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Question: Observe that the sequence 12, 15, 8, 13, 7, 18, 19, 11, 14, 10 has three increasing subsequences of length four: 12, 15, 18, 19; 12, 13, 18, 19; and 8, 13, 18, 19. It also has one decreasing subsequence of length four: 15, 13, 11, 10. Show that in any sequence of n2 + 1 distinct real numbers, there must be a sequence of length n + 1 that is either strictly increasing or strictly decreasing.
summation and proof using mathematical induction.suppose that xn is a sequence of positive real numbers for which the
A wheel of radius 2 feet begins moving down a ramp of height 6 and length 24 feet , turning at 23 revolutions per minute clockwise as it does. At time t = 0 the point P on the wheel is at [0, 6]
Let A be a symmetric and positive definite (SPD) matrix. Is A^-1 ( inverse of matrix A) a SPD matrix? If so, prove it. If not, explain and give an example.
Using the preliminary calculations from a data set of 9 sensors, determine the equation of the line. (Round your intermediate calculations to 3 decimal places)
a boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that
For all (smooth) polar curves r = f(θ), 0 ≤ θ ≤ π/2, with f(0) = 1 and f(π/2) = 1, and f(θ) ≥ 1 for all 0 ≤ θ ≤ π/2, show that their arc-lengths are greater than or equal to π/2.
What are Equitable Adjustments and Value Engineering in regards to Federal Contracting and Federal Aquisition Regulation (FAR)?
A rental car costs $25 plus a fixed rate charge per mile driven. The total charge for 210 miles of use was $67. Write an equation for the cost, C (in dollars), in terms of the miles driven, x.
DRIVING AGE REQUIREMENTS The minimum age requirement for a regular driver's license differs from state to state. The frequency distribution for this age.
The perimeter of a rectangular playing field is 244 feet. If its length is 2 feet longer than twice its width, what are the dimensions of the field?
A car is traveling on a straight road with velocity 55 ft/sec at time t = 0. For 0 ≤ t ≤ 18 seconds, the car's acceleration a(t) , in ft/sec2, is the piecewise linear function defined by the graph above.
Suppose you want to carry on a bag whose length is twice its height. What is the largest volume bag of this shape that you can carry on a flight?
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