sketch-the-graphs-of-the-given-equations-in-the-rectangular-coordinate-system-in-three-dimensions-29

Question

Sketch the graphs of the given equations in the rectangular coordinate system in three dimensions.
$$z=2 x^{2}+y^{2}+2$$

Vikash Ranjan · Accepted Answer

In the problem, we have this question, and from the question this is arranged here, so this is the our integration. Now we have to do the diagram. So here we have the diagram of the situation introduced, so this is the answer to the problem.

Rebecca Polasek · Answer

which the graph of X class y minus Z equals three. So you&#x27;re coordinate. Plain is going, Teoh, have the Y X is coming towards you. The x axis and the Z axis going vertical two graphics. I think the easiest option is to find your ex intercept your Y intercept in your Z intercept. So to find the X intercept, we want to make both why and z zero. So if I make both y and Z zero, then I find that the X intercept happens at three. If I want to find the Y intercept and this is similar to what you do in two dimensions, then we want to make the X and the Z into a zero. That leaves just a Why. So the Y intercept happens at three. And then if I want to find the Z intercept, then I want to make both the X and the why into zero. And actually, that shows then that Z is negative three. So I want to come down here below the axis and I would count down three to make it a negative three. So as I&#x27;m connecting these points, we&#x27;re going to see that the X and the Y connect. And then the wind, the Z and then X and dizzy. So we have this plane that is angling away from us down towards that negative three on the Z axis and then connecting with straight line the X in the light.

Rebecca Polasek · Answer

sketch the equation in a three dimensional coordinate system. And I&#x27;m given X plus two y plus Z equal to six. Now, just like graphene in your two dimensional system LA Times It&#x27;s easiest to look for your intercepts to try and connect those points together. So to find my ex intercept, I would want to make everything else zero. So I would want to make why and z zeros and then solve for X. Well, that would make my ex intercept happen where X is six. So for my why intercept? I would want to make everything else zero so I would make Axe and Z zeros. But here, as I saw for why I would find that the Y intercept happens at three and then for the Z intercept, well, more time I&#x27;m going to make everything else see grow. So I&#x27;m gonna make the X zero, and I&#x27;m gonna make the y zero. So I confined Z and in this case, the equal six. So to connect it to make my coordinate plain we&#x27;re sorry to make this plane in three dimensions. I&#x27;m just gonna connect those points and then we&#x27;re really looking at this figure that is angling out towards us makes the plane

Rebecca Polasek · Answer

I want to sketch the A graph of two X plus y minus is the equal six and that why access coming towards us, the X is running really parallel, and then the Z axis is that vertical axis going up into space. So if I want to graph the similar to what I would do in two dimensions is it&#x27;s helpful to look for the intercepts and then just connected with straight line so defined intercepts. You always want everything else to be zero. For instance, If I want to find the X intercept, then I would want to make both why and z into zeros. So that would leave two X equal to six, which makes our X intercept where X equals three. So I can put a point here on the graph where X equals three. So then define the Y intercept to know where to put it on the y axis. I would want to make the X and the Z into zeros, so you get rid of everything except for the variable you&#x27;re looking for. So then I have just a why by itself, equal six. So I know my why intercept happens all the way out where it equals 26 And then for the Z intercept. I want to make everything but Z into a zero. So I want to make X and y into zeros, which leaves behind a negative Z. So I saw this. I actually get negative six as my Z intercept, which means I want to count down six on that vertical axis. So I&#x27;m now below. I&#x27;m under this graph so that if I connect Thies to make that plane, we&#x27;re gonna draw a straight line from the X to the Y. Why dizzying and then ecstasy. So that&#x27;s gonna be my answer for the graph for two x plus y minus Z equal to six.

Karly Williams · Answer

Okay, so we have just sketch of this graph. Well, we have our equation, right? Here&#x27;s let&#x27;s go ahead and find a white intercept or are intercepts. So far, Exeter said we&#x27;re gonna have X plus zero plus zero to well, these with equal zero. So X equals two for why we&#x27;re gonna do zero plus y plus zero equals two the gun zero plus zero. So why equals two and then for Z, we have zero plus zero plus Z equals two z equals two because those equal zero. So this isn&#x27;t a B 200 zero comma, two commas zero and the oak up zero to All right, So let&#x27;s start drafting these. No, to me about right here. This one is gonna be bar here, and this one&#x27;s gonna be about right here. So I&#x27;m gonna draw the arrows civilities old match up. So we get this little triangle

Rebecca Polasek · Answer

we&#x27;re going to sketch a graph of this equation in a three dimensional coordinate system. So we wanna have an ex in A Y and a Z plane here. As we&#x27;re looking at drawing this graph typical. You&#x27;re going to see the Y axis as the one coming towards you X and then Z as that vertical axis. And the easiest way to go through and to draw this graph is actually to find your extra why in your Z intercepts. So just like you would do if you&#x27;re trying to find an X and Y intercept on your two dimensional coordinate plain if you&#x27;re trying to find, like in this case, the X intercept, Do you want everything else to be zero? So if I want to find the X intercept here, then I would want to make both y and Z zero. Well, then, that tells me my ex intercept happens over here where X is five. And so I can put a point where X is five for the Y intercept. I would want to make everything else heroes. I would want to make the X and the Z zero and again, in this case, I&#x27;ll find that. Why is five and then for the Z intercept? One more time? I know that I&#x27;m gonna make everything else zero. So I&#x27;m going to make ex and why Zero? Which tells me that the Z intercept happens at five. So then you connect them as best you can, making a three dimensional triangle out of this plane. So seeing that it&#x27;s coming forward. And actually, if you&#x27;re picturing it like it was a piece of paper, it&#x27;s kind of leaning towards us coming out towards the X and the Y axes and then up to the Z coordinate. So that would be my sketch for that coordinate system.

Problem

Sketch the graphs of the given equations in the r…

Problem 17 Easy Difficulty

Sketch the graphs of the given equations in the rectangular coordinate system in three dimensions.
$$z=2 x^{2}+y^{2}+2$$

Answer

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