What is the equation of a hyperbola with a = 8 and c = 20? Assume that the transverse axis is horizontal.

Answers

Answer 1

Answer:

[tex]\frac{x^{2} }{64} -\frac{y^{2} }{336} =1[/tex]

Step-by-step explanation:

The equation of hyperbola is given by:

[tex]\frac{x^{2} }{a^{2} } -\frac{y^{2} }{b^{2} }[/tex]

Where [tex]c^{2} =a^{2} +b^{2}[/tex]

∵ [tex]a=8,c=20[/tex]

∴ [tex]b^{2} =c^{2} -a^{2}[/tex]

⇒ [tex]b= \sqrt{20^{2} -8^{2} } =4\sqrt{21}[/tex]

Now, [tex]\frac{x^{2} }{a^{2} } -\frac{y^{2} }{b^{2} } =1[/tex]

⇒ [tex]\frac{x^{2} }{8^{2} } -\frac{y^{2} }{y(4\sqrt{21} )^{2} } =1[/tex]

⇒ [tex]\frac{x^{2} }{64} -\frac{y^{2} }{336} =1[/tex]

Hence, equation is [tex]\frac{x^{2} }{64} -\frac{y^{2} }{336} =1[/tex]

Hope this helps,

ROR


Related Questions

Find the distance between the two points rounding to the nearest tenth (if necessary). (-1,5) and (-7, -1) ​

Answers

Distance formula:

[tex]d = \sqrt{(x_{2}-x_1)^2 +(y_2-y_1)^2}[/tex]

Now replace the variables with the numbers (When you replace the numbers, it doesn't matter which is the first variable and second variable. Just do whatever is easiest).

[tex]d = \sqrt{(-1-(-7))^2+(5-(-1))^2}\\d = \sqrt{(-1+7)^2+(5+1)^2}\\d = \sqrt{6^2+6^2}\\d = \sqrt{36+36}\\d = \sqrt{72} \\d = 8.5[/tex]

Thus, the distance between the two points is 8.5

(4.5 x 10^9) + (4.5 x 10^-4)

Answers

This should be the correct answer,
4.5×10^9x + 0.00045x

Also, some good free calculators that can help with problems like this would be c y m a t h and m a t h w a y .

Two pens and one eraser cost $35 and three pens and four erasers cost $65. Find the cost of the pencil and eraser separately.

Answers

Answer:

Pencil is $15 and erasers are $5

What is the value of y in the equation 5y - 3y + 1 = -4y + 13?

Answers

Answer:

y = 2

Step-by-step explanation:

   5y - 3y + 1 = -4y + 13

We only have addition and subtraction so move the terms on the other side of the equal sign with changed sign. +1 will be -1 and -4y will be +4y

terms with y = terms without y

    5y -3y +4y = 13 -1

                 6y = 12

                   y = 12/6

                  y = 2

An IV solution of 320 mL at a drip rate of 25 gtt/min using a tubing factor of 10 gtt/mL has been ordered to be initiated at 1145. Calculate the infusion time. (Round your answer to the nearest tenth of an hour.)

Answers

The infusion time for the IV solution that was prescribed = 128 mins.

Calculation of IV infusion time

To calculate the infusion time the formula for IV drip rate is used which is;

Drip rate = volume/time × Drop factor

Drip rate = 25gtt/min

Volume = 320mL

Drop factor= 10 gtt/mL

Time = ?

From the formula above, make time the subject of formula. That is,

Time = vol × drop factor/drip rate

= 320 × 10/25

= 3200/25

= 128 mins

Therefore, the infusion time for the IV solution that was prescribed = 128 mins

Learn more about drip rates here:

https://brainly.com/question/24356835

help please if you can thanks! ​

Answers

Answer:

The last option 8.5

Step-by-step explanation:

hope it helps

Roberto is having his house painted. The job takes three days, and he pays the painter the same hourly rate everyday. The cost of the job is in the chart below.
Which of the following equations, where “h” represents hours worked and “p” the amount paid in dollars, represent an hourly pay rate that is Greater than the painter’s hourly rate?

Day 1: 5 hours worked; Paid $300
Day 2: 4 hours worked; Paid $240
Day 3: 6 hours worked; Paid $360

Choose all answers that apply:
A) P=6.5h
B) P=50h
C) P=65h
D) P=70h

Answers

Answer:

a is the answer

Step-by-step explanation:

Solve for x to the nearest tenth!

Answers

Step-by-step explanation:

REFER TO THE ATTACHMENT!!

HOPE IT WILL HELP YOU

Answer:

my answer is 11.4

Step-by-step explanation:

solve for the first triangle which has both sides then solve the other

can someone explain this pls

brainliest

Answers

You need to add up the sides in order to find your answer

What is 10÷2/3?

