use-a-computer-with-three-dimensional-graphing-software-to-graph-the-surface-experiment-with-viewp-3

Question

Use a computer with three-dimensional graphing software to graph the surface. Experiment with viewpoints and with domains for the variables until you get a good view of the surface.

$ -4x^2 - y^2 + z^2 = 0 $

Wen Zheng · Accepted Answer

travel on this. Use a computer place, read a match. Not Graffin Southwire to grasp the surface. Experimental ways when points and the ways the mines. But Laura Bo&#x27;s interior cattle could weigh up the surface. Negative or X square? My sweat square past the square is equal to zero. Here, use some grafting the wise to graft the service. It looks like this, so it is corn.

Tattwamasi Amrutam · Answer

All right. We want to plot the graph of minus for it&#x27;s just a and the flying experience. Mhm. Loss score. Yeah. Thanks. This return at lunch. Yeah. Uh, there is a problem. So, what we need to do is to change this year. Mhm. So this should be are you guys? Thank you. Mhm. Yeah. Mhm. That&#x27;s right. Yeah. And a small square root. Okay. Right. Mhm. Yes. Yeah. Mhm. Okay. So this is how the ground looks like. But if you see this is basically yes one the top part of it because I took not spread it to protect the negative spirit. Let&#x27;s stick with that. So it&#x27;s kind of right. Eight files Dinos. I need Oh cool. That&#x27;s just scraps glad. Right, spare. That&#x27;s right. Mhm Yeah. Yeah. Yeah. Okay. Okay. Now I can see that this is downstairs. So this is how the excellent in the beginning fact we saw that it was in the top knowledge is in the Mhm No baby. Mhm. Sure. Yeah. Yeah. Yeah. Yeah. We&#x27;ve only been soon, but this is how it is. So the top act is for the square before accessing care as well. On the bottom part is for the negative. And you can see this is a hyperbolic side of acoustics. Okay. Yeah. Mhm. This is our concept.

Tattwamasi Amrutam · Answer

So now we want to yeah. Excuse This one and then she is a system administrator here. Okay. Yeah, this is how the graph looks like. Yeah, Okay. And like you can see this is this is a I have a parable. So yeah. Mhm. This is another girl. Mhm. Mhm. Thank you. So from the top this is the top you can see in this part here, I have a parabola and then in this side I have desire desires. So each at each plane, if you caught the plane, if you put a planner any point then what you get is a is a hyperbole and that is exactly how it works. Work. Thank you. This was easy

Tattwamasi Amrutam · Answer

So you want to photograph of E. Because the four success Access where -66 And then 6 6 last four. This is the ground that they want the blood. Let&#x27;s throw the Red one. Okay so this is the ground that we&#x27;re looking at. And you can see this is this is a cylinder. Mhm. And bandage. So this is an unfinished basement at each point to get this is what you get a circle. And so this is the season and then there&#x27;s a card here. This is for the parabolic part which is the four Y squared. This is for them. So at every point you get a four widespread. So these these these black things are for the parabola and then the other things are for the circle. This is how the graphics. Yeah.

Linh Vu · Answer

in this question would you use on a couple cackle? Rita? And a question with even is Z equals June. Why? Being finding by one blast? Why power far. And here as we expect the graph the surface here we&#x27;re but allowed tuna excesses because the variable X is not in the question. So does we. Made it grabbed? Looks like here.

Carson Merrill · Answer

so we&#x27;re going to be using our calculator eventually. But before we do that, we want to set up this double integral. And we know that area is equal to three double integral of the square root of one plus z x squared plus z y squared d a. So with that, we know that since Z equals one plus X squared over one plus y squared, we want to take the partial derivatives of Z with respect to X. That&#x27;ll be two x over one plus y squared and then the partial derivatives e with respect to why it will be a little bit more complicated at two i times, um, two y times one plus x squared over one plus y squared, squared. Then, um, if we take these values and square um, underneath the radical add one What we&#x27;re gonna end up getting is the area being equal to this double integral inside the region D of the square root um, would actually be able to simplify this to move something out of the radical. It&#x27;ll be 1/1 plus y squared squared times the square root of one plus Why square to the fourth plus four x squared times one plus y squared, squared plus four y squared times one plus x squared, squared D A And again, these are things where we would never want to calculate this by hand. So instead we can write on a calculator to do the work for us instead. So the only thing we need to do now is just get our bounds of integration. So we know that the region that we have is going to be, um, negative one toe, one for the X. So this is now D y DX. It&#x27;ll be negative 1 to 1 for the X based on the region were given, and it&#x27;s going to be the absolute value of X minus one to one, minus the absolute value of X. Andi. When we use a calculator to approximate this, what we end up getting is 2.6959 because we want to correct to four decimal places. So this will be our final answer for that surface area

Wen Zheng · Answer

Yes. So you want to plot the graph G squared equals two for access to the square. So here&#x27;s what I would do is I do last ready? Uh huh. Yes four X squared talking about them. Yeah. Oh, excess square last night. Square glass riots. Yeah. Yeah. This is how it looks like can see this as a phone. Yeah. And each point is an ellipse at each planning narcotic. Get any lips and this is how it looks like. Mhm. Yeah. Older case. And if you can if you view it from the top this is our visit is a cool and if you are protected under the plane will be in the lips. I also and then I just took a positive part and next leads to the negative point. If you do the negative part, you can see that the surface below which is for the negative of spirit of exactly the same thing. It&#x27;s just a reflection media reflection. Yeah. Thank you. Mhm. Mhm. And again it&#x27;s the same thing. Again, if you if you just cut it out, then you&#x27;ll get another ellipse at every place. So this is the graph of uh G square First report accessible restaurants. Yeah. And the top parties for the positive one, which is the blue, the red parties for the -1, which is in there. Mm.

Problem

Use a computer with three-dimensional graphing so…

Problem 41 Easy Difficulty

Use a computer with three-dimensional graphing software to graph the surface. Experiment with viewpoints and with domains for the variables until you get a good view of the surface.

$ -4x^2 - y^2 + z^2 = 0 $

Answer

elliptic cone

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