If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

005. `query 5

Question: `qexplain 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

Your solution:

Confidence Rating:

Given Solution:

`a the specific idea is that ave rate of depth change is [change in depth / change in time] ; rise represents change in depth and run represents change in time so slope = rise/run represents ave rate of depth change. **

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Question: `qexplain 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

Your solution:

Confidence Rating:

Given Solution:

`a The average altitude represents the avg. velocity. The area of a trapezoid involves the altitude, which represents the avg. velocity, and the width, which represents the change in clock time.

When you multiply ave altitude by width you are representing ave vel * change in clock time, which gives change in position.

This reasoning isn't confined to velocities. For any rate vs. clock time graph, average altitude represents approximate average rate, which multiplied by the change in time (not by the time itself) gives you the change in quantity **

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Question: `qtext problem 0.5 #10 add x/(2-x) + 2/(x-2)

Your solution:

Confidence Rating:

Given Solution:

`a common denominator could be [ (2-x)(x-2) ]. In this case we have

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

= [ (x-2) / (x-2) ] * [ x / (2-x) ] + [ (2-x) / (2-x) ] * [ 2 / (x-2) ]

= x(x-2) / [ (2-x)(x-2) ] + 2 (2-x) / [ (2-x)(x-2) ]

= [x(x-2) + 2(2-x) ] / [ (2-x)(x-2) ]

= [ x^2 - 2x + 4 - 2x ] / [ (2-x)(x-2) ]

= (x^2-4x+4) / [ -x^2+4x-4 ]

= (x-2)^2 / [-(x-2)^2]

= -1.

NOTE however that there is a SIMPLER SOLUTION:

We can note that x-2 = -(2-x) so that the original problem is -x/(x-2) + 2 /(x-2) = (-x + 2) / (x-2) = -(x-2)/(x-2) = -1. **

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Question: `qtext problem 0.5 #50 cost = 6 x + 900,000 / x, write as single fraction and determine cost to store 240 units

Your solution:

Confidence Rating:

Given Solution:

`a express with common denominator x:

[x / x] * 6x + 900,000 / x

= 6x^2 / x + 900,000 / x

= (6x^2 + 900,000) / x so

cost = (6x^2+900,000)/x

Evaluating at x = 240 we get cost = (6 * 240^2 + 900000) / 240 = 5190. **

Self-critique (if necessary):

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