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liq [111]
3 years ago
12

Select the correct answer from each drop-down menu. The equation (y-2)^2/3^2 - (x-2)^2/4^2=1 represents a hyperbola whose foci a

re blank and blank .
Mathematics
1 answer:
aev [14]3 years ago
5 0

Answer:

The foci are (2 , 7) and (2 , -3)

Step-by-step explanation:

* lets revise the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the y-axis is

  (y - k)²/a² - (x - h)²/b² = 1

- The coordinates of the vertices are ( h ± a , k )  

- The coordinates of the co-vertices are ( h , k ± b )

- The coordinates of the foci are (h , k ± c), where c² = a² + b²

* Now lets solve the problem

∵ The equation of the hyperbola of vertex (h , k) is

    (y - k)²/a² - (x - h)²/b² = 1

∵ The equation is (y - 2)²/3² - (x - 2)²/4² = 1

∴ k = 2 , h = 2 , a = 3 , b = 4

∵ The foci of it are (h , k + c) and (h , k - c)

- Lets find c from the equation c² = a² + b²

∵ a = 3

∴ a² = 3² = 9

∵ b = 4

∴ b² = 4² = 16

∴ c² = 9 + 16 = 25

∴ c = √25 =  5

- Lets find the foci

∵ The foci are (h , k + c) and (h , k - c)

∵ h = 2 , k = 2 , c = 5

∴ The foci are (2 , 2 + 5) and (2 , 2 - 5)

∴ The foci are (2 , 7) and (2 , -3)

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Answer:

Option (C)

Step-by-step explanation:

Coordinates of the point representing the location of Miya → (1, 10)

Coordinates of the point representing the location of Drea → (13, 1)

Coordinates of the point representing the location of Francine → (16, 1)

Coordinates of the point representing the location of Beach → (19, 4)

Distance between Miya and Drea = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

                                                        = \sqrt{(13-1)^2+(1-10)^2}

                                                        = \sqrt{144+81}

                                                         = 15 miles

Distance between Drea and Francine = \sqrt{(16-13)^2+(1-1)^2}

                                                               = 3 miles

Distance between Francine and Beach = \sqrt{(19-16)^2+(4-1)^2}

                                                                  = \sqrt{9+9}

                                                                  ≈ 4.2 miles

Total distance between Miya and the beach = 15 + 3 + 4.2

                                                                          = 22.2 miles

Option (C) is the answer.

5 0
3 years ago
4% of what number is 5
Papessa [141]
4%n = 5

Simplify the equation

1/25n = 5

Multiply by 25

25 (1/25n) = (25) (5)

n = 125.
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Step-by-step explanation:

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Step-by-step explanation:

Because the teacher can grade 25 assignments in 20 minutes, we can dive 25 by 20 to get the constant rate.

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