Assigments 678

course Mth 151

?w??|???????assignment #008008. `Query 8

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College Algebra

06-17-2007

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15:31:08

** The total of all numbers on the clock is 78. So the numbers in the three sections have to each add up to 1/3 * 78 = 26.

This works if we can divide the clock into sections including 11, 12, 1, 2; 3, 4, 9, 10; 5, 6, 7, 8. The numbers in each section add up to 26.

To divide the clock into such sections the lines would be horizontal, the first from just beneath 11 to just beneath 2 and the second from just above 5 to just above 8. Horizontal lines are the trick.

You might have to draw this to see how it works. **

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self critique assessment: 3

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15:31:50

** You have to work this one backwards.

If they were left with 35 on Friday they had 70 at the beginning (after bringing in the 32) on Friday, so they had 70 - 32 = 38 at the end on Thursday.

So after bringing in the 32 they had 2 * 38 = 76 at the beginning of Thursday, which means they had 76 - 32 = 44 before the 32 were added.

So they had 44 Wednesday night ... etc. **

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RESPONSE -->

70-32=38

self critique assessment: 2

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15:32:05

Query 1.3.30 Frog in well, 4 ft jump, 3 ft back.

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confidence assessment:

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15:32:13

Query 1.3.30 Frog in well, 4 ft jump, 3 ft back.

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RESPONSE -->

one ft up

confidence assessment: 3

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15:32:54

Query 1.3.48 How many ways to pay 15 cents?

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confidence assessment: 3

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15:33:20

** To illustrate one possible reasoning process, you can reason this out in such a way as to be completely sure as follows:

The number of pennies must be 0, 5, 10 or 15.

If you don't use any pennies you have to use a dime and a nickle.

If you use exactly 5 pennies then the other 10 cents comes from either a dime or two nickles.

If you use exactly 10 pennies you have to use a nickle.

Or you can use 15 pennies.

Listing these ways:

1 dime, 1 nickel

1 dime, 5 pennies

2 nickels, 5 pennies

3 nickels

15 pennies

1 nickel 10 pennies

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RESPONSE -->

0,5,10,15

self critique assessment: 3

&#

Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the given solution, and if necessary asking specific questions.

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15:33:50

** Divide the coins into two piles of 4. One pile will tip the balance.

Divide that pile into piles of 2. One pile will tip the balance.

Weigh the 2 remaining coins. You'll be able to see which coin is heavier. **

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RESPONSE -->

2 piles and weigh them

self critique assessment: 3

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assignment #006

006. Sequences and Patterns

Liberal Arts Mathematics I

06-17-2007

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15:04:12

`q001. Note that there are 6 questions in this assignment.

Find the likely next element of the sequence 1, 2, 4, 7, 11, ... .

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confidence assessment: 3

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15:04:36

The difference between 1 and 2 is 1; between 2 and 4 is 2; between 4 and 7 is 3; between 7 and 11 is 4. So we expect that the next difference will be 5, which will make the next element 11 + 5 = 16.

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RESPONSE -->

11+5=16

self critique assessment: 3

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15:08:46

`q002. Find the likely next two elements of the sequence 1, 2, 4, 8, 15, 26, ... .

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confidence assessment: 0

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15:09:33

The difference between 1 and 2 is 1; the difference between 2 and 4 is 2, the difference between 4 and 8 is 4; the difference between 8 and 15 is 7; the difference between 15 and 26 is 11.

The differences form the sequence 1, 2, 4, 7, 11, ... . As seen in the preceding problem the differences of this sequence are 1, 2, 3, 4, ... .

We would expect the next two differences of this last sequence to be 5 and 6, which would extend the sequence 1, 2, 4, 7, 11, ... to 1, 2, 4, 7, 11, 16, 22, ... .

If this is the continuation of the sequence of differences for the original sequence 1, 2, 4, 8, 15, 26, ... then the next two differences of this sequence would be 16 , giving us 26 + 16 = 42 as the next element, and 22, giving us 42 + 26 = 68 as the next element. So the original sequence would continue as

1, 2, 4, 8, 15, 26, 42, 68, ... .

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RESPONSE -->

42 and 68

self critique assessment: 2

&#

In a good self-critique you need identify the specific things you do and do not understand in the given solution, and either demonstrate your understanding or ask specific questions about what you don't understand. It doesn't accomplish the intended learning goals to simply say that you understand.

That way, once you have defined your difficulties I can help you address them. &#

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15:11:10

`q003. What would be the likely next element in the sequence 1, 2, 4, 8, ... . It is understood that while this sequence starts off the same as that in the preceding exercise, it is not the same. The next element is not 15, and the pattern of the sequence is different than the pattern of the preceding.

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confidence assessment: 1

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15:11:12

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confidence assessment: 1

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15:11:50

`q004. There are two important types of patterns for sequences, one being the pattern defined by the differences between the numbers of the sequence, the other being the pattern defined by the ratios of the numbers of the sequence. In the preceding sequence 1, 2, 4, 8, 16, ..., the ratios were 2/1 = 2; 4/2 = 2; 8/4 = 2; 16/8 = 2. The sequence of ratios for 1, 2, 4, 8, 16, ..., is thus 2, 2, 2, 2, a constant sequence. Find the sequence of ratios for the sequence 32, 48, 72, 108, ... , and use your result to estimate the next number and sequence.

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8x2=16

confidence assessment: 3

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15:16:57

The ratios are 48/32 = 1.5; 72 / 48 = 1.5; 108/72 = 1.5, so the sequence of ratios is 1.5, 1.5, 1.5, 1.5, ... . The next number the sequence should probably therefