All categories

4 years ago

Which equations represent the asymptotes of the hyperbola?

Mathematics

1 answer:

makvit [3.9K]4 years ago

4 0

Answer:

see below

Step-by-step explanation:

The equation of the hyperbola can be written as ...

((x -h)/a)² -((y -k)/b)² = 1

This has asymptotes ...

(x -h)/a ± (y -k)/b = 0

Solving for y, we have ...

y = ±(b/a)(x -h) +k

Filling in the given values a=6, b=8, h=1, k=2, we have ...

y = ±8/6(x -1) +2

$y=\dfrac{\pm4x\mp4+6}{3}\\\\\boxed{y=\dfrac{4x+2}{3}\ \text{and }y=\dfrac{10-4x}{3}}$

You might be interested in

Each Saturday the gym holds 45 minute yoga classes. The weekday yoga classes last 30 minutes. The number of weekday classes vari

yanalaym [24]

For this case we have that the total minutes spent in yoga classes last week was 165.

Subtracting the 45 minutes of the Saturday day we have:

$165-45 = 120$

Those 120 minutes were distributed in the weekly yoga classes

where each lasted 30 minutes.

$\frac {120} {30} = 4$

So, 4 week yoga classes were held

ANswer:

4 week yoga classes were held

6 0

3 years ago

Is a rational number divided by a rational number always rational?

miss Akunina [59]

Answer:

Yes

Step-by-step explanation:

When two rational numbers are divided, the outcome will always come out rational.

3 0

4 years ago

Use the sample data and confidence level given below to complete parts (a) through (d). A drug is used to help prevent blood c

Alla [95]

Answer:

a) $\hat p=\frac{148}{4167}=0.036$

b) $0.0355 - 1.96\sqrt{\frac{0.036(1-0.036)}{4167}}=0.030$

$0.0355 + 1.96\sqrt{\frac{0.036(1-0.036)}{4167}}=0.041$

Step-by-step explanation:

The sample proportion have the following distribution

$\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part a

The estimated proportion for this case can be calculated like this:

$\hat p=\frac{148}{4167}=0.036$

Part b

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: