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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
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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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 distances. 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 = (41, 92) would be dgria(P, Q) = |P1 – 91| + \p2 – 921; i.e. how far you travel along streets to get from P to Q. Q a. Prove that darid 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 dgrid- c. Considering your answers from part b, which is greater? Explain why this agrees with your expectations.
Transcribed Image Text: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 distances. 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 = (41, 92) would be dgria(P, Q) = |P1 – 91| + \p2 – 921; i.e. how far you travel along streets to get from P to Q. Q a. Prove that darid 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 dgrid- c. Considering your answers from part b, which is greater? Explain why this agrees with your expectations.
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