A key lime pie in a 10.00 inch diameter plate is placed upon a rotating tray. Then, the tray is rotated such that the rim of the pie plate m

Question

A key lime pie in a 10.00 inch diameter plate is placed upon a rotating tray. Then, the tray is rotated such that the rim of the pie plate moves through a distance of 108 inches. Express the angular distance that the pie plate has moved through in revolutions, radians, and degrees.(________) revolutions(________)radians(________)degreeIf the pie is cut into 9 equal slices, express the angular size of one slice in radians, as a fraction of pie?

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Kiệt Gia 5 years 2021-07-18T23:47:26+00:00 1 Answers 265 views 1

Answers ( )

  1. quangkhai
    1
    2021-07-18T23:48:55+00:00
    Reply

    Answer:

    The angular distance in revolution is revolution = 3.439 \ revolution

    The angular distance in radians  is \theta_{rad}= 21.6 \ radians

    The angular distance in degrees  is   \theta =1238.04^o

    The angular size is   Z = \frac{2}{9} \pi \ radians

    Explanation:

    From the question we are told that  

      The diameter is d = 10 \ inches

       The distance moved by the rim is D = 108 \ inches

    Generally the circumference of the pie plate is mathematically represented as

                   C = \pi d

    Substituting the values  

              C = 10 *3.142

                 = 31.42 \ inches

    The number resolution carried out by the pie plate is evaluated as

               revolution = \frac{D}{C}

    Substituting value

                revolution = \frac{108}{31.4}

                                  revolution = 3.439 \ revolution

    The angular  distance \theta_{rad} is mathematically evaluated as

                    \theta_{rad} = \frac{D}{r}

                 Where r is the radius which is mathematically evaluated as

                            r = \frac{d}{2} = \frac{10}{2} = 5 \ inches

    Substituting  this into the equation for angular distance

                          \theta_{rad} = \frac{108}{5}

                                  \theta_{rad}= 21.6 \ radians

    The angular distance traveled in degrees is

                       \theta = 3.439 *360

                          \theta =1238.04^o

    When  the pie is cut into 9 equal parts

    The angular size would be mathematically evaluated as

                             Z = \frac{2\pi}{9}

                               Z = \frac{2}{9} \pi \ radians

                                 

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