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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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Ok so first we need to distribute so:
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<span>=<span><span><span>4b</span>+8</span>+<span>−<span>3b
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<h3>Answer:   60 minutes</h3>

=====================================================

Explanation:

Let's find the LCM of 4 and 5, which are the first two items of the list.

  • multiples of 4 are: 4,8,12,16,20,24,...
  • multiples of 5 are: 5,10,15,20,25,...

The smallest item in each list is 20, so the LCM of 4 and 5 is 20.

We can replace the "4,5" in the list "4,5,12,15" with "20". So our new list would be "20,12,15".

We then repeat the process of finding the LCM of the first two items

  • multiples of 20 are: 20,40,60,80,...
  • multiples of 12 are: 12,24,36,48,60,72,...

LCM of 20 and 12 is 60.

The list "20,12,15" condenses to "60,15".

Repeat this process of finding the LCM once more and you'll find the overall LCM is 60.

Therefore, the LCM of the entire set {4,5,12,15} is 60. This is the smallest multiple shared by all four values. Interestingly enough, the outer values pair up to multiply to 60, and so do the inner values.

4*15 = 60

5*12 = 60

The bells ring together every <u>60 minutes</u>

In other words, all of the bells ring together at the same time every hour (perhaps at the top of every hour; eg at 7:00 pm and at 8:00 pm, etc).

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