Homework Help: Sketching graph.

1. Apr 17, 2010

Gameowner

1. The problem statement, all variables and given/known data

Question attached

2. Relevant equations

3. The attempt at a solution

I have no idea at all how to start this, I've plotted all 3 separated as x=, y= and z=, which gave me 3 different curves, would I then just join them together?

any hint, tips would be much appareciated

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• q4.jpg
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2. Apr 17, 2010

LCKurtz

$$x =\sqrt z \sin(\theta),\ y = \frac{\sqrt z} 2 \cos(\theta)$$

Hint: Multiply the second equation by 2, square both and add and see if that helps.

3. Apr 19, 2010

Gameowner

yes! that has helped a lot, although when it came to plotting the equation, I was not sure about the domain of the graph. But this is what I got

I assume since the question specifies that theta is between 0 and 2pi, the maximum allowable value for x-axis and y-axis is -1/1?

As for the h, which is any number greater than 0, I just substituted an arbitrary point greater than 0.

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• Line plot.JPG.jpg
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4. Apr 19, 2010

LCKurtz

Try this code for a nicer plot,which might help you with your domain. I used h = 10 for an example:

restart;
h := 10;
surface := [sqrt(z)*cos(theta), sqrt(z)*sin(theta), z];
domain := [sqrt(z)*cos(theta), sqrt(z)*sin(theta), 0];
plot3d({domain, surface}, theta = 0 .. 2*Pi, z = 0 .. h, style = patchcontour);