UIL 2012 B questions

[smeag]

Can you please provide explanations for problems: 28, 29, 36, 37, 47, 49, 50, and 58

[smeag]

please!

[FabensMath]

28. (16700-5700)/(31*24*60*60) giving you gal/s then convert to tbsp/s
29. .92 = pi*(.615/2)*sqrt(x^2+(.615/2)^2) + pi*(.615/2)^2 then solve for x
47. Mr. Shawn just gave an explanation, check on proportions and regressions topic.
49. Just take the volume of a normal cylinder, the cavity and the hemisphere cancel out.

[smeag]

I tried the regression and the cylinder problem numerous times and still ended up with the wrong answer, can you provide an explanations for the remaining questions?

[FabensMath]

[Shawn]

I don't see the exam in downloads, so I will need either a link to the exam or the questions posted.

[FabensMath]

[Shawn]

Thanks. Appartently I have lousy download finding skills.
I'll start with the ones nothing has been posted about.
50) What are they wanting diagonal or height? I will just start working and find out off the key.
Notice that the edges of the triangular base are all diagonals of squares.
Find base area:
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No that isn't it....
The wierd height looks tilted 75 degrees (I can't explain this well)
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I feel my solution got a little shady at the end, because I just kinda guesstimated the tilt. Probably would be better for someone else to do it that is able to explain where exactly the triangle is.
58) Multiply matrix to get
57.3b-248.4,199.5
-10.8b-340.2,5.4
Equation solve by determent set to 55
55=5.4*(57.3b-248.4)-199.5*(-10.8b-340.2)
TI-89 Spits out answer
-26.977
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On this problem use copy paste and equation solver on 89 alot.

[Shawn]

36) I just posted this somewhere, but I will do it again.
Compound interest
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[Shawn]

That is it for tonight, I might do some more tomorrow.

[Shawn]

Sorry for not answering for awhile, have had a few exams.
37) Fun problem, I always wonder the raw material cost for a potato chip....
First number of chips from potato
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Mass/Chip
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Cost/Chip
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Cost/Bag
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Now for ratio retail/bag to cost/bag
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That is a really cool problem.

[Shawn]

58) Two options TI-89 equation solver or start writing systems.
TI-89
3*[[19.1,9.2][-3.6,12.6]]*[[b,3][-9,1]]=
57.3b-248.4 199.5
-10.8b-340.2 5.4
solve(det(above copied using copy paste)=55)
Using wolfram to solve this it says: b=-26.8988
-26.9 within margin of error
By hand:
You would multiply each element out (not the way to do it)