course 271 掶篥儭晨魷j胙r遘陼黎撿I腿assignment #005
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04:44:33 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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RESPONSE --> The rise over run notion of slope correlates to the depth change over time change approach for the average rate of change self critique assessment: 3
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04:47:58 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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RESPONSE --> The more the y value of the trapezoid, the higher the value of the area in relation to the x value. This is true for any graph. self critique assessment: 3
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10:38:06 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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RESPONSE --> A common denominator is obtained by multiplying both sides by the denominator of the other. This gives the fraction (x^2-4x+4)/(2-x)(x-2) which is then simplified to (x-2)/(2-x) or -1 self critique assessment: 3
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10:44:51 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. **
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RESPONSE --> Substitute in 240 for x to get the cost. =5190 Simply add an x to 6x in order to put one underneath it, giving you (6x^2+900,000)/x self critique assessment: 3
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