What are the equations for the asymptotes of this hyperbola?
Y^2/36 - x^2/121=1

Answers

Answer 1

Answer:

[tex]\huge{\mathfrak{Solution}}[/tex]

[tex]\huge{\bold{ \frac{ {y}^{2} }{36} - \frac{ {x}^{2} }{121} = 1 }}[/tex]

[tex]\huge{\bold{ \frac{(y - k) {}^{2} }{ {a}^{2} } - \frac{(x - h) {}^{2} }{ {b}^{2} } = 1 \: is \: the \: standard \: equation \: with \: center \: (h ,k),semi-axis \: a \: and \: semi-conjugate \: -axis \: b.}}[/tex]

[tex]\huge\boxed{\mathfrak{We \: get,}}[/tex]

[tex](h,k) = (0,0),a = 6,b = 11[/tex]

[tex]For \: hyperbola \: assymtoms \: are \: y = + \frac{a}{b} (x - h) + k[/tex]

[tex]Therefore,y = \frac{6}{11} (x - 0) + 0,y = - \frac{6}{11} (x - 0) + 0[/tex]

[tex]\large\boxed{\bold{y = \frac{6x}{11},y = - \frac{6x}{11} . }}[/tex]

Answer 2

If y²/36 - x²/121 = 1, the asymptotes are y = (36/121) x and y = -(36/121) x.

To find the equations for the asymptotes of the hyperbola represented by the equation y²/36 - x²/121 = 1, we can compare it with the standard form of a hyperbola:

(y - k)² / a² - (x - h)² / b² = 1

where (h, k) represents the center of the hyperbola.

In the given equation, we have y²/36 - x²/121 = 1. To put it in standard form, we need to divide both sides by 1 (which is essentially dividing by 1 on the right side):

y²/36 - x²/121 = 1 / 1

Now, we can see that a² = 36 and b² = 121.

To find the equations of the asymptotes, we use the center (h, k) and the values of a and b. The asymptotes of a hyperbola have equations of the form:

y = k ± (a/b)(x - h)

In this case, the center (h, k) is (0, 0), a² = 36, and b² = 121:

The equations for the asymptotes are:

y = 0 ± (36/121) x

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Related Questions

the quotient of a number and 7 is greater than or equal to 20

Answers

Answer:

a is greater than or equal to 140

Step-by-step explanation:

Multiply both sides by 7, which cancels out the 7 and turns 20 into 140


A basket contains four apples, three pears, two peaches, if we draw one fruit from the basket, what is the probability of getting a peach or an apple?

Answers

Answer:

The probability of getting a peach or an apple is 2/3.

Step-by-step explanation:

There are two peaches and four apples, so six fruits we want to know the probability of getting, and there are also three pears, which means we have nine fruits total. The chance of getting an apple or a pear is six out of nine, which simplifies to two out of three.

PLLZ HELLP QUESTION IS BELOW!! :D

Answers

Answer:

The answer to the first question is 32 but I don't know the slope of the line, sorry

3х + 4y= 4
12х + 16y = 8

Answers

Answer:

No Solution.

Step-by-step explanation:

3x+4y=4

12x+16y=8

--------------

-4(3x+4y)=-4(4)

12x+16y=8

--------------------

-12x-16y=-16

12x+16y=8

-----------------

0=-8

no solution

a store is handing out scratch-off cards to its customers .for each card a customer wins either a coupon or a free t-shirt .the ratio of coupon cards to t-shrits is 9:2 .the total of 8,250 cards how many of the cards are t-shirts cards

Answers

Step-by-step explanation:

Ratio 9:2, therefore total number of shares is 11.

because 9+2 = 11

total cards = 8,250

8,250/11 = 750

This is the value for one of the shares.

As the ratio is 9:2 we can find:

9 X 750 : 2 X 750

To see what everyone has won.

T-shirts : 2 X 750 = 1,500.

Hope you understand how it's done, if not leave a comment and I'll try to be more thorough

What are the steps to convert a number from standard notation to scientific notation? ​

Answers

Answer:

Consider a big number 3,400,000. To convert this number into scientific notation:

Place a decimal by counting the steps to the left until the coefficient of the number is between 1 and 9.

Count the number of steps moved. This will be the power of the base 10.

In this case, the coefficient is 3.4 and the 6 steps are moved.

Multiply the coefficient by 106,

Therefore, the answer is 3. 4 x 10 6

Step-by-step explanation:

What is the slope of any line parallel to the graph of y=8x+20?

Answers

Answer:

m = 8

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

When any 2 lines are parallel, they will have the same slope but different y-intercepts.

∴ Our parallel line's slope will be 8.

Marhannah must make a costume for the school play. She needs a piece of fabric that’s is 8/3 yards long and 3/2 yards wide. What is the area of the piece of fabric Marhannah needs?

Answers

Answer:

Our material is 54" wide. Here is a helpful chart to help you quickly convert linear yards into inches and feet.

How big is one linear yard of fabric?

Yards Length Width

3 108 Inches (9 Feet) 54 Inches (4.5 Feet)

4 144 Inches (12 Feet) 54 Inches (4.5 Feet)

Step-by-step explanation:

C A R R Y

O N

L E A R N I N G

The area of the piece of fabric Marhannah needs is 4 yards.

