course Mth 271 ÂÓ}äÀûs–ÍÒͼÐv_•â§¨ï»ñ”Â÷ìýãassignment #005
......!!!!!!!!...................................
21:17:22 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
......!!!!!!!!...................................
RESPONSE --> Slope= Average rate of depth= change in depth/ change in time
.................................................
......!!!!!!!!...................................
21:18:35 ** 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. **
......!!!!!!!!...................................
RESPONSE --> I think that I answered this one is ok. Rise/ Run= slope
.................................................
......!!!!!!!!...................................
21:19:31 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
......!!!!!!!!...................................
RESPONSE --> average alitude multiplied to with
.................................................
......!!!!!!!!...................................
21:21:59 ** 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 **
......!!!!!!!!...................................
RESPONSE --> Wow...I answered this one pretty badly. I needed to talk about the velocity.
.................................................
......!!!!!!!!...................................
21:27:58 text problem 0.5 #10 add x/(2-x) + 2/(x-2)
......!!!!!!!!...................................
RESPONSE --> common denominator 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/ (2-x)(x-2) = (2-x)(2-x)/ (2-x) (x-2) = (2-x)/ (x-2) = (2-x)/ -(x-2) = (2-x) /( -x+2) =1
.................................................
......!!!!!!!!...................................
21:29:29 ** 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. **
......!!!!!!!!...................................
RESPONSE --> Opps! I worked it all out right but then got to the bottom and messed up a bit....I knew to put that - on there but I just didnt.......I dont know why I worked all that out when I could have takin a short cut
.................................................
......!!!!!!!!...................................
21:31:49 text problem 0.5 #50 cost = 6 x + 900,000 / x, write as single fraction and determine cost to store 240 units
......!!!!!!!!...................................
RESPONSE --> cost= 6x + 900000/x 6 (240) + 900000/ 240= 3756
.................................................
......!!!!!!!!...................................
21:33:26 ** 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. **
......!!!!!!!!...................................
RESPONSE --> I sure did a number on this one! I dont know what I am thinking! I knew to find a common denominator but I just didnt .....I know how to do this I promise I just am having a brain thing going on!
.................................................
"