Need help with 2 SAT math problems

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1

<p>haha normally math is my strong point</p>

<p>both are grid ins
The first one, </p>

<p>Tameka cut a ciruclar pizza into wedged shaped pieces, one of which is shown above. The tip of each piece is at the center of the pizza and the angle at the tip is always greater than 20* but less than 30*. What is one possible calue for teh number of pieces into which the pizza is cut?</p>

<p>so basically 20<x<30</p>

<p>I took x as 25 and divided by 360. Easy problem, and I put 14.4 </p>

<p>the answer was 13,14,15,16,17 would a decimal cut it? </p>

<p>the second one, this is the last grid in (#18)</p>

<p>its probablility which is my worst subject in HS</p>

<p>basically there are 5 symbols, Ill call them</p>

<p>A B C D E</p>

<p>the thing is object C cannot be placed on either end of the row.
How many possible arrangements are possible?</p>

<p>what I did was:</p>

<p>4 possible for the 1st slot (A,B,D,E) say A is used
4 possible for the 2nd slot (B,C,D,E) say C is used
3 possible for the 3rd slot (B,D,E) say B is used
2 possible for the 4th slot (D,E) say D is used
1 possible for the 5th slot (E)</p>

<p>I multiplyed and got 96, but the answer is supposedly 72. Not sure how to work this out?</p>

2

<p>No, 14.4 wouldn't cut it because they wanted how many whole pieces of pizza can be cut by that angle.</p>

<p>Here's how to do the second problem:
A B C D E</p>

<p>Since the restrictions are on the ends, you must do these first</p>

<p>1st blank: Say A is used out of (A, B, D, E) 4 possibilities
Last blank: Say B is used out of (B, D,E) 3 possibilities
2nd blank: C is used (C D, E) 3 possibilities
3rd blank: D is used (D, E) 2 possibilties
4th blank: E is used (E) 1 possibility</p>

<p>4 * 3* 3 * 2 * 1 = 72!</p>

3

<p>hey thanks! I guess I was on the right track, but I thought incorrectly regarding the last blank, and I should of appraoched that after the 1st blank.</p>

4

<p>No problem =)</p>

<p>It's tricky with those problems... you just have to do the restricted spots first and then it becomes easy.</p>

5

<p>Prism:
A cleaner way to do the first problem is:</p>

<p>20 < x < 30, so (360/20) > (360/x) > (360/30)
or 18 > #slices > 12
so #slices (which must be an integer) must be > 12 and < 18
i.e. it can be any one of 13,14,15,16,17</p>

6

<p>so look for the restrictions first...</p>

<p>good idea</p>

<p>optimizer dad, didnt think of that, but I will keep it in mind, basically the overlying strategy for both the problems is </p>

<p>'solve against the provided materal'</p>

7

<p>you can't have decimals... Think about it.. If you have one slice, and another slice that is half that size, you still essentially have two slices. LOL hope that made sense...</p>

8

<p>I also had trouble the first time I attempted the second question. The trick to this question is how to deal with the restriction. When dealing with limitations in probability, you have to attack them first. So you'd start like this:</p>

<hr>

<p>4 _ _ _ 3</p>

<p>THEN only can you continue with the remaining spots. Now that you've selected 2 choices, 3 are remaining:</p>

<p>4 3 2 1 3</p>

<p>multiply through and u get 72.</p>

9

<p>I think the first problem's answer is 15. If it's:
20<x<30
then you can guess and check by plugging in each possible answer. for number of peaces.
WHOLE PIZZA = 360 degrees.
Divide 360 by each answer=
13=27.69
14=25.71
15=24 (perfect pieces with 24 as angle. which fits the 20<x<30)
16=22.5 (.6?? wouldn't work)
17=21.5 (doesn't work. </p>

<p>Therefore. I'm guessing it's C) 15??</p>

10

<p>protege: I don't believe there was a restriction on the angle; it need not necessarily be an integer.</p>

11

<p>it was a grid in.</p>