Steps:
area = l x w
area = 8/3 x 3/2

8/3 • 3/2 = 4

What is the product of 44(4-7)(4)?
-16
O
ОО
-1 -12
-100
8
DONE

Answers

Hey there!

44(4 - 7)(4)

= 44(-3)(4)

= -132(4)

= -528

Therefore, your answer is: -528

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Which number is closest to 1/2

Answers

Answer:

0.56

it's basically the number closest to 50. Don't get tricked by the 0.05 because that's only 5% not 50%

What two numbers multiplied together equal 8 but when added together equal -6

Answers

Answer:

i believe its -4 and -2

Step-by-step explanation:

hope tha work

Does any one mind helping me on this question I have struggle solving it

Answers

-1=0

0.5=4.5

3=3.1

this is the answer

Elliott needs 3/4 of a cup of sugar to make a dozen chocolate chip cookies. How many cups of sugar does he
need to make 4 dozen.

Answers

Answer:

3 cups

Step-by-step explanation:

3/4 times 4 equals 12/4. divide and get 3.

What is the equation of the line that passes through the points (-4, 2) and (-2, 10)?

Answers

Answer:

y=4x+18

Step-by-step explanation:

HOPE THIS HELPS :)

Which of the following best describes the slope of the line below?
• A. Negative
• B. Undefined
• C. Zero
D. Positive

Answers

Answer:

A. Negative

Step-by-step explanation:

This line cannot have a slope of zero or undefined because it's a linear negative line. This line is not positive because it's not heading to the right, it's heading to the left which is the negative side, the slope Rise/Run goes up 1 and left 1, which means the slope for this equation is possibly -1x.

Answer:

Negative

Step-by-step explanation:

We can see that as x increases, y decreases. Therefore, the change in y over the change in x is negative. The line goes down from left to right.

4.8 multiplied to 10 to the power -9

Answers

Answer:

000000004.8

Hope it help!

how do you evaluate numbers in math?

Answers

To evaluate an expression in maths, plug in he value of the variable, then simplify the expression following the order of operation.

Assuming we are given the expression, 3x + (2x - 1), and we are required to evaluate the expression, the following shown below is how to evaluate the expression if we are told that x = 1.

First step is to plug in the value of the variable, x, into the expression:

3(1) + (2(1) - 1)

3 + 2 - 1

Using the order of operation, simply

4

Therefore, to evaluate an expression in maths, plug in he value of the variable, then simplify the expression following the order of operation.

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What is the scale factor of the
dilation shown?

Answers

Answer:

2

Step-by-step explanation:

Given the function f(x) x^2-2x/x^3 +9x^2-10x Find any holes, vertical asymptotes, and horizontal asymptotes there may be.

Answers

Answer:

See below

Step-by-step explanation:

I assume you mean [tex]f(x)=\frac{x^2-2x}{x^3+9x^2-10x}[/tex]:

Holes: Since [tex]f(x)=\frac{x^2-2x}{x^3+9x^2-10x}[/tex] reduces to [tex]f(x)=\frac{x(x-2)}{x(x^2+9x-10)}[/tex], then there is a hole at [tex]x=0[/tex] as [tex]x[/tex] exists in both the numerator and denominator (however, its limit as x approaches 0 is 1/5).

Vertical Asymptotes: If we further reduce [tex]f(x)=\frac{x(x-2)}{x(x^2+9x-10)}[/tex] to [tex]f(x)=\frac{x-2}{(x+10)(x-1)}[/tex], then we see that there are vertical asymptotes at [tex]x=-10[/tex] and [tex]x=1[/tex]

Horizontal Asymptotes: As the degree of the numerator is less than the degree of the numerator ([tex]2<3[/tex]), then there is a horizontal asymptote at [tex]y=0[/tex]

find x,y,z : 4x^2+2y^2+2z^2-4xy-4xz+2yz-2y+6z+10=0

Answers

I hope this helps.

Answer:-

   ∴x−3y−4z=0

Explanation:

First we rearrange the equation of the surface into the form f(x,y,z)=0

   x2+2z2=y2

   ∴x2−y2+2z2=0

And so we have our function:

   f(x,y,z)=x2−y2+2z2

In order to find the normal at any particular point in vector space we use the Del, or gradient operator:

   ∇f(x,y,z)=∂f∂xˆi+∂f∂yˆj+∂f∂zˆk

remember when partially differentiating that we differentiate wrt the variable in question whilst treating the other variables as constant. And so:

   ∇f=(∂∂x(x2−y2+2z2))ˆi+

                    (∂∂y(x2−y2+2z2))ˆj+

                    (∂∂z(x2−y2+2z2))ˆk

      =2xˆi−2yˆj+4zˆk

So for the particular point (1,3,−2) the normal vector to the surface is given by:

   ∇f(1,3,−2)=2ˆi−6ˆj−8ˆk

So the tangent plane to the surface x2+2z2=y2 has this normal vector and it also passes though the point (1,3,−2). It will therefore have a vector equation of the form:

   →r⋅→n=→a⋅→n

Where →r=⎛⎜⎝xyz⎞⎟⎠; →n=⎛⎜⎝2−6−8⎞⎟⎠, is the normal vector and a is any point in the plane

Hence, the tangent plane equation is:

   ⎛⎜⎝xyz⎞⎟⎠⋅⎛⎜⎝2−6−8⎞⎟⎠=⎛⎜⎝13−2⎞⎟⎠⋅⎛⎜⎝2−6−8⎞⎟⎠

   ∴(x)(2)+(y)(−6)+(z)(−2)=(1)(2)+(3)(−6)+(−2)(−8)

   ∴2x−6y−8z=2−18+16

   ∴2x−6y−8z=0

   ∴x−3y−4z=0

find the domain of f(x). f(x) = √9x+36​

Answers

Answer:

The domain in interval notation is [-4,∝) or set build: {x|x[tex]\geq[/tex]

Step-by-step explanation:

I'm assuming the 9x and the 36 are in the root

[tex]\sqrt{9x+36}[/tex]

first we must solve for x

[tex]{9x+36}\geq 0[/tex]

substract 36 to both sides

[tex]{9x}\geq -36[/tex]

divide by 9 to both sides

[tex]\frac{9x}{9} }\geq \frac{-36}{9}[/tex]

simplify left side

[tex]x\geq \frac{-36}{9}[/tex]

simplfy right side

[tex]x\geq -4[/tex]

The domain in interval notation is [-4,∝) or set build: {x|x[tex]\geq[/tex]-4}

the Following table shows alexandra's investment options over the course of three years. Her initial investment was $1,000 . write one function for each option to describe the value of the investment f(n), in dollars, after n years.

Answers

The pattern in the given series of amount in the account are in the form of

arithmetic and geometric progression.

The function for Option 1 is;  [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]The function for Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]

Reasons:

The given table of values is presented as follows;

[tex]\begin{tabular}{c|c|c|c|}Number of years&1&2&3\\Option 1 (Amount in dollars)&1,100&1,200&1,300\\Option 2 (Amount in dollars)&1,100&1,210&1,331\end{array}\right][/tex]

In Option 1, the amount in dollars for each year has a common difference of d = 100

The first term, a = 1,100

Therefore;

The Option 1 can be represented as an arithmetic progression , A.P. in the

form, tₙ = a + (n - 1)·d as follows;

For the Option 1, we have;

The amount in dollars after n years, [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]

For Option 2, it is possible to find;

1,331 ÷ 1,210 = 1,210 ÷ 1,100 = 1.1

Therefore;

The terms in the Option 2 have a common ratio of r = 1.1

The Option 2 is a geometric progression, G.P.

The first term in Option 2 is a = 1,100

Which gives, the nth term, tₙ = a·r⁽ⁿ ⁻ ¹⁾

Therefor;

The function for the Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]

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Diego has a skateboard, scooter, bike, and go-cart. He wants to know which vehicle is the fastest. A friend records how far Diego travels on each vehicle in 5 seconds. For each vehicle, Diego travels as fast as he can along a straight, level path.

Answers

Answer:

Are there any numbers?

Step-by-step explanation:

What is the area of a cross section that is parallel to
face ABCD?
Enter your answer in the box.
cm2

Answers

Answer:

1296cm².

Step-by-step explanation:

= 12×36×6÷2 ................

plz check weather correct or notn

Find EG

Please help

Answers

Answer:

EG = 12.2

Step-by-step explanation:

Since HG = HE = 14 then the triangle is isosceles.

HF is a perpendicular bisector of EG , then

EF = FG = 6.1 , so

EG = EF + FG = 6.1 + 6.1 = 12.2

If a new car is valued at $26,000 and 10 years later it is valued at $7000, then what is the average rate of change
of its value during those 10 years?

Answers

Answer:

The change in value is 19,000 altogether and 1900/year

Step-by-step explanation:

Change in value:

initial value - final value

= $26,000 - $7000

= $19,000

Change in value/year:

change in value/time

= $19,000/10

= $1900/year

1. Make a Prediction Write a rule that you can use to find the number of star beads in a bracelet when you know the number of moon beads. Then write a rule that you can use to find the number of moon beads when you know the number of star beads.​

Answers

Heheh fijándome de. Benne’s

Find the midpoint of the segment with the following endpoints. (10,6) and (4,9)​

Answers

Answer:

(7,7.5)

Step-by-step explanation:

midpoint formula:

(10+4)/2=7

(6+9)/2=7.5

(7,7.5)

Question 14
Determine if the given lines are parallel or perpendicular or neither.
3y=2-x
y=-1/3x+4

Answers

Answer:

The given lines are parallel.

Step-by-step explanation:

3y=2-x

y=-1/3x+4

-------------

y=2/3-1/3x

y=-1/3x+2/3

y=-1/3x+4

----------------

Since the two lines have exact same slopes, it follows that these two lines are parallel.

Use the quadratic formula to solve for x.

9x^2-3x=1
Round the answer to the nearest hundredth
Last question.

Answers

Answer should be if not sorry
X= 1-5/6
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