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We have claimed that a randomly generated point lies on the equator of the sphere independent of where we pick the North Pole. To test this claim randomly generate ten vectors in 128 dimensions whose coordinates have value ±1. Think of these ten vectors as ten choices for the North Pole. Then generate some additional random vectors with ±1 coordinates. For each of the new vectors determine how many of the original vectors they are close to being perpendicular to. That is, they lie close to the equator.
Quadric Surfaces Earlier we have looked at lines and planes in three dimensions (or R 3 ) and when these are used fairly heavily at times in a Calculus class there are several
Graph for the Sequence First we wish to think about the term graphing a sequence. To graph the sequence {a n } we plot the points {n, a n } as n ranges over every possible valu
A rectangular garden has a width of 20 feet and a length of 24 feet. If each side of the garden is increased through the similar amount, how many feet is the new length if the new
The cost of a student ticket is $1 more than half of an adult ticket. Six adults and four student tickets cost $28. What is the cost of one adult ticket? Let x = the cost of a
Christie purchased a scarf marked $15.50 and gloves marked $5.50. Both items were on sale for 20% off the marked price. Christie paid 5% sales tax on her purchase. How much did she
carlie is now fivetimes as old as henry. in nine years her age will be twice henry''s age then. how old is carly now
Adison earned $25 mowing her neighbor''s lawn. Then she loaned her friend $18, and got $50 from her grandmother for her birthday. She now has $86. How much money did Adison have to
Calculate Moving Average The table given below represents company sales; calculate 3 and 6 monthly moving averages, for data Months Sales
sin3θ = cos2θ find the most general values of θ satisfying the equatios? sinax + cosbx = 0 solve ? Solution) sin (3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x) = 2sin(x)cos(
1+2i=a+ib so find a and b
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