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alexira [117]
2 years ago
13

Please need solution .. Thank you ​

Mathematics
1 answer:
hjlf2 years ago
6 0

anong edad mo na Kasi 13 na ko

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The center of a hyperbola is located at the origin. One focus is located at (−50, 0) and its associated directrix is represented
leva [86]

The equation of the hyperbola is : \frac{x^{2}}{48^2}  - \frac{y^{2}}{14^2}  = 1

The center of a hyperbola is located at the origin that means at (0, 0) and one of the focus is at (-50, 0)

As both center and the focus are lying on the x-axis, so the hyperbola is a horizontal hyperbola and the standard equation of horizontal hyperbola when center is at origin: \frac{x^{2}}{a^{2}}  - \frac{y^{2}}{b^{2}}    = 1

The distance from center to focus is 'c' and here focus is at (-50,0)

So, c= 50

Now if the distance from center to the directrix line is 'd', then

d= \frac{a^{2}}{c}

Here the directrix line is given as : x= 2304/50

Thus, \frac{a^{2}}{c}  = \frac{2304}{50}

⇒ \frac{a^{2}}{50}  = \frac{2304}{50}

⇒ a² = 2304

⇒ a = √2304 = 48

For hyperbola, b² = c² - a²

⇒ b² = 50² - 48² (By plugging c=50 and a = 48)

⇒ b² = 2500 - 2304

⇒ b² = 196

⇒ b = √196 = 14

So, the equation of the hyperbola is : \frac{x^{2}}{48^2}  - \frac{y^{2}}{14^2}  = 1

5 0
3 years ago
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There are several houses for sale in a local neighborhood. One house is on the market for $105,000. Four houses are on sale for
abruzzese [7]
600,457 is correct answer
8 0
3 years ago
Radium-226 has a half life of 1622 years. If you start off with a 200
sweet [91]

Answer:

≈23.6 kg left.

Step-by-step explanation:

For determining this, we can simply use an exponential decay equation representing this scenario:

y= a(0.5)^{\frac{t}{h} }

a: the initial amount

t: the amount of time

h: the half life

Now, substitute the numbers into the equation:

y=200(0.5)^{\frac{5000}{1622} }

Now, solve this equation:

y=220(0.5)^{3.08}

Use a calculator to solve for y:

y= 200(0.118)

y≈23.6 kg left.

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3 years ago
What are the x-intercepts of the parabola?
Natasha_Volkova [10]

Answer:

(5, 0) and (4, 0)

Step-by-step explanation:

According to the graph shown, the parabola passes trough the points (4,0) and (5,0). Therefore, they are the x-intercepts of the parabola.

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3 years ago
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maria put two angles together to form a straight angle. One angle measures 112 degrees. what is the measure of the other angle?
Kitty [74]

its the same angle 112 degrees


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