An object is translated by (x-2, y-6). If one point in the pre-image has the coordinates (-3, 7), what would be the coordinates of its image? (-1,7) O (-5,1) O(-9,5) O (-1, 13)

Answers

Answer 1

Answer:

Answer:(-5,1)

Step-by-step explanation:! X= -3 so -3-4= -7, Y= 7 so 7+2=9, So the coordinates will be (-7,9) I hope that I could help you

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What is the x-and y-intercept of the graph 4x -5y =40??

80 total students 6/2 are girls how many are girls

Answers

Answer:

Step-by-step explanation:

Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region. (x2 + y2)y' = y2 1. A unique solution exists in the region y ≥ x.
2. A unique solution exists in the entire xy-plane.
3. A unique solution exists in the region y ≤ x.
4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.
5. A unique solution exists in the region x2 + y2 < 1.

Answers

A unique solution exists in the region consisting of all points in the xy-plane except the origin.

The correct option is 4.

The given differential equation is:

(x² + y²)y' = y²

The equation can be rewritten as:

$x^2 + y^2 (dy)/(dx) = y^2$

We need to determine a region of the xy-plane for which the differential equation would have a unique solution whose graph passes through a point (x₀, y₀) in the region.

To determine the region, we can use the existence and uniqueness theorem for first-order differential equations.

According to the theorem, a unique solution exists in a region if the differential equation is continuous and satisfies the Lipschitz condition in that region.

To check if the differential equation satisfies the Lipschitz condition, we can take the partial derivative of the equation with respect to y:

dy/dx = y / (x² + y²)

The partial derivative is continuous and bounded in the entire xy-plane except at the origin (x=0, y=0).

Therefore, the differential equation satisfies the Lipschitz condition in the entire xy-plane except at the origin.

Since the differential equation is continuous in the entire xy-plane, a unique solution exists in any region that does not contain the origin. Therefore, the correct answer is:

A unique solution exists in the region consisting of all points in the xy-plane except the origin.

To learn more about the Lipschitz condition;

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Final answer:

The differential equation will have a unique solution in the entire xy-plane except at the origin, as both the function and its partial derivatives are continuous and well-defined everywhere except at that point.

Explanation:

To determine a region of the xy-plane where the differential equation (x2 + y2)y' = y2 has a unique solution passing through a point (x0, y0), we need to consider where the function and its derivative are continuous and well-defined. According to the existence and uniqueness theorem for differential equations, a necessary condition for a unique solution to exist is that the functions of x and y in the equation, as well as their partial derivatives with respect to y, should be continuous in the region around the point (x0, y0).

We note that both the function (x2 + y2)y' and its partial derivative with respect to y, which is 2y, are continuous and well-defined everywhere except at the origin where x = 0 and y = 0. Therefore, a unique solution exists in the region consisting of all points in the xy-plane except the origin.

From the given options, the correct answer is:

4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.

Learn more about Differential Equations here:

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5a - 3b if a=5 and b=7

Answers

Answer:

5(5) - 3(7) = 4

what are the steps for multiplying monomial algebraic terms where they have exponents with like bases

Answers

Answer:

See below.

Step-by-step explanation:

Rule:

$a^m * a^n = a^(m + n)$

Explanation:

When multiplying monomials with the same base, write the same base and add the exponents.

What is the result of 72 divided by 12? 6 8 9 12

Answers

Answer:

the answer is 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hope this helps!!!!!!

a radio station claims that the amount of advertising per hour of broadcast time has an average of 17 minutes and a standard deviation equal to 2.7 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 11 minutes. Calculate the z-score for this amount of advertising time

Answers

Answer:

z-score for 11 minutes of advertising time is $z=(-6)/(2.7)\approx -2.222$

Step-by-step explanation:

Z-scores measure the distance of any data point from the mean in units of standard deviations and are useful because they allow us to compare the relative positions of data values in different samples.

The z-score for any single data value can be found by the formula:

$z=(data \:value- \:mean)/(standard \:deviation)$