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3 years ago

Given the hyperbola (x2/4) – (y2/9) = 1, find the equations for its asymptotes

1 answer:

7 0

$\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\\\\The\ equations\ of\ asymptotes:\\\\m:y=\dfrac{b}{a}x\ and\ n:y=-\dfrac{b}{a}x\\-------------------------\\\dfrac{x^2}{4}-\dfrac{y^2}{9}=1\to\dfrac{x^2}{2^2}-\dfrac{y^2}{3^2}=1\\\\a=2;\ b=3\to\dfrac{b}{a}=\dfrac{3}{2}\\\\Answer:\boxed{y=-\frac{3}{2}x\ and\ y=\frac{3}{2}x}$

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Classify each statement as a definition, postulate, or theorem. Select the correct answer from the drop-down menu. through

Alex

postulate,

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3 years ago

A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the

devlian [24]

Answer:

The probability that Harry will be chosen as either as Secretary or as treasurer but not as president out of those 10 members will be $\frac{1}{5}$ .

Step-by-step explanation:

We have 10 members out of which one is Harry, we need to choose one of the 10 members as President, one to be as secretary out of the remaining 9, one as the treasurer of the remaining 8 members.

We want harry to be as either as secretary or as treasurer. so we will consider both the cases

Probability is given by = No of favorable outcomes/ Total no of outcomes

(1) Harry as secretary : If harry is to be chosen as secretary then he can't be a president or he cant be a Treasurer

As president = $\frac{1}{10}$

Not as president = $1 - \frac{1}{10}$ = $\frac{9}{10}$

Now he is selected for the secretary so he can't be selected as treasurer.

Not as treasurer = 1

Probability for chosen as secretary = $\frac{9}{10}*\frac{1}{9}*1$ = $\frac{1}{10}$

(2) Harry as treasurer : If harry is to be chosen as the treasurer so he can't be chosen as a President or as a Secretary.

Probability for not chosen as president = $\frac{9}{10}$

Probability for not chosen as secretary = $1-\frac{1}{9} = \frac{8}{9}$

Probability to be chosen as treasurer = $\frac{1}{8}$

Probability to be chosen as Treasurer = $\frac{9}{10}*\frac{8}{9}*\frac{1}{8}$ = $\frac{1}{10}$

Total probability for Harry to be chosen as either secretary or as treasurer will be = P(Secretary) +P(Treasurer)

= $\frac{1}{10} +\frac{1}{10} = \frac{1}{5}$

Therefore the probability that Harry will be chosen as either as Secretary or as treasurer but not as president out of those 10 members will be $\frac{1}{5}$ .

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3 years ago

Aubrey and Charlie are driving to a city that is 120 mi from their house. They have already traveled 20 mi, and they are driving

Zarrin [17]

Answer: The function that models the distance they drive is

f(x) = 50x + 20 where x is the time in hours

reasonable domain: 0 ≤ x ≤ 3

Step-by-step explanation:

examples:

95 = 50(1.5) + 20 After driving another hour and a half, they will have driven a total of 95 miles.

120 = 50(2) + 20 This means that after 2 more hours they will reach their destination.

There is a little ambiguity in the question. The function could be written as if they are starting out. f(x) = 50t

20 = 50(.4) At 50 mph it took .4 hours to go 20 miles.

120 = 5(2.4) The whole trip took 2.4 hours.

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3 years ago

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FrozenT [24]

The answer is C.

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b = -6 (number attached to x)
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Now we can put this into the quadratic equation.

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4 years ago

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n200080 [17]

I think the answer would be d

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3 years ago