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Q1. Pick integers a, b > 0 and solve the corresponding hyperbolic equation
x2 - ax - b2 = 0
Q2. Explain why x = BC in Descartes construction for hyperbolic equations is a solution. (That is use algebra to PROVE x = BC is a solution of x2 - ax - b2 = 0. Definition of a circle, Pythagorean Theorem, and simple symbol shuffling should suffice.)
Q3. Pick integers a, b > 0 and solve the corresponding hyperbolic equation
x2 + ax - b2 = 0
using Descartes' method. Make a careful sketch and measure the solution on your sketch.
Q4. Pick integers a. b > 0, such that a/2 > b > 0 and solve the corresponding elliptic equation
x2 - ax + b2 = 0
Q5. Explain why x = SB and x = AS in Descartes construction for elliptic equations solutions. (That is use algebra to PROVE x = SB and x = AS are solutions. As part of your solution be sure to explain why is ∠AQB a right angle?)
Determine the bead's speed at point B. Determine the bead's speed at point C. Determine the net work done on the bead in moving it from A to C.
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The set of bit strings that have 3k ones, where k is a non-negative integer; the set of bit strings that contain 3k+1 ones, where k is a non-negative integer; and the set of bit strings that contain 3k+2 ones, where k is a non-negative integer.
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Simplify all variables
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