A.) 1/15

B.) 3/20

C.) 20/3

D.) 15

Answers

Let's first write out 10 ÷ 2/3:

  [tex]\frac{10}{\frac{2}{3} }[/tex]

When we divide by a fraction, we flip the fraction 2/3 into 3/2 so that we can multiply it by 10, so:

      [tex]\frac{10}{\frac{2}{3} } =10*\frac{3}{2} =5 * 3=15[/tex]

Thus the answer is 15

Hope that helps!

   

What is the third quartile of the 8, 9, 12, 14, 15?

Answers

Answer:

14.5

Step-by-step explanation:

Case 2

Q3 =

[tex]( \frac{3}{4} (n + 1 ) - \frac{1}{2} )th[/tex]

and

[tex]( \frac{3}{4} (n + 1) + \frac{1}{2} )th[/tex]

[tex] \frac{3}{4} (5 + 1) - \frac{1}{2} = 4th \: = 14[/tex]

[tex] \frac{3}{4} (5 + 1) + \frac{1}{2} = 5th = 15[/tex]

[tex] \frac{14 + 15}{2} = 14.5[/tex]

given ab and ac are lines that are tangent to the circle with m

Answers

Answer:

B

Step-by-step explanation:

the opposite angles of the quadrilateral ABDC are supplementary , that is

∠ BDC + 40° = 180° ( subtract 40° from both sides )

∠ BDC = 140°

Which object would weigh closest to 1 ton? ​

Answers

Answer:

The answer is 73 billion bars of gold

I believe it would be a car


Using positive and negative integers, find four pairs of integers with a sum of 5.

Answers

Answer:

-8, 13

-3, 8

6, -1

10, - 5

Step-by-step explanation:

the picture below is my question please hurry

Answers

Answer:

B) 70 °

Step-by-step explanation:

Given that the triangles AOC and BOC are congruent, the triangles OA and OB are likewise congruent and both represent the radius of a circle. Geometry tells us that an angle formed by two radii that are parts of two congruent triangles has the following dimensions:

m ∠ AOB = 2 · x (1)

Where x is the measure of angle BOC, in degrees.

And the measure of the angle AOC is: ( x= 70°)

∠ AOC = 70°

How much tax will be paid on an item with a 7.5% tax rate that is $1425.89? Round to the nearest cent and do not include a dollar sign

Answers

Answer:

1,616.00

Step-by-step explanation:

sorry if this is wrong

The tax on the item costs $1425.89 is 106.94175 dollars.

What is tax?

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

Given that, tax rate =7.5% and the cost of an item = $1425.89.

Here, tax = 7.5% of 1425.89

= 7.5/100 ×1425.89

= 0.075×1425.89

= $106.94175

Therefore, the tax on the item costs $1425.89 is 106.94175 dollars.

To learn more about the tax visit:

brainly.com/question/16423331.

#SPJ2

what is the area of the figure below

Answers

135in.^2

Step-by-step explanation:

split into 2 shapes :

Triangle

A=bxh/2

= 5 x 6/2

= 15

Rectangle

A=bxh

= 20x6

= 120

120+15=135in.^2

Hope this helps!

If bryan ate 3\8 of a pizza, and d'marjay ate 3\6 of the same pizza, who ate more pizza?

Answers

Answer:

d'marjay ate more pizza , because if bryan ate 3/8 , then d'marjay ate the rest of the pizza , so she could've eaten more

Answer: 3/6

Step-by-step explanation: If the "top number" of multiple fractions is the same, then the smaller "bottom number" is the larger one.

Kara is mixing paint. Each batch has twice as much blue paint as well as yellow paint. Plot points to represent the amount of blue and yellow paint used in three different sized batches.

Answers

(b, y) twice as much blue as yellow

(2, 1)

(4, 2)

(6, 3)

I don't get this I need help?

Answers

Answer: 864

Step-by-step explanation:

The formula is 4/3 pie radius ^3 but since it says 3 just use three. Now the radius is 6. So you do 4/3 times 3 times 6^3 and you get 864. I hope this helps.

Jill went shopping from 3:45 pm to 5:00 pm for how long did she shop​

Answers

Answer:

total 1 hour 15 mins

Step-by-step explanation:

3:45 - 5:00

lets count one by one

3:45 - 4:00 = 15 mins

4:00 - 5:00 = 1 hour

total 1 hour 15 mins

The proportions of multiple samples of registered voters who vote are normally distributed, with a mean proportion of 0.38 and a standard deviation of 0.0485. what is the probability that a sample chosen at random has a proportion of registered voters who vote between 0.37 and 0.39? use the portion of the standard normal table below to help answer the question. z probability 0.00 0.5000 0.04 0.5160 0.21 0.5832 0.37 0.6443 0.38 0.6481 0.39 0.6517 1.00 0.8413 2% 17% 58% 65%

Answers

Then the probability of a sample being chosen at random has a proportion of registered voters who vote between 0.37 and 0.39 will be 0.1632.

What is a normal distribution?

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

The proportions of multiple samples of registered voters who vote are normally distributed, with a mean proportion of 0.38 and a standard deviation of 0.0485.

