consider a finite rectangle in the plane. we will draw some number of lines that cut...

consider a finite rectangle in the plane. we will draw some number of lines that cut through the rectangle. In section 28.7.6 we define what we mean when we say that a map can be colored using two colors. Treat the rectangle that we just drew as a map, with regions defined by the lines that cut through it. Use induction to prove that, no matter how many lines we draw, the rectangle can be colored using two colors.

Expert Solution

Colby Messinger answered 2 years ago

Consider the solid that lies above the rectangle (in the xy-plane) R=[−2,2]×[0,2], and below the surface...

Consider the solid that lies above the rectangle (in the xy-plane) R=[−2,2]×[0,2], and below the surface z=x2−4y+8. (A) Estimate the volume by dividing R into 4 rectangles of equal size, each twice as wide as high, and choosing the sample points to result in the largest possible Riemann sum. Riemann sum =? (B) Estimate the volume by dividing R into 4 rectangles of equal size, each twice as wide as high, and choosing the sample points to result in the...

We consider a rectangular parallelepiped-shaped box based on a rectangle and open from above. The height...

We consider a rectangular parallelepiped-shaped box based on a rectangle and open from above. The height of the box is 4 dm. The base of the box has a fixed perimeter 20 dm and one side of it is x with 0 <x <10. a. Prove that the total area of the box as a function of x is E(x)=-x2+10x=80, x belongs to (0,10) b. Find for which value of x the box has a maximum area. c. Show that...

If we had 20,000(subscript 10) memory locations, what would be the least number of address lines...

If we had 20,000(subscript 10) memory locations, what would be the least number of address lines needed to describe each location? (Hint: Change 20,000 to binary or hex and determine the number of bits needed.)

We draw 6 cards from a 52 card deck and let X = the number of...

We draw 6 cards from a 52 card deck and let X = the number of heart cards drawn. a. What is the expected value of X? b. What is the variance of X? What is the standard deviation of X?

Consider some of the disaster events we have experienced or that you have seen in the...

Consider some of the disaster events we have experienced or that you have seen in the news during the past few years, occurring locally, across a state, nationally, or globally. What event do you think is most likely to be the next "big" disaster? Tell why you chose this event, and what you think the Public Health Response system's role should be in responding to it.

in class we discussed a number of situations where a seller could recognize(at least some) revenue...

in class we discussed a number of situations where a seller could recognize(at least some) revenue before it had fully completed every obligation under a contract which of the following items does NOT represent one of these situations a) a partially fulfilled sales contract with multiple performance obligations b) a sales contract where cash collection is not probable c) a partially completed sales contract that qualifies for revenue recognition overtime d) a bill-and-hold sale e) a sales contract with a...

We discussed a number of theories related to personality and personality differences. 1. When you consider...

We discussed a number of theories related to personality and personality differences. 1. When you consider your own personality and personalities of others you know, which of these theories can you relate to most or which of them best describes who you are? (1 paragraph) 2. Can you think of an example for the following Freudian defense mechanisms, using popular tv/movie/book characters? a. Repression : b. Projection c. Regression: d. Displacement e. Compensation 3. Research has found a 50/50 relationship...

There has been some discussion of late that we should consider free community college education for...

There has been some discussion of late that we should consider free community college education for all students. What are your thoughts about free community college education?

Some consider fair access to health care a moral right, while others disagree. We have defined...

Some consider fair access to health care a moral right, while others disagree. We have defined the term moral right as "a privilege to act in some specific, intentional manner or to obtain some specific benefit because one is a moral agent living in a community of moral agents under a shared moral standard." ANSWER THE TWO QUESTIONS BELOW !!!!! (IN YOUR OWN WORDS) Is access to health care a moral right? Why or why not?

number of things affect the price we pay for auto insurance. Discuss some of the things you've done to reduce the cost of insurance.

Question