# P02Ans - B above where y is the cost in dollars of...

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Project 2 MAC 2233 1. Suppose that at the base of a mountain range, the diversity of an insect species (measured in average number of species N per acre) depends linearly upon the elevation E in hundreds of feet below sea level according to the equation N = 11 . 26 + 1 . 35 E . Draw the line on axis A below. A B What is the slope of the line? 1.35 It signiﬁes that for every 1 unit change in E , the value of N will change by 1.35 units. For every 100 feet that one descends below sea level, the average number of species will increase by EXACTLY 1.35 Think about what this statement means: The linear relationship scales the rate of change in perfect proportion and independently of the elevation. By how much does N change if: you are 200 feet below sea level and descend 100 feet? 1.35 you are 200 feet below sea level and ascend 100 feet? -1.35 you are 500 feet below sea level and descend 100 feet? 1.35 you are 500 feet below sea level and descend 50 feet? 0.675 2. Give a quick sketch of the function y = x on the axis
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Unformatted text preview: B above, where y is the cost in dollars of producing x items. By how much does y change as x changes from to 1 unit? from 1 to 2 units? How does this show the relationship is not linear? Find the equation of the line between the points on the graph when x = 1 and x = 2 and draw it on the graph. This is called a secant line to y = √ x . Show that the graph above and the line y = 1 2 x + 1 2 intersect in just one point P . Draw the line and point P on the axes. This line is called the tangent line to the graph of y = √ x at P . point P is ( 1 , 1 ) Find an equation for the line perpendicular to the tangent line at point P , and draw it on the axes. This line is called the normal line to the graph of y = √ x at P . normal line is: y = 3-2 x Open-ended question: What might the slopes of the tangent and secant lines tell you about the relation y = √ x ? That is, do they tell us anything signiﬁcant?...
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## This note was uploaded on 12/27/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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