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A satellite of mass 500 kg undergoes a circular orbit of radius 8000 km and a constant speed of 7060 m/s.  What is the force on the satellite?

p4.png A way to simulate gravity in space is to shape the space station like a cylindrical shell that rotates, with the astronauts living on the inside surface as shown.  If the radius of the space station is 750 m, at what angular speed would it have to rotate so that the astronauts experience the same normal force standing on the station that they would on Earth?

Suppose for the same problem as in the previous question, the profit per unit produced of X and Y was 8 and 4 dollars, respectively.  The appropriate objective function for this would be:

Consider the following information for an item for which you must develop an inventory policy.  Annual demand:                         4000 units                                  Order cost:                                  $50 per order                            Per unit holding cost / year:      25% of unit purchase price    Per unit purchase cost:              $10.00 if order quantity < 1000 units                                                       $ 9.50 if 1000  5000 units If your supplier decided to stop offering the quantity discounts you see above, and just told you that all items would cost $10 each, your economic order quantity would be

p6(2).png If the radius of the loop is 50.0 m, what is the minimum speed the roller coaster can travel around the loop without falling off the track?  (The coaster leaves the track when the normal force on it equals zero.)

Assume a safety stock level of 40 and an order quantity of 800, along with the cost, annual demand, average demand, and average lead time information listed previously (which is repeated below): Annual demand = 5000                                                 Holding cost = $4 / unit / year Working days per year = 200 days                               Order cost = $50 Average daily demand = 25 units                                 Average lead time = 6 days The total annual order costs for this item would be

Assume a safety stock level of 40 and an order quantity of 800, along with the cost, annual demand, average demand, and average lead time information listed previously (which is repeated below): Annual demand = 5000                                                 Holding cost = $4 / unit / year Working days per year = 200 days                               Order cost = $50 Average daily demand = 25 units                                 Average lead time = 6 days How much is the extra recurring cost annually to keep you from running out of stock during half your lead times?

At what angle would a circular track of radius 75 m need to be banked, so that a car traveling at 25 m/s around the track would not need friction to keep from sliding off?

Assume a safety stock level of 40 and an order quantity of 800, along with the cost, annual demand, average demand, and average lead time information listed previously (which is repeated below): Annual demand = 5000                                                 Holding cost = $4 / unit / year Working days per year = 200 days                               Order cost = $50 Average daily demand = 25 units                                 Average lead time = 6 days Assume that the standard deviation of demand during the lead time was equal to 40 and you wanted a service level of 84.13%. To the nearest integer (round up if the decimal is .5), how many units per year would be short (unavailable when needed)?  (Take calculations to as many as 6 decimal places.)

For the next three questions, consider the following information for an item for which you must develop an inventory policy.  Annual demand:                         4000 units                                  Order cost:                                  $50 per order                            Per unit holding cost / year:      25% of unit purchase price    Per unit purchase cost:              $10.00 if order quantity < 1000 units                                                       $ 9.50 if 1000 5000 units The only “candidate” order quantities that need to be considered for the best overall answer would be