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eduard
3 years ago
10

The question asks, "Find the equation of the ellipse with the following properties.

Mathematics
2 answers:
boyakko [2]3 years ago
8 0

Answer:

\frac{x^2}{25}+\frac{y^2}{9}=1

Step-by-step explanation:

Equation of ellipse is of form \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 where (a,0) , (-a,0) are the x-intercepts and (0,b) , (0,-b) are the y-intercepts . If a > b then it is a horizontal ellipse and if a < b then it is a vertical ellipse .

For horizontal axis ,

Here, (a,0) , (-a,0) are known as the vertices of ellipse and (0,b) , (0,-b) are the co-vertices of ellipse .

Horizontal axis is known as the major axis and vertical axis is known as the minor axis .

Here, x-intercepts are (5,0) , (-5,0) , take a = 5

y-intercepts are (0,3) , (0,-3) , take b = 3

As a > b , it is a horizontal ellipse .

On putting a = 5 and b = 3 , we get equation as

\frac{x^2}{5^2}+\frac{y^2}{3^2} =1\\ \frac{x^2}{25}+\frac{y^2}{9} =1

Alex777 [14]3 years ago
5 0

Answer:

x^2 / 25 + y^2 / 9 = 1

Step-by-step explanation:

The major axis is along the x axis and the minor axis is on the y axis.

Major axis = 2a =  5--5 =10 so a = 5 and a^2 = 25.

Similarly b^2 = 3^2 = 9.

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Can someone please help me with this?!
Alinara [238K]

Answer: y=\frac{1}{4}x-3


Step-by-step explanation:

- The equation of the line in the slope intercept form is: y=mx+b

Where m is the slope and b is the y-intercept of the line

- Let's choose two points of the line: (8,-1) and (-4,-4).

- You must calculate the slope of the line as following:

m=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-(-1)}{-4-8}=\frac{1}{4}

- As you can see in the graph attached, the line intersects the y-axis at -3, then b=-3.

- Substituting values into the equation of the line, you obtain:

y=\frac{1}{4}x-3


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Simplify the expression. (–5 – c)(–1) A.5 + c B.–5 + c C.5 – c D.–5 – c
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Evaluate 18 -8(14 + 4) + 42.
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Step-by-step explanation:

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The perimeter of the garden is 84 feet. The length of one side of fencing is 8 yards. What is the area of the garden?
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A laptop producing company also produces laptop batteries, and claims that the batteries
gregori [183]

Answer:

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).

The null and alternative hypothesis are:

H_0: \mu=4\\\\H_a:\mu< 4

Step-by-step explanation:

<em>The question is incomplete: To test this claim a sample or population standard deviation is needed.</em>

<em>We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.</em>

<em> NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.</em>

This is a hypothesis test for the population mean.

The claim is that the batteries power the laptops for significantly less than 4 hours.

Then, the null and alternative hypothesis are:

H_0: \mu=4\\\\H_a:\mu< 4

The significance level is 0.05.

The sample has a size n=500.

The sample mean is M=3.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902

The degrees of freedom for this sample size are:

df=n-1=500-1=499

This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):

P-value=P(t

As the P-value (0) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.

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