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A set A is call a partially-ordered set if there is a relation R on A such that R is reflexive and transitive. If A is any set, prove that the power set P(A) is a partially ordered set under the relation "is a subset of".
Create 2 sets. Set A will be the list of the 5 items you personally need to buy the most (essential items). Set B will be the list of 5 items that you want to buy the most ( fun stuff).
Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). Also, suppose that f(a) = f(b) and that c is a real number in the interval such that f'(c) = 0.
Find the slope of the line passing through the points (1990, 3.5) and (2005, 5.15). Interpret the slope as a rate of change.
If H and K are subgroup of G, with K a normal subgroup of G, K intersect H=1 and KH=G, then G is called a semidirect product (or split extention) of K by H.
Find the slope-intercept form of a line that is the perpendicular bisector of a line segment connecting (-7,3) and (1,17)
The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $380 to drive 480 mi and in June it cost her $460 to drive 800 mi.
Discuss the case when b = 6. Interpret your solutions in terms of the kernel and image of the linear transformation T: o^3 --> o^3 represented by the equations.
Your company plans to transport 20 horses to a racetrack in Denver. It takes 12 hours to drive from Phoenix to Denver. You have to stop and feed the horses every 2 hours.
Supppose a baseball is thrown at 85 miles per hour.The ball will travel 320 ft when hit by a bat swung at 50 miles per hour and will travel 440 ft when hit by a bat swung at 80 miles per hour.
Complementary events. A pair of fair dice is rolled. Let E denote the event that the number landing uppermost on the first die is a 3, and let F denote the event that the sum of the numbers landing uppermost is 6. Determine whether E and F are ind..
Evaluate critical points, end points, local extrema and global extrema - Evaluate f at its critical points and at the endpoints of the given interval. Identify local and global maxima and minima of f in the interval.
Solve the system of equation by matrix method - Use augmented matrices to solve the following 2 x 2 systems of equations.
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