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sebastiangonzagonza

  • one year ago

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.

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  1. mathstudent55
    • one year ago
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  2. mathstudent55
    • one year ago
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  3. mathstudent55
    • one year ago
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    If you rotate that rectangle about the y-axis, you get the cylinder in the figure.

  4. sebastiangonzagonza
    • one year ago
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    so i would need three other points?

  5. sebastiangonzagonza
    • one year ago
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    its 0,3

  6. mathstudent55
    • one year ago
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    |dw:1439785177727:dw|

  7. mathstudent55
    • one year ago
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    Here is the given point, (0, 3)

  8. mathstudent55
    • one year ago
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    |dw:1439785243134:dw|

  9. sebastiangonzagonza
    • one year ago
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    okay so i would i have to use (0,0), (2,3), and (2,0)?

  10. mathstudent55
    • one year ago
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    |dw:1439785297447:dw|

  11. sebastiangonzagonza
    • one year ago
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    i believe that would make a rectangle and when its rotated, itll become a cylinder

  12. nincompoop
    • one year ago
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    how did you determine the rest of the dimensions when you were only given one point?

  13. mathstudent55
    • one year ago
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    Excellent job! Are you sure you need to ask me questions. Maybe I should be asking you to help me.

  14. mathstudent55
    • one year ago
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    Arbitrary.

  15. sebastiangonzagonza
    • one year ago
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    HAH I dont want to make you fail @mathstudent55

  16. sebastiangonzagonza
    • one year ago
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    @nincompoop i used 0,3 as a starting point. I then used the other points to create a rectangle.

  17. mathstudent55
    • one year ago
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    When a rectangle that has an edge on the y-axis rotates about the y-axis, it creates a cylinder.

  18. sebastiangonzagonza
    • one year ago
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    if you plug that all into geogebra or another graphing thing, you'll be able to see that it forms a rectangle

  19. sebastiangonzagonza
    • one year ago
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    was i correct to do that??

  20. mathstudent55
    • one year ago
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    Yes. Good job!

  21. nincompoop
    • one year ago
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    |dw:1439785459572:dw|

  22. nincompoop
    • one year ago
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    |dw:1439785618426:dw|

  23. mathstudent55
    • one year ago
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    The problem asked for points, not equations. Also your triangle will yield a cone of rotation, not a cylinder.

  24. nincompoop
    • one year ago
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    good job at pointing out the concept, regardless

  25. sebastiangonzagonza
    • one year ago
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    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

  26. sebastiangonzagonza
    • one year ago
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    i believe that i just needed to provide the points.

  27. mathstudent55
    • one year ago
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    |dw:1439785772669:dw|

  28. nincompoop
    • one year ago
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    cylinder is simply a cone, particularly when we are talking about projective geometry

  29. mathstudent55
    • one year ago
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    @sebastiangonzagonza What is the arc measure in degrees of a full circle?

  30. sebastiangonzagonza
    • one year ago
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    wait what?

  31. sebastiangonzagonza
    • one year ago
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    im confused

  32. mathstudent55
    • one year ago
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    |dw:1439785904928:dw|

  33. mathstudent55
    • one year ago
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    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?

  34. sebastiangonzagonza
    • one year ago
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    im not sure

  35. mathstudent55
    • one year ago
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    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.

  36. mathstudent55
    • one year ago
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    Ok so far?

  37. sebastiangonzagonza
    • one year ago
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    ohhh okay yes, i understand

  38. mathstudent55
    • one year ago
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    |dw:1439786146598:dw|

  39. mathstudent55
    • one year ago
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    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.

  40. mathstudent55
    • one year ago
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    |dw:1439786232600:dw|

  41. mathstudent55
    • one year ago
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    In the case of an inscribed angle, the measure of the intercepted arc is twice the measure of the inscribed angle.

  42. mathstudent55
    • one year ago
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    Are you ok with central angle and arc & inscribed angle and arc?

  43. sebastiangonzagonza
    • one year ago
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    i believe so

  44. sebastiangonzagonza
    • one year ago
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    im just a bit slow rn

  45. sebastiangonzagonza
    • one year ago
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    its 12:40AM where i am rn

  46. mathstudent55
    • one year ago
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    Here's a summary: central angle measure = arc measure inscribed angle measure = 1/2 arc measure

  47. mathstudent55
    • one year ago
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    Ok. I'll just finish this problem and that 'll be it for tonight.

  48. sebastiangonzagonza
    • one year ago
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    and this is for the Quadrilateral OPQR is inscribed inside a circle question?

  49. mathstudent55
    • one year ago
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    Yes. Now let's get back to our inscribed quadrilateral.

  50. sebastiangonzagonza
    • one year ago
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    perfect okay

  51. sebastiangonzagonza
    • one year ago
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    lets do it

  52. mathstudent55
    • one year ago
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    |dw:1439786524663:dw|

  53. mathstudent55
    • one year ago
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    Here is the inscribed quadrilateral. Let's call the circle circle C with center at point C.

  54. mathstudent55
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  55. mathstudent55
    • one year ago
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    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?

  56. sebastiangonzagonza
    • one year ago
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    yes

  57. mathstudent55
    • one year ago
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    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.

  58. sebastiangonzagonza
    • one year ago
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    okay..

  59. mathstudent55
    • one year ago
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    Now let's deal with angles O and Q to prove they are supplementary.

  60. sebastiangonzagonza
    • one year ago
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    so hold on just a second

  61. sebastiangonzagonza
    • one year ago
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    how should i write this for the answer?

  62. mathstudent55
    • one year ago
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    |dw:1439786878092:dw|

  63. mathstudent55
    • one year ago
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    I'm doing it now.

  64. sebastiangonzagonza
    • one year ago
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    but in words

  65. mathstudent55
    • one year ago
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    The two arcs, x and y, add up to the full circle, so their measures add up to 360 deg. x + y = 360

  66. mathstudent55
    • one year ago
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    If we solve for y, we get y = 360 - x That means we have two arcs of measures x and 360 - x.

  67. mathstudent55
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    |dw:1439787014371:dw|

  68. mathstudent55
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    |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

  69. mathstudent55
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    |dw:1439787236852:dw|

  70. sebastiangonzagonza
    • one year ago
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    okay

  71. mathstudent55
    • one year ago
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    |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

  72. mathstudent55
    • one year ago
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    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.

  73. mathstudent55
    • one year ago
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    Since we want to show that angle O and angle Q are supplementary angles, we add their measures. m<O + m<Q = 1/2 x + 180 - 1/2 x m<O + m< Q = 1/2 x - 1/2 x + 180 m<O + m<Q = 180 Since we just showed that the measures of angles O and Q add up to 180 deg, we have proved that the angles are supplementary.

  74. mathstudent55
    • one year ago
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    Ok, gtg, it's very late for me. If you have any questions, just ask. I'll try to answer them tomorrow.

  75. sebastiangonzagonza
    • one year ago
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    okay

  76. sebastiangonzagonza
    • one year ago
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    thank you

  77. mathstudent55
    • one year ago
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    yw

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