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2 years ago

Foci of ellipse of 3x2 + y2 =9

Mathematics

1 answer:

Oksi-84 [34.3K]2 years ago

8 0

Answer:

x=√-1/3 y^2 +3 or x=-√-1/3 y^2 +3

Step-by-step explanation:

Let's solve for x.

3x2+y2=9

Step 1: Add -y^2 to both sides.

3x2+y2+−y2=9+−y2

3x2=−y2+9

Step 2: Divide both sides by 3.

3x^2/3= -y^2+9/3

x^2=-1/3 y^2 +3

x=√-1/3 y^2 +3 or x=-√-1/3 y^2 +3

Hope it helped!

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Pls Help!!! Worth 99 Pts!!

Alenkasestr [34]

First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)

To find the zeros, you set the equation equal to 0 and solve for x
x^3+2x^2-8x=0
x(x^2+2x-8)=0
x(x+4)(x-2)=0
x=0 x=-4 x=2

So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)

And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.
Plugging in a -5 gets us -35
-1 gets us 9
1 gets us -5
3 gets us 21

So now you know end behavior, zeroes, and signs of intervals

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6 0

2 years ago

Read 2 more answers

A computer code is based on the prime factorization of 160.Find the prime factorization of 160

lilavasa [31]

Ndhdjjdjdjshduhdjskakksjdnfbbfbbnfbbbdbdvdbdbbdbdbfhf

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3 years ago

What is the midpoint ?

inn [45]

Answer:

Step-by-step explanation:

A(-5,-4) B(-3, 3)

(-5 + -3)/2 = -8/2= -4

(-4 + 3)/2 = -1/2

(-4, -1/2) the midpoint

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2 years ago

suppose X and Y are independent random variables, both with normal distributions. If X has a mean of 45 with a standard deviatio

djyliett [7]

Answer:

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

$\mu_X = 45, \sigma_X = 4, \mu_Y = 35, \sigma_Y = 3$

What is the probability that a randomly generated value of X is greater than a randomly generated value of Y

This means that the subtraction of X by Y has to be positive.

When we subtract two normal variables, the mean is the subtraction of their means, and the standard deviation is the square root of the sum of their variances. So

$\mu = \mu_X - \mu_Y = 45 - 35 = 0$

$\sigma = \sqrt{\sigma_X^2+\sigma_Y^2} = \sqrt{25} = 5$

We want to find P(X > 0), that is, 1 subtracted by the pvalue of Z when X = 0. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0 - 10}{5}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228

1 - 0.0228 = 0.9772

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

4 0

3 years ago

A rectangular board has an area of 648 square centimeters. The triangular part of the board has an area of 162 square centimeter

maksim [4K]

Answer:

25%.

Step-by-step explanation:

Let E be the event that the dart lands inside the triangle.

We have been given that a rectangular board has an area of 648 square centimeters. The triangular part of the board has an area of 162 square centimeters.

We know that probability of an event represents the chance that an event will happen.

$\text{Probability}=\frac{\text{Favorable no. of events}}{\text{Total number of possible outcomes}}$