15.1Ex50-53

# 15.1Ex50-53 - 622 C H A P T E R 15 D I F F E R E N T I AT I...

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622 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES (ET CHAPTER 14) 50. Find the change in elevation from A and B . SOLUTION The segment AB spans 7 level curves and the contour interval is 10 meters. Therefore, the change in elevation from A to B is 10 · 7 = 70 m. 51. Estimate the average ROC from A and B and from A to C . The change in elevation from A to B is 70 m. The scale shows that is approximately 1500 m. Therefore, Average ROC from A to B = 70 1500 0 . 047 . The change in elevation from A to C is obtained by multiplying the number of level curves between A and C , which is 8, by the contour interval 10 meters, giving 8 · 10 = 80 m. Using the scale, we approximate the distance AC by 3500 km. Therefore, Average ROC from A to C = 80 3500 0 . 023 . 52. Estimate the average ROC from P to points i, ii, iii, and iv. The points i, ii, and iii are on a level curve adjacent to the level curve of P , hence the change in elevation is 10 meters. Using the scale we approximate the distances from P to the points i, ii, and iii: From P to i: 400 m From P to ii: 400 m From P to iii: 640 m Therefore, Average ROC from
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