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Let G be a connected graph. Let p1 and p2 be two paths in G.
1) Prove that if p1 and p2 have no vertex in common, then there exists a path p3 with its vertex in p1 and its last vertex in p2 and any remaining vertices that are not in vertices of p1 and p2.
2) Prove that if p1 and p2 are two longest paths of G, then they have a vertex in common. You may assume 1).
1 prove the following vector calculus identity in r3 where f is a twice continuously dierentiable scalar eld and f is a
Consider the double integral 0∫20∫√(1-(x-1)2) xy3/(x2+ y2) dydx. Explain why this integral is inconsistent with the definition of the double integral. Explain why Fubini's Theorem does not apply to this integral as written
What is the expected value of the coin selected (in cents)?
MATH 54 QUIZ 11. Express the given system of differential equations in matrix notation - x'1 = -2x2 + x1 - 4x3
Applying principles of probability, how can we improve random number generators and make them more unpredictable and thus more realistic? Share your thoughts and possible scenarios.
Erin left a 15% tip for a meal. The total cost of the meal, including the tip, was $21.16. What was the cost of the meal before the tip was added?
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Do these lines intersect each other or not? If they do then find out the intersection points.
a trough is 10ft long and its ends have the shape of isoceles triangles that are 3ft across at the top and have a
All incoming calls received a busy signal during that time. How many calls would you predict were not received by the Emergency 911 system while it was not operating?
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