All categories

3 years ago

Which equation represents a hyperbola with a center at (0,0), a vertex at (0,60), and a focus at (0,-65)

Mathematics

2 answers:

Leona [35]3 years ago

7 0

Given that the hyperbola has a center at (0,0), and its vertices and foci are on y-axis. This, the equation of the hyperbola is of the form
x²/a²-y²/b²=-1 (a>0, b>0)
In the equation, vertices are (0, +/-b) .
Thus,
b=60
Foci (0,+/-√(a²+b²))
thus
√(a²+60²)=65
hence solving for a²
a²=65²-60²
a²=625
a²=25²
hence the equation is:
x²/25²-y²/60²=-1

Scrat [10]3 years ago

4 0

Answer:

So for everybody in the future, a clarification is d)y^2/60^2 -x^2/25^2=1

You might be interested in

What is 48,100,000,000,000 in scientific notation? 4.81×10−11 4.81×10−13 4.81×1011 4.81×1013

SSSSS [86.1K]

Given number is 4,8100,000,000,000.

In this number of zero is 11. So we can write it as $481 * 10^{11}$

But for scientific notation we will enter decimal after two place in reverse direction.For this we will also multiply number by 10^2.

So number will be $4.81 * 10^{11} *10^2 = 4.81 * 10^{13}$

So fourth option is correct.

4 0

3 years ago

Read 2 more answers

Is brainly working for anyone right now

Tom [10]

Answer:

no i cant see the answers haha

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

your job pays 8$ per hour Write a variable expression for your pay in dollars for working h hours. What is your pay if you work

lawyer [7]

Answer:

$8h

Your pay is $288 for working 36 hours

Step-by-step explanation:

I hope this helps :)

7 0

3 years ago

Can anyone help me on this problem, please? It's from a section on literal equations.

Agata [3.3K]

If he charges $145 he worked for 5 hours at $20 an hour

4 0

3 years ago

Read 2 more answers

If Upper X overbar equals 62, Upper S equals 8, and n equals 36, and assuming that the population is normally distributed, c

marishachu [46]

Answer:

The 99% confidence interval would be given by (58.373;65.627)

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=62$ represent the sample mean

$\mu$ population mean (variable of interest)

s=8 represent the sample standard deviation

n=36 represent the sample size

Part a: Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=36-1=35$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,35)".And we see that $t_{\alpha/2}=2.72$

Now we have everything in order to replace into formula (1):

$62-2.72\frac{8}{\sqrt{36}}=58.373$

$62+2.72\frac{8}{\sqrt{36}}=65.627$

So on this case the 99% confidence interval would be given by (58.373;65.627)

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

3 0

3 years ago