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3 years ago

Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)

Mathematics

2 answers:

sergeinik [125]3 years ago

8 0

Answer:

Hope this helps :)

Step-by-step explanation:

Nitella [24]3 years ago

5 0

The equation of a hyperbola is:

(x – h)^2 / a^2 - (y – k)^2 / b^2 = 1

So what we have to do is to look for the values of the variables:

For the given hyperbola : center (h, k) = (0, 0)
a = 3(distance from center to vertices)
a^2 = 9

c = 7 (distance from center to vertices; given from the foci)
c^2 = 49

By the hypotenuse formula:
c^2 = a^2 + b^2
b^2 = c^2 - a^2

b^2 = 49 – 9

b^2 = 40

Therefore the equation of the hyperbola is:

(x^2 / 9) – (y^2 / 40) = 1

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204 times .46 equals 93.84, to round of it would be 93.8

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3 years ago

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Novay_Z [31]

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3 years ago

Read 2 more answers

Match the features of the graph of the rational function.

Sunny_sXe [5.5K]

After applying algebraic analysis we find the right choices for each case, all of which cannot be presented herein due to length restrictions. Please read explanation below.

<h3>How to analyze rational functions</h3>

In this problem we have a rational function, whose features can be inferred by algebraic handling:

Holes - x-values that do not belong to the domain of the rational function:

x³ + 8 · x² - 9 · x = 0

x · (x² + 8 · x - 9) = 0

x · (x + 9) · (x - 1) = 0

x = 0 ∨ x = - 9 ∨ x = 1

But one root is an evitable discontinuity as:

y = (9 · x² + 81 · x)/(x³ + 8 · x² - 9 · x)

y = (9 · x + 81)/(x² + 8 · x - 9)

Thus, there are only two holes. (x = - 9 ∨ x = 1) Besides, there is no hole where the y-intercept should be.

Vertical asymptotes - There is a vertical asymptote where a hole exists. Hence, the function has two vertical asymptotes.

Horizontal asymptotes - Horizontal asymptote exists and represents the end behavior of the function if and only if the grade of the numerator is not greater than the grade of the denominator. If possible, this assymptote is found by this limit:

$y = \lim_{x \to \pm \infty} \frac {9\cdot x + 81}{x^{2}+8\cdot x - 9}$

y = 0

The function has a horizontal asymptote.

x-Intercept - There is an x-intercept for all x-value such that numerator is equal to zero:

9 · x + 81 = 0

x = - 9

There is a x-intercept.

Lastly, we have the following conclusions:

How many holes? 2
One horizontal asymptote along the line where y always equals what number: 0
This function has x-intercepts? True
One vertical asymptote along the line where x always equals what number: 1
There is a hole where the y-intercept should be? False

To learn more on rational functions: brainly.com/question/27914791

#SPJ1

5 0

2 years ago

Pleas help me alot of points

alekssr [168]

Answer:

Step-by-step explanation:

its a square all sides of the square are the same so 48 divided by 4 is 12

5 points is not a lot of points

6 0

3 years ago

A bag contains 25 balls 20 of which are blue what percentage of balls are not blue

Artist 52 [7]

Answer:

20%

Step-by-step explanation:

20/25 = blue

This means 5/25 of the balls in the bag are NOT blue

(25-20 = 5)

We need to convert 5/25 to a percentage

$\dfrac{5}{25} = \dfrac{5\times4}{25\times4}=\dfrac{20}{100}$

% = per cent

"per" means "out of"

"cent" means "one hundred"

20/100 = 20%

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2 years ago