QUERY 5

course MTH 271

09/18,1700

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assignment #005

005. `query 5

Applied Calculus I

09-18-2009

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16:50:21

explain why the slope of a depth vs. time trapezoid represents the average rate of change of the depth with respect to the time during the time interval represented

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RESPONSE -->

The diagonal side of a trapezoid connects two points representing time interval with a line. This slope of this line is equal to the change in y values divided by the change in t (x values). This is also equal to the average rate of depth change.

confidence rating: 2

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16:53:44

explain why the area of a rate vs. time trapezoid for a given time interval represents the change in the quantity corresponding to that time interval

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RESPONSE -->

Area of a trapezoid is equal to the height (or altitude) times the width. With respect rate v. time, the area of the trapezoid equals the change in quantity for the time interval. This is b/c height is equal to the average velocity and the width equals the change in time. Average velocity= (change in amount)/(change in time)

(change in amount)/(change in time) * (change in time)=change in amount

confidence rating: 2

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16:57:23

text problem 0.5 #8 add x/(2-x) + 2/(x-2)

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RESPONSE -->

x/ (2-x) + 2/ (x-2)

(x/(2-x)) ((x-2)/(x-2)) + (2/(x-2)) ((2-x)/(2-x))

(x^2-4x +4)/((2-x)(x-2))

(x-2)^2/(-(x-2)(x-2))

(x-2)^2/-(x-2)^2

-1

confidence rating: 2

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16:58:55

text problem 0.5 #48 cost = 6 x + 900,000 / x, write as single fraction and determine cost to store 240 units

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RESPONSE -->

C=(6(x^2) + 900 000)/x

x=240

C=(6(240^2) + 900 000)/240

C=5190

confidence rating: 3

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