Either a typo or anything
. They pulled that a few times in the homework, making you prove arbitrary statements from contradictions.
I'm not sure whether I'd prefer the professor to have messed up the question, or me to be stupid...
[1] This facsimile operated in part by synAC.Yeah. There's an example in the Wikipedia article; it goes
- Lemons are yellow and lemons are not yellow.
- From 1, lemons are yellow.
- From 2, lemons are yellow or Santa Claus exists *.
- But from 1, lemons are not yellow.
- So from 3 and 4, Santa Claus must exist.
Logic's weird.
[1] This facsimile operated in part by synAC.I can write it out, wait a sec.
..wait, did you seriously do a truth table for four variables? Why
- (F⊃J)⊃(G⊃Q)
- J•~Q
- J [2, simp]
- J∨~F [3, add]
- ~F∨J [4, comm]
- F⊃J [5, mat imp]
- G⊃Q [1, 6, MP]
- ~Q [2, simp]
- G [7, 8, MT]
edited 16th Dec '10 1:44:38 PM by Tzetze
[1] This facsimile operated in part by synAC.I know, but... so tedious!
When I bitched about it before Nornagest mentioned doing one for six variables or something. -_____-
Well, in any case, this has reassured me that I did more or less know what I was doing.
[1] This facsimile operated in part by synAC.Oh yeah, so it does. Brainfart! ^_^; I didn't do that on the final, though.
Huh, I wonder what happens if he really did make a mistake... after staring at it up to ~G for half an hour I just wrote out «It's impossible to use the principle of explosion to prove an unrelated proposition, because there is no contradiction in the premises.» Hopefully that's well thought out enough to get whatever.
[1] This facsimile operated in part by synAC.Math question. "Contour" integrals. Complex numbers. (These integrals are probably named different things in different areas, I think, so don't get scared as long as you already know what integrals are.)
I am expecting that |z| = 16 will become (x1 = -16, x2 = 16) and (y1 = -16, y2 = 16), but that just seems a little suspect to me.
EDIT: Solved this on my own, but I still don't know if my converseion of C to R was correct. (die)q/(die)x- (die)p/(die)y = 0, integration results in C (constant), C - C (due to range integral) = 0. Repeat for y. Still get 0.
EDIT: Got my answer to that too.
edited 18th Dec '10 10:24:37 PM by Barcode711
Worshipper of Ahura Mazda, as proclaimed by Zoroadster http://twitter.com/bpglobalprA container is supported by three cables. The maximum allowable tension in any of the cables is 460 N. What is the maximum weight of the container?
All three cables are attached to the container at A = (0, -.60, 0); the other ends are at B = (.45, 0, 0), C = (0, 0, -.32), and D = (-.50, 0, .36). Assume massless straight cable, etc.
I'm trying to calculate the fractions in which any weight is distributed between the three cables in order to determine which experiences the greatest tension, then simply substitute 460 N into the force on the weakest cable; however, while I'm reasonably sure the weakest cable is AD due to the acuter angle of attachment, I haven't managed either to prove it yet, or even to relate the cable strengths to each other beyond the obvious (Only cables AB and AD have an x-component to their tension vectors, so they must be of equal magnitude in that direction, and the same goes for AC and AD along the z-axis).
I feel as though either there's something blatant that I'm missing, or I'm simply overthinking the problem and trying to solve it the wrong way.
There was, but nothing I didn't describe... Imagine three cables bolted irregularly into the ceiling at points B, C, and D, with the hanging ends joining together to suspend a bucket at point A.
ERROR: The current state of the world is unacceptable. Save anyway? YES/NOThe tension of the cables on the container can be divided into two components, one parallel to the y-axis, the other parallel to the xz-plane (the ceiling). Now, since the container isn't moving (implying that acceleration is zero), we can assume that there is no net force acting on it. There's gravity, but it's being canceled out by the net force of the tension of the cables on the box, which should be completely vertical.
Which means that the sum of the components parallel to the xz-plane should equal to zero. From there, it's a matter of deriving their magnitudes, since you already know their directions.
You could try three test cases where you max out the tension for one cable, and check whether any of the other two cables exceed the limit for that case... I think. I'm not entirely sure about this part.
This "faculty lot" you speak of sounds like a place of great power...Ah, now I get it. It's centered at the origin and then dropped, okay. I couldn't figure out the reason for giving the anchor a position. Yeah, AD is going to be the weakest point, because it's got the longest cable.
Fight smart, not fair.Okay... I'm still stuck about how to calculate the relative tensions on the cables, though.
ERROR: The current state of the world is unacceptable. Save anyway? YES/NOCalculate the triangular angles so that you have the force balance. Then you add in the vertical thing. I think that's related to what you're trying to do, I've got a pounding headache and I'm not sure.
Fight smart, not fair.

Yeah, I've read tons of professional essays which use the first person.
Anyway, this isn't homework, but could somebody versed in symbolic logic help me stop driving myself crazy
[1] This facsimile operated in part by synAC.