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Let T(n) denote an equilateral triangular board with side length of 2^n units, subdivided into 4^n equilateral triangles with side length of one unit each. A trapezoidal tile (or triangular triomino) is a tile consisting of 3 adjacent equilateral triangles, each with side length one. (See picture in the textbook on page 277) Prove, using mathematical induction, that if any corner triangle is removed from a T(n) then the rest of the triangular board can be tiled using trapezoidal tiles for any positive integer n. Use part (a) and mathematical induction to show that if all three of the corner triangles and one additional triangle is removed from T(n) then rest of the triangular board can be tiled using trapezoidal tiles for any positive integer n.
How many revolutions will a car wheel of diameter 20 inches make as the car travels a distance of 3.14 miles?
Ellie bought a circular etched-glass tabletop to use as her dining room table. The glass is 18 ft in diameter. Find the cost of the tabletop at $ 96 per square yard of glass.
Considering window size w=2, design a Markov chain and evaluate how much improvement can be achieved. What is the tradeoff of the scheme in order to gain a better throughput?
What is the length of the wave that gives the minimum velocity?
choose one of the following pairs of items and compare and contrast the two items listed. be sure to provide examples
What is a probability that 2 females and 1 male will be in a group? What is a probability of 3 females only?
Jack babysat 2 hours each night for 10 nights.she earned a total $180 babysitting.Jack wants to calculate her hourly rate.How much did jack earn per hour babysitting?
a farmer wishes to enclose a rectangular region with 210 m of fencing in such a way that the length is twice the width and the region is divided into two equal parts. What length and width should be used?
one rope pulls a barge directly east with a force of 82 n and another rope pulls the barge directly north with a force
A particle is moving along the curve y= 2 sqrt{4 x + 4}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this i..
Compute the coecients of the polynomials using the term recurrence relation.
Simply supported beam- Maximum bending moment, The bending moment M at position x m from the end of a simply supported beam of length L m carrying a uniformly distributed load of w Kn m-1 is given by
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