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Margaret [11]
2 years ago
6

Give me a correct answer, My answer probably wrong.

Mathematics
1 answer:
Georgia [21]2 years ago
3 0

Hello!

This is a problem about the general solution of a differential equation.

What we can first do here is separate the variables so that we have the same variable for each side (ex. dy with the y term and dx with the x term).

\frac{dy}{dx}=\frac{x-1}{3y^2}

3y^2dy=x-1dx

Then, we can integrate using the power rule to get rid of the differentiating terms, remember to add the constant of integration, C, to at least one side of the resulting equation.

y^3=\frac{1}{2}x^2-x+C

Then here, we just solve for y and we have our general solution.

y=\sqrt[3]{\frac{1}{2}x^2-x+C}

We can see that answer choice D has an equivalent equation, so answer choice D is the correct answer.

Hope this helps!

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This is the standard form equation \frac{(x - 10)^2}{100} + \frac{(y + 10)^2}{-100} = 1

What is the ellipse?

The equation for an ellipse is typically written as x² a²  + y² b² = 1. x²  a² + y² b²  = 1. An ellipse with its origin at the center is defined by this equation. The ellipse is stretched further in both the horizontal and vertical directions if a > b, a > b, and if b > a, b > a, respectively.

The standard form of the equation of an ellipse with center (h, k)and major axis parallel to the x-axis is:

\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1

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a > b

the length of the major axis is 2a

the coordinates of the vertices are (h±a,k)

the length of the minor axis is 2b

the coordinates of the co-vertices are (h,k±b)

the coordinates of the foci are (h±c,k),

where c² = a² − b².

so,

\frac{(x - 10)^2}{100} + \frac{(y + 10)^2}{-100} = 1

Hence, this is the standard form equation \frac{(x - 10)^2}{100} + \frac{(y + 10)^2}{-100} = 1.

To learn more about ellipse, visit

brainly.com/question/16904744

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