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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?`
Use the formula to determine how long it takes the ball to return to the earth and Evaluate the maximum height of ball using given equation
Vanilla Box Company is going to make open-topped boxes out of 11 × 11-inch rectangles of cardboard by cutting squares out of the corners and folding up the sides. What is the largest volume box it can make this way? (Round your answer to the neare..
A certain aircraft can fly 1064 miles with the wind in 4 hours and travel the same distance against the wind in 7 hours. What is the speed of the wind?
What is the projected average out-of-pocket costs for beneficiaries in 2010
A body has dimensions 20cm x 30 cm x 50 cm and has a density of 9000 kg/m3. Find the weight of the body in kilograms.
The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number? answer and explanation.
Consider the function f(x) = 7 - 3x2 on the interval [-2, 4]. Find the average or mean slope of the function on this interval, i.e. f(4)- f(-2) 4 - (-2)=?
Juiceco manufactures two products: premium orangejuice and regular orange juice. Both products are made bycombining two types of oranges: grade 6 and grade 3. Theoranges in premium juice must have an average grade of atleast 5, those in regular juice..
the lenght of a steel beam is a linear function of the temperature when temperature is 40F a certain steel beam is 50 feet long and at 95 F the same beam is 50.12 feet long.what is the lenght of the beam at 70F? at what temperature is the beam 49...
What are complex numbers? What does imaginary parts of equal magnitude and opposite signs mean?
If the correlation coefficient is 0.930, what is the unexplained variation?
Characterize completely the random variable that is Bin(49, 0.3).
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