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2 years ago

Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?

Mathematics

1 answer:

tester [92]2 years ago

8 0

Answer:

x^2/12 - y^2/4 = 1

Step-by-step explanation:

As the diretrices have simetrical values of x and have y = 0, the center is located at (0,0)

The formula for the diretrices is:

x1 = -a/e and x2 = a/e

And the foci is located at (a*e, 0) and (-a*e, 0)

So we have that:

a/e = 3

a*e = 4

From the first equation, we have a = 3e. Using this in the second equation, we have:

3e*e = 4

e^2 = 4/3

e = 1.1547

Now finding the value of a, we have:

a = 3*1.1547 = 3.4641

Now, as we have that b^2 = a^2*(e^2 - 1), we can find the value of b:

b^2 = 3.4641^2 * (1.1547^2 - 1) = 4

b = 2

So the equation of the hyperbola (with vertical diretrices and center in (0,0)) is:

x^2/a^2 - y^2/b^2 = 1

x^2/12 - y^2/4 = 1

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2 years ago

Read 2 more answers

Factor the polynomial expression 15x^2 - 2x - 8

AVprozaik [17]

Answer:

(3 x + 2) (5 x - 4)

Step-by-step explanation:

Factor the following:

15 x^2 - 2 x - 8

Factor the quadratic 15 x^2 - 2 x - 8. The coefficient of x^2 is 15 and the constant term is -8. The product of 15 and -8 is -120. The factors of -120 which sum to -2 are 10 and -12. So 15 x^2 - 2 x - 8 = 15 x^2 - 12 x + 10 x - 8 = 5 x (3 x + 2) - 4 (3 x + 2):

5 x (3 x + 2) - 4 (3 x + 2)

Factor 3 x + 2 from 5 x (3 x + 2) - 4 (3 x + 2):

Answer: (3 x + 2) (5 x - 4)

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2 years ago

Leo and Maggie volunteer at the local bird sanctuary. Volunteers carry walkie-talkies. Leo notices that his walkie-talkie’s batt

Fiesta28 [93]

12 * 20% = 12 * 0.20 = 2.4 hours

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Write 9.054 X 10-6 in standard form.

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Answer:

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Have a nice day!!! :-)

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2 years ago

I WILL AWARD BRAINLIEST!! PLEASE HELP!!! The figure below shows the movement of a pedestrian from point B to point E. Using the

MissTica

A) The speed of the pedestrian BC is 5 km/h

The speed of the pedestrian CD is 0 km/h

The speed of the pedestrian DE is 5 km/h

B) He arrived E since the stop after 6 hours

C) The formula for section BC is d(t) = 40 - 5t

The formula for section CD is d(t) = 20

The formula for section DE is d(t) = 50 - 5t

Step-by-step explanation:

In the time-distance graph the speed is the rate of change of distance

and that mean speed = Δd/Δt ⇒ (slope of the line)

In line BC:

1. Δd = 40 - 20 = 20 km

2. Δt = 4 - 0 = 4 hours

3. The speed = 20 ÷ 4 = 5 km/h

The speed of the pedestrian BC is 5 km/h

In line CD:

1. Δd = 20 - 20 = 0 km

2. Δt = 6 - 4 = 2 hours

3. The speed = 0 ÷ 2 = 0 km/h

The speed of the pedestrian CD is 0 km/h

In line DE:

1. Δd = 20 - 0 = 20 km

2. Δt = 10 - 6 = 4 hours

3. The speed = 20 ÷ 4 = 5 km/h

The speed of the pedestrian DE is 5 km/h

∵ He stop at t = 4 hours

∵ He arrived at point E at t = 10 hours

∵ 10 - 4 = 6 hours

He arrived E since the stop after 6 hours

The speeds are represented by lines

The form of the equation of a line is f(x) = mx + c, where m represents

the slope of the line and c is the y-intercept (y when x = 0)

1. f(x) is d(t)

2. m is the speed

3. x is t

4. You can find c by substitute d and t by any point on the line

Line BC

Line BC has negative slope because d decreases when t increases

∵ m = -5 and c = 40

∴ d(t) = 40 - 5t

The formula for section BC is d(t) = 40 - 5t

Line CD

Line CD is a horizontal line (equation any horizontal line is y = c)

∴ m = 0 and c = 20

∴ d(t) = 20

The formula for section CD is d(t) = 20

Line DE

Line DE has negative slope because d decreases when t increases

∵ m = -5

∴ d(t) = -5t + c

To find c substitute the coordinates of point D in the equation

∵ The coordinates of point D are (6 , 20)

∴ 20 = -5(6) + c

∴ 20 = -30 + c

Add 30 to both sides

∴ c = 50

∴ d(t) = 50 - 5t

The formula for section DE is d(t) = 50 - 5t

Learn more:

You can learn more about the distance, speed, and time in

brainly.com/question/5102020

#LearnwithBrainly

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