Question 4In lecture we learned about the distance between two points in R" and saw that itwas related to the Pythagorean Theorem. It turns out that this is not the only wayto measure distances. If you lived in a city that was arranged in a grid (such asManhattan), you would need to move along streets to get from point P to point Q.In this situation, a better way to measure the distance between points P= (P1- P2)and Q = (41, 92) would bedgria(P, Q) = |P1 – 91| + \p2 – 921;i.e. how far you travel along streets to get from P to Q.Qa. Prove that darid satisfies the triangle inequality. (Hint: Which property doesla + b| satisfy?)b. Find the distance between P = (-1,2) and Q = (2,3) first using the defini-tion of distance from lecture and again using dgrid-c. Considering your answers from part b, which is greater? Explain why thisagrees with your expectations.

Triangle inequality: The triangle inequality for any x, y, z ∈ ℝn is given by x - y ≤ |x - z| + |z -…

Question 4 In lecture we learned about the distance between two points in R" and saw that it was related to the Pythagorean Theorem. It turns out that this is not the only way to measure distanoes. If you lived in a city that was arranged in a grid (such as Manhattan), you would need to move along streets to get from point P to point Q. In this situation, a better way to measure the distance between points P = (p1, P2) and Q = (91, 92) would be dyria(P. Q) = [p1 – 91| + \P2 – 92l. i.e. how far you travel along streets to get from P to Q. a. Prove that drid satisfies the triangle inequality. (Hint: Which property does la + b] satisfy?) b. Find the distance between P = (-1,2) and Q = (2, 3) first using the defini- tion of distance from lecture and again using dyrid- c. Considering your answers from part b, which is greater? Explain why this agrees with your expectations. '

Question 4 In lecture we learned about the distance between two points in R" and saw that it was related to the Pythagorean Theorem. It turns out that this is not the only way to measure distanoes. If you lived in a city that was arranged in a grid (such as Manhattan), you would need to move along streets to get from point P to point Q. In this situation, a better way to measure the distance between points P = (p1, P2) and Q = (91, 92) would be dyria(P. Q) = [p1 – 91| + \P2 – 92l. i.e. how far you travel along streets to get from P to Q. a. Prove that drid satisfies the triangle inequality. (Hint: Which property does la + b] satisfy?) b. Find the distance between P = (-1,2) and Q = (2, 3) first using the defini- tion of distance from lecture and again using dyrid- c. Considering your answers from part b, which is greater? Explain why this agrees with your expectations. '

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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