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Nataliya [291]
3 years ago
12

The equation x2 − xy + y2 = 3 represents a "rotated ellipse," that is, an ellipse whose axes are not parallel to the coordinate

axes. Find the points at which this ellipse crosses the x-axis.(x, y) = smaller x-value (x, y) = I larger x-value
Mathematics
1 answer:
Setler [38]3 years ago
3 0

Answer:

the points where the ellipse crosses the x- axis are (1.73, 0) and (-1.73, 0)

Step-by-step explanation:

To find the points at which a graphic crosses the x-axis we need to find the values for x where y = 0.

Therefore, in the equation x²- xy + y² = 3 we are going to make y = 0 and solve for x

x² - xy + y² = 3

x²- x(0) + (0)² = 3

x² = 3

x = ±√3

x₁ = 1.73 and x₂ = -1.73

Therefore, the points where the ellipse crosses the x- axis are (1.73, 0) and (-1.73, 0)

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Easy :).

Remove the flat rate to see how much money she has to spend: 10 - 1.95 = 8.15.

We have 8.15 (remaining money) / 0.60 (per mile) = 13 miles (or <span>13.5833333333 [copy pasted from a calculator moderators] but I assume you want a rounded version)</span>
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3 years ago
Dy/dx = 2xy^2 and y(-1) = 2 find y(2)
Anarel [89]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2887301

—————

Solve the initial value problem:

   dy
———  =  2xy²,      y = 2,  when x = – 1.
   dx


Separate the variables in the equation above:

\mathsf{\dfrac{dy}{y^2}=2x\,dx}\\\\&#10;\mathsf{y^{-2}\,dy=2x\,dx}


Integrate both sides:

\mathsf{\displaystyle\int\!y^{-2}\,dy=\int\!2x\,dx}\\\\\\&#10;\mathsf{\dfrac{y^{-2+1}}{-2+1}=2\cdot \dfrac{x^{1+1}}{1+1}+C_1}\\\\\\&#10;\mathsf{\dfrac{y^{-1}}{-1}=\diagup\hspace{-7}2\cdot \dfrac{x^2}{\diagup\hspace{-7}2}+C_1}\\\\\\&#10;\mathsf{-\,\dfrac{1}{y}=x^2+C_1}

\mathsf{\dfrac{1}{y}=-(x^2+C_1)}


Take the reciprocal of both sides, and then you have

\mathsf{y=-\,\dfrac{1}{x^2+C_1}\qquad\qquad where~C_1~is~a~constant\qquad (i)}


In order to find the value of  C₁  , just plug in the equation above those known values for  x  and  y, then solve it for  C₁:

y = 2,  when  x = – 1. So,

\mathsf{2=-\,\dfrac{1}{1^2+C_1}}\\\\\\&#10;\mathsf{2=-\,\dfrac{1}{1+C_1}}\\\\\\&#10;\mathsf{-\,\dfrac{1}{2}=1+C_1}\\\\\\&#10;\mathsf{-\,\dfrac{1}{2}-1=C_1}\\\\\\&#10;\mathsf{-\,\dfrac{1}{2}-\dfrac{2}{2}=C_1}

\mathsf{C_1=-\,\dfrac{3}{2}}


Substitute that for  C₁  into (i), and you have

\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}}\\\\\\&#10;\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}\cdot \dfrac{2}{2}}\\\\\\&#10;\mathsf{y=-\,\dfrac{2}{2x^2-3}}


So  y(– 2)  is

\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot (-2)^2-3}}\\\\\\&#10;\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot 4-3}}\\\\\\&#10;\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{8-3}}\\\\\\&#10;\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{5}}\quad\longleftarrow\quad\textsf{this is the answer.}


I hope this helps. =)


Tags:  <em>ordinary differential equation ode integration separable variables initial value problem differential integral calculus</em>

7 0
3 years ago
55/(4+1)+3-three cubed​
Charra [1.4K]

Answer:38

Step-by-step explanation:

6 0
2 years ago
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hodyreva [135]

Answer:

Step-by-step explanation:

x = 8

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1,995,298 rounded to the nearest ten thousand
ss7ja [257]
200,000,000 that your answer

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