sebastiangonzagonza
  • sebastiangonzagonza
A point A is graphed at (0, 3). Complete the coordinates of a shape that can be rotated about the y-axis to create a cylinder. Provide an explanation for your answer to receive full credit.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
If you rotate that rectangle about the y-axis, you get the cylinder in the figure.

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More answers

sebastiangonzagonza
  • sebastiangonzagonza
so i would need three other points?
sebastiangonzagonza
  • sebastiangonzagonza
its 0,3
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
Here is the given point, (0, 3)
mathstudent55
  • mathstudent55
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sebastiangonzagonza
  • sebastiangonzagonza
okay so i would i have to use (0,0), (2,3), and (2,0)?
mathstudent55
  • mathstudent55
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sebastiangonzagonza
  • sebastiangonzagonza
i believe that would make a rectangle and when its rotated, itll become a cylinder
nincompoop
  • nincompoop
how did you determine the rest of the dimensions when you were only given one point?
mathstudent55
  • mathstudent55
Excellent job! Are you sure you need to ask me questions. Maybe I should be asking you to help me.
mathstudent55
  • mathstudent55
Arbitrary.
sebastiangonzagonza
  • sebastiangonzagonza
HAH I dont want to make you fail @mathstudent55
sebastiangonzagonza
  • sebastiangonzagonza
@nincompoop i used 0,3 as a starting point. I then used the other points to create a rectangle.
mathstudent55
  • mathstudent55
When a rectangle that has an edge on the y-axis rotates about the y-axis, it creates a cylinder.
sebastiangonzagonza
  • sebastiangonzagonza
if you plug that all into geogebra or another graphing thing, you'll be able to see that it forms a rectangle
sebastiangonzagonza
  • sebastiangonzagonza
was i correct to do that??
mathstudent55
  • mathstudent55
Yes. Good job!
nincompoop
  • nincompoop
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nincompoop
  • nincompoop
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mathstudent55
  • mathstudent55
The problem asked for points, not equations. Also your triangle will yield a cone of rotation, not a cylinder.
nincompoop
  • nincompoop
good job at pointing out the concept, regardless
sebastiangonzagonza
  • sebastiangonzagonza
Quadrilateral OPQR is inscribed inside a circle as shown below. Write a proof showing that angles O and Q are supplementary. Here is the question again
sebastiangonzagonza
  • sebastiangonzagonza
i believe that i just needed to provide the points.
mathstudent55
  • mathstudent55
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nincompoop
  • nincompoop
cylinder is simply a cone, particularly when we are talking about projective geometry
mathstudent55
  • mathstudent55
@sebastiangonzagonza What is the arc measure in degrees of a full circle?
sebastiangonzagonza
  • sebastiangonzagonza
wait what?
sebastiangonzagonza
  • sebastiangonzagonza
im confused
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
Look at the figure above. It shows circle O and a central angle of 80 degrees. What is x, the arc measure of the arc intercepted by the central angle of 80 degrees?
sebastiangonzagonza
  • sebastiangonzagonza
im not sure
mathstudent55
  • mathstudent55
Ok, no problem. The arc measure is the same as the central angle measure. Since the central angle is 80 deg, then x is also 80 deg.
mathstudent55
  • mathstudent55
Ok so far?
sebastiangonzagonza
  • sebastiangonzagonza
ohhh okay yes, i understand
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
That was the case of a central angle. Now we need the case of an inscribed angle. An inscribed angle is an angle whose vertex is on the circle itself.
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
In the case of an inscribed angle, the measure of the intercepted arc is twice the measure of the inscribed angle.
mathstudent55
  • mathstudent55
Are you ok with central angle and arc & inscribed angle and arc?
sebastiangonzagonza
  • sebastiangonzagonza
i believe so
sebastiangonzagonza
  • sebastiangonzagonza
im just a bit slow rn
sebastiangonzagonza
  • sebastiangonzagonza
its 12:40AM where i am rn
mathstudent55
  • mathstudent55
Here's a summary: central angle measure = arc measure inscribed angle measure = 1/2 arc measure
mathstudent55
  • mathstudent55
Ok. I'll just finish this problem and that 'll be it for tonight.
sebastiangonzagonza
  • sebastiangonzagonza
and this is for the Quadrilateral OPQR is inscribed inside a circle question?
mathstudent55
  • mathstudent55
Yes. Now let's get back to our inscribed quadrilateral.
sebastiangonzagonza
  • sebastiangonzagonza
perfect okay
sebastiangonzagonza
  • sebastiangonzagonza
lets do it
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
Here is the inscribed quadrilateral. Let's call the circle circle C with center at point C.
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
If you use CA as the side of a central angle, and you go around a full rotation until you end up again at CA, that would be a 360-deg angle, right?
sebastiangonzagonza
  • sebastiangonzagonza
yes
mathstudent55
  • mathstudent55
Then since that central angle measures 360 degrees, that means that a circle is considered to be an arc of measure 360 deg. Remember, we saw before that the arc measure is the same as the central angle measure.
sebastiangonzagonza
  • sebastiangonzagonza
okay..
mathstudent55
  • mathstudent55
Now let's deal with angles O and Q to prove they are supplementary.
sebastiangonzagonza
  • sebastiangonzagonza
so hold on just a second
sebastiangonzagonza
  • sebastiangonzagonza
how should i write this for the answer?
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
I'm doing it now.
sebastiangonzagonza
  • sebastiangonzagonza
but in words
mathstudent55
  • mathstudent55
The two arcs, x and y, add up to the full circle, so their measures add up to 360 deg. x + y = 360
mathstudent55
  • mathstudent55
If we solve for y, we get y = 360 - x That means we have two arcs of measures x and 360 - x.
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
|dw:1439787195206:dw| Now let's look at angle Q. Angle Q is an inscribed angle, An inscribed angle is half of its intercepted arc. The intercepted arc of angle Q is arc ROP Since arc ROP has measure x, then the inscribed angle Q has half of that measure, 1/2 x
mathstudent55
  • mathstudent55
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sebastiangonzagonza
  • sebastiangonzagonza
okay
mathstudent55
  • mathstudent55
|dw:1439787388301:dw| Now we do the same with angle Q. Angle Q is an inscribed angle. Angle Q intercepts arc PQR. The measure of angle Q is half the measure of angle PQR. That means the measure of angle Q is 1/2 (360 - x) = 180 - 1/2 x
mathstudent55
  • mathstudent55
Now that we have measures for angles O and Q, we recall the definition of supplementary angles: Two angles are supplementary if the sum of their measures is 180 deg.
mathstudent55
  • mathstudent55
Since we want to show that angle O and angle Q are supplementary angles, we add their measures. m
mathstudent55
  • mathstudent55
Ok, gtg, it's very late for me. If you have any questions, just ask. I'll try to answer them tomorrow.
sebastiangonzagonza
  • sebastiangonzagonza
okay
sebastiangonzagonza
  • sebastiangonzagonza
thank you
mathstudent55
  • mathstudent55
yw

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