Spinning in Circles

We humans are traveling around in circles without even knowing it. We travel a circle around the axis of the earth once a day, and an almost-circle around the sun once a year. Considering each trip independently, how fast do we travel in each circle? (Assume we’re on the equator.) Here are some helpful data:

  • The diameter of the Earth is 12,756 km at the equator;
  • The distance from the Earth to the sun is 149,600,000 km;
  • There are 365.26 days in a year.
  • Give each answer in kilometers per hour.

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    Function as Average

    Let xk = (-1)k for any positive integer k. Let f(n) = (x1 + x2 + … + xn)/n, where n is a positive integer. Give the range of this function.

    1. 0
    2. 1/n (where n is any positive integer)
    3. 0 and -1/n (where n is any odd positive integer)
    4. 0 and 1/n (where n is any positive integer)
    5. 1 and 1/n (where n is any odd positive integer).

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    Okla Homer Baggage

    When Homer Smith and his wife Okla flew to Rome, they had together 94 pounds of baggage. Homer paid $15.00 and Okla paid $20.00 for the excess weight of their baggage. If Homer had made the trip by himself with the combined baggage of both of them, he would have had to pay $135.00 for excess baggage. How many pounds of baggage can one person take along without charge?

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