation:
5 x 4 x 8 = 160cm^3
The fair spinner shown in the diagram above is spun. Work out the probability of getting a 3. Give your answer as a fraction in its simplest form.
Answer:
The number of fours divided by the total number of possibilities. If there are two fours and 8 spaces, the probability is 2/8 = 1/4.Step-by-step explanation:
So i have a puppy that im bottle feeding because the momma died. I have to feed him 4 ounces a day every 3 hours. I'm using a syringe that goes up to 3ML. There are 29MLs in an ounce so that means i would fill up my syringe 9 times for an ounce. There are 8 feeding sessions in 24hours and I'm trying to figure out how many MLs to feed every 3 hours. I know this is simple math but I haven't slept in 4 days since I've had the puppy and my brain hurts from the lack of sleep.. Pleae help!!
Answer:
116ML every 3 hours, 928ML a day
Step-by-step explanation:
You said it yourself if there is 29ML in one once and you need 4 ounces every 3 hours then 29 x 4 = 116.
