course Mth 151
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09:03:18 `q001. . There are five questions in this set. Draw four points in a square pattern (i.e., if the points were properly connected, they should form a square). From each of the points, draw a straight line to each of the other points. How many lines did you draw?
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RESPONSE --> 2
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09:05:18 Each corner of the square will connected to each of the other three corners, so from each corner you would have drawn three lines. Since there are four corners, had you followed the instructions precisely you would have drawn 4 * 3 = 12 lines. However each of these lines will be identical with another line you would have drawn, since for any two corners you would be drawing a line from the first to the second then another overlapping line from the second to the first. Therefore you might have said that there are 6 lines.
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RESPONSE --> My response was 2, but I had the correct 6 lines total. I thought it was asking for how many lines we added.
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09:07:13 `q002. How many triangles are there in the figure you drew?
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RESPONSE --> 8, the square has 4 small triangles. The square halved, has a triangle from each corner, totaling 4 more=8.
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09:07:18 You should have a total of 8 triangles. The diagonals divide the square up into 4 small triangles. Each diagonal also divides the square into 2 larger triangles. Since there are 2 diagonals there are 4 larger triangles. The 4 small triangles and the 4 larger triangles total 8 triangles.
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RESPONSE --> ok
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09:10:15 `q003. The lines you drew should form a square with its two diagonals. Label the corners of the square A, B, C and D, going in order around the square, and label the center where the diagonals cross E. Now list all possible combinations of 3 of the letters A, B, C, D, E (note: combinations don't care about order, so A D E is the same as D A E or E A D or any other combination of these same three letters, so list each possible combination only once. That is, if you list for example ADE you won't list DAE).
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RESPONSE --> ADE, ABE, BCE, CED
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09:10:35 The easiest way to list these sequences is alphabetically: ABC, ABD, ABE all start with AB; then ACD and ACE start with AC and ADE starts with AD. This is a list of all possible combinations containing A. We next list all possible remaining combinations containing B: BCD, BCE and BDE. Then we write down CDE, the only remaining combination containing C. We thus have the 10 combinations ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE.
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RESPONSE -->
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09:12:18 `q004. Of the 10 combinations ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE, which form triangles on your figure?
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RESPONSE --> ADE, ABE, BCE, CED
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09:14:28 ABC forms a large triangle from A to B to C and back to A. The same is true of ABD, ACD and BCD. These are the large triangles in the figure. ACE and BDE form straight lines, not triangles. ABE, ADE, BCE and CDE form small triangles. Thus of the 10 possible combinations of labeled points, we find the 4 large triangles and the 4 small triangles we saw earlier, in addition to 2 straight lines which do not form triangles. Since any triangle in the figure must be labeled by three of the five points A, B, C, D, E, we see that these are the only triangles that can be formed.
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RESPONSE --> Ok, I thought that the larger traingles wouln't work, because they have 4 points, but now I understand
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09:15:20 `q005. Sketch the same figure as before, but without the line segment from A to B. Now how may triangles are there?
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RESPONSE --> 5
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09:15:32 Any possible triangle must still come from the list ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE. We again see that ACE and BDE form straight lines so do not count as triangles. Now ABC, ABD and ABE do not form triangles because the line segment AB is now missing. This leaves us the five triangles ACD, ADE, BCE, BCE and CDE.
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RESPONSE --> ok
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ϞT{͵Y{\ assignment #011 űpZ Liberal Arts Mathematics I 02-19-2006
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08:53:58 Query 1.4.24 1 to any power is what?
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RESPONSE --> raising one to any power, gives you the number one.
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08:54:03 ** The meaning is 1^2, 1^3, 1^4. We take a power of the base. The result is always 1. **
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RESPONSE --> ok
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08:55:52 Query 1.4.30 sqr of neg gives what?
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RESPONSE --> Taking the sqr of neg gives you an error/nonreal number on the calculator.
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08:56:04 ** The square root of a negative will often give you an error (what can you square to get a negative, since any number squared is positive?), but on certain calculators it gives a complex number (actually two complex numbers). These are not real numbers; for the purposes of this course there is no real square root of a negative number. There is no real number that can be squared to give a negative. If you square a negative number you get a negative times a negative, which is positive. If you square a positive number you get a positive number. So a negative number has no real square root. **
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RESPONSE --> ok
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08:57:52 Query 1.4.42 drawer has 18 compartments; how many drawers to hold 204 tapes?
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RESPONSE --> it will take 12 drawers to hold all the tapes, 11 wouln't be enough to hold them all.
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08:58:01 ** 204 / 18 = 11 with remainder 6. If we had 11 drawers they would hold all but 6 of the tapes. The leftover tapes also have to go into a drawer, so we need a 12th drawer. **
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RESPONSE --> ok
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w샂˟ assignment #011 űpZ Liberal Arts Mathematics I 02-19-2006
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08:59:31 Query 1.4.24 1 to any power is what?
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RESPONSE -->
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08:59:36 ** The meaning is 1^2, 1^3, 1^4. We take a power of the base. The result is always 1. **
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RESPONSE -->
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08:59:39 Query 1.4.30 sqr of neg gives what?
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RESPONSE -->
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08:59:44 ** The square root of a negative will often give you an error (what can you square to get a negative, since any number squared is positive?), but on certain calculators it gives a complex number (actually two complex numbers). These are not real numbers; for the purposes of this course there is no real square root of a negative number. There is no real number that can be squared to give a negative. If you square a negative number you get a negative times a negative, which is positive. If you square a positive number you get a positive number. So a negative number has no real square root. **
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RESPONSE -->
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08:59:47 Query 1.4.42 drawer has 18 compartments; how many drawers to hold 204 tapes?
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RESPONSE -->
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08:59:50 ** 204 / 18 = 11 with remainder 6. If we had 11 drawers they would hold all but 6 of the tapes. The leftover tapes also have to go into a drawer, so we need a 12th drawer. **
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RESPONSE -->
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