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timofeeve [1]
3 years ago
7

Find the slopes of the asymptotes of the hyperbola with the following equation.

Mathematics
1 answer:
frosja888 [35]3 years ago
3 0
You are given the equation 36 = 9x² + 4y². You are asked to find the slopes of the asymptotes of the hyperbola. A hyperbola has the following general equation x²/a² + y²/b² = 1. the goal here is to find the slopes of the hyperbolic equation. So divide both sides by 36

36 = 9x² + 4y²
(1/36)[36 = 9x² + 4y²]
1 = x²/4 + y²/9
a² = 4
a = 2
and
b² = 9
b = 3

To find the slope, divide a/b and you will get 2/3.
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<img src="https://tex.z-dn.net/?f=2a%20%7B%20%7D%5E%7B2%7D%20b%20%7B%7D%5E%7B2%7D%20-%207ab%20-%2030" id="TexFormula1" title="2a
yarga [219]

Answer:

(ab - 6)(2ab + 5)

Step-by-step explanation:

Assuming you require the expression factorised.

2a²b² - 7ab - 30

Consider the factors of the product of the coefficient of the a²b² term and the constant term which sum to give the coefficient of the ab- term

product = 2 × - 30 = - 60 and sum = - 7

The factors are - 12 and + 5

Use these factors to split the ab- term

= 2a²b² - 12ab + 5ab - 30 ( factor the first/second and third/fourth terms )

= 2ab(ab - 6) + 5(ab - 6) ← factor out (ab - 6) from each term

= (ab - 6)(2ab + 5) ← in factored form

5 0
3 years ago
1. An orange is peeled . 18 identical sectors are found . What angle do does each semicircular surface make with another in a wh
KatRina [158]

Answer:

<h3>#1</h3>

<u>Since the circle covers 360°, each sector will be:</u>

  • 360°/18 = 20°

The same angle will be made between two adjacent semicircles.

<h3>#2</h3>

The points have same latitude but different longitude.

35°W and 15° are at different sides from zero longitude.

<u>The difference is:</u>

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8 0
2 years ago
Someone that can help me out please
MAXImum [283]

Answer: I got 32

Step-by-step explanation:

I got 32

8 0
3 years ago
Michael is doing an underwater handstand. His feet are sticking up 0.5 meters above the surface of the water Michael's hands are
Jlenok [28]
1.3 meters below the surface of the water
6 0
3 years ago
Read 2 more answers
An appliance company uses the function f(h) = 40h + 120 to calculate the total repair bill, f(h), for h number of hours worked.
Verdich [7]

Answer:

fh. = 40h + 120,  fh. = $200

200 = 40h + 120

200 - 120 = 40h

80 = 40h

80/40  = h

 2 = h

h = 2 hours.

Step-by-step explanation:

4 0
3 years ago
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