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Question: 1. Draw three overlapping circles. Color the resulting regions using two colors, so that no two regions that share a curve get the same color. (This is known as 2-coloring the regions. Grey and white are popular colors for experimenters who use pencil on white paper.) Now draw two pairs of overlapping circles and a single circle overlapping none of the others; 2-color this configuration. Using the understanding gained from these experiments, prove that n circles drawn in the plane can be 2-colored, using induction.
2. Challenge: Analyze the proof you gave for the previous problem. Would it work for n overlapping squares? Triangles? What about for spheres in space?
A commuter traveled 36.0 km to work at an average speed of v1 km/h and later returned over same route at an average speed of 8.00 km/h less.
Write a formal negation for each of the following statements: ? a band b such that b has won at least 10 Grammy awards.
Poisson Kernel and Harmonic Function, Let P_r(t)=R((1+z)/(1-z)), z=re^it be the Poisson kernel for the unit disc |z|
How many ways can five different graduation scholarships be awarded to 20 students if there is no limit to the number of scholarships awarded to each student?
Find the arc length function for the curve y=2x3/2 with starting point p0(9, 54). Use Simpson's Rule with n = 10 to estimate arc length of the curve. Compare your answer with value of the integral produced by your calculator.
How must traditional thinking be adjusted when implementing empowerment? What is the goal of empowerment?
Assignment 6. Without attempting to evaluate the following indefinite integrals, find f'(x) in each case if f(x) is equal to 0∫x(1 + t2)-3 dt And 0∫x^2(1 + t2)-3 dt
Suppose that for each line of a 2-variable truth table, you are told whether the final column in that line should evaluate to true or to false.
What is an equation relating chord segments a,b,c, d, and shown in Fig.? The dashed chords are an aid in the solution.
Explain how alpha-beta pruning can be used to simplify the computation of the value of a game tree.
In the English Common Law, various Statutes of Limitations exist to bring forward either a civil or criminal case before the court. For the stated reason of equity, Judge Gladstone's ancient opinion set forth the proposition that it is neither rea..
A Cooling evaporator in a fridge case with a design temperature of 5 Deg C. The Air off and Air on the fridge coil varies pending Ambient, Product, Product temperature/Mass etc.
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