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Mth 277
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** Question Form_labelMessages **
Question 8 continuted Ch 12
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8. Convert the equation 3x^2 + 3y^2 + 3z^2 = 1 to cylindrical coordinates.
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What exactly are we trying to accomplish here? I see that the 3x^2 + 3y^2 is 3(x^2 + y^2) = 3r^2 which then if we divide both sides by 3 we end up with the r^2 = x^2 + y^2 which is one of the given equations for conversion. So how do we use this? Is this all that we have to show when solving one of these problems? Or is there more to it? And then how do we continue by finding the other two cylindrical coordinates such as theta and z. I get the equations and all.. I am having a hard time seeing exactly what we are trying to solve for and the steps to get there to show it.
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The equation becomes 3 r^2 + 3 z^2 = 1.
This is the cylindrical-coordinate form of the given equation.
Any point in the plane that satisfies one equation also satisfies the other. The graphs will be identical.
Both equations have graphs that are spheres of radius 1, centered at the origin or the pole.
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