622CHAPTER 15DIFFERENTIATION IN SEVERAL VARIABLES(ET CHAPTER 14)50.Find the change in elevation fromAandB.SOLUTIONThe segmentABspans 7 level curves and the contour interval is 10 meters. Therefore, the change inelevation fromAtoBis 10·7=70 m.51.Estimate the average ROC fromAandBand fromAtoC.The change in elevation fromAtoBis 70 m. The scale shows thatis approximately 1500 m. Therefore,Average ROC fromAtoB=701500≈0.047.The change in elevation fromAtoCis obtained by multiplying the number of level curves betweenAandC, which is 8,by the contour interval 10 meters, giving 8·10=80 m. Using the scale, we approximate the distanceACby 3500 km.Therefore,Average ROC fromAtoC=803500≈0.023.52.Estimate the average ROC fromPto points i, ii, iii, and iv.The points i, ii, and iii are on a level curve adjacent to the level curve ofP, hence the change in elevationis 10 meters. Using the scale we approximate the distances fromPto the points i, ii, and iii:FromPto i: 400 mFromPto ii: 400 mFromPto iii: 640 mTherefore,Average ROC from
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