The z-score is given as

[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

Then the probability of a sample is chosen at random has a proportion of registered voters who vote between 0.37 and 0.39 will be

For x = 0.37, then we have

[tex]z = \dfrac{0.37 - 0.38}{0.0485} \approx -0.206[/tex]

For x = 0.39, then we have

[tex]z = \dfrac{0.39- 0.38}{0.0485} \approx 0.206[/tex]

Then the probability will be

[tex]\rm P(0.37 < x < 0.39) = P(-0.206 < z < 0.206)\\\\ P(0.37 < x < 0.39) =0.58160 - 0.41839 \\\\P(0.37 < x < 0.39) =0.1632[/tex]

More about the normal distribution link is given below.

https://brainly.com/question/12421652

Answer:

B. 17%

Step-by-step explanation:

Got it from a quizlet with very many five star reviews

The table below shows the number of people that attended a family reunion each year. (Need help ASAP)

Answers

The table of attendees in the family reunion is a linear regression

The equation of the line of best fit is y = 4.9x + 112186 attendees are expected in the 15th year

How to draw the scatter plot?

To do this, we represent the years on the x-axis and the attendees on the y-axis

See attachment for the scatter plot

The equation of the line of best fit?

The scatter plot passes through the points

(0, 112) and (5, 136.5)

Start by calculating the slope, m using:

m = (y2 - y1)/(x2 - x1)

This gives

m = (136.5 - 112)/(5 - 0)

m = 4.9

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 4.9 * (x - 0) + 112

y = 4.9x + 112

Hence, the equation of the line of best fit is y = 4.9x + 112

The attendees in the 15th year

This means that x = 15.

So, we have:

y = 4.9 * 15 + 112

Evaluate

y = 186

Hence, 186 attendees are expected in the 15th year

Read more about regression at:

https://brainly.com/question/4341286

billy took a 3/4 mile hike in the woods. if the stopped every 1/4 of a mile to drink from his water bottle, how many times did the top?​

Answers

The answer is: He stopped 3 times
He stopped 3 times in total

Three baseball players are playing catch. Rosanne is 6.4 meters south of Lillian and 5.2
meters west of Jenna. How far does Lillian need to throw the ball to get it to Jenna? If
necessary, round to the nearest tenth.
meters
Submit

Answers

Answer:

8.2 meters

Step-by-step explanation:

This problem will form a Right angle triangle.

Where;

6.4 m and 5.2 m are the adjacent and opposite sides of the triangle while the distance that Lillian needs to throw the ball to get it to Jenna is the hypotenuse of the right angle triangle. Thus;

h = √(6.4² + 5.2²)

h = √68

h = 8.2

A ten sided die is rolled.
P (3 or 5)

Answers

Answer: 1/5 or 20%



Step by Step Explanation:

Since there is 10 possible out comes, and you favor 2 of them, roling the die once will give you a 10/2 or 1/5 chance of getting 3 or 5.

Formula:  Number of outcomes divided by Favorable Outcomes

the westside bakery uses 320 pounds of flour to make 1000 loaves of bread each loaf contains the same amount of flour.How many pounds of flour are used in each loaf of bread?

Answers

Answer:

1000/320=100/32=25/8 pounds of flour per piece of bread

Step-by-step explanation:

[tex]if \: each \: loaf \: contains \: the \: same \: amount \: of \: flour \: then \: each \: loaf \: contains \\ = \frac{1000}{320} \\ = 3.125[/tex]

therefore each loaf contains 3.125 pounds

32° x x
Please help

Answers

180°-32°=2x (angles in a triangle always sum up to 180)

2x= 148°

x= 74° (they are (at least) 2 angles that are even in an isosceles triangle)

In order to qualify for letter sorting l, applicants are given a speed-reading test. The scores are normally distributed, with a mean of 80 and a standard deviation of 8. If only the top 15% of the applicants are selected, find the score needed to qualify

Answers

Using the normal distribution, it is found that the score needed to qualify is of 88.32.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 80[/tex] and [tex]\sigma = 8[/tex].

The top 15% of the applicants are selected, hence the score needed to qualify is the 85th percentile, which is X when Z = 1.04, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.04 = \frac{X - 80}{8}[/tex]

X - 80 = 1.04(8)

X = 88.32.

The score needed to qualify is of 88.32.

More can be learned about the normal distribution at https://brainly.com/question/24663213

A random number, x, is generated, where x is any real number.

(a) Manuel adds 2 to x. He subtracts x from 10. Manuel then multiplies these two results to give his number, y.

Show that y = 20 + 8x - x?.​

Answers

Step-by-step explanation:

Say that x = 1, since x can be any real number.

From part a -> x +2 = 3

and -> 10-x =9

then multiply the two results to get y -> 3x9 = 27

Now look at y=20+8x-x and plug in the same value for x where x = 1

you get -> y = 20 + 8(1) -(1) which simplifies out to 27. Therefore the equation is proven since they equal the same value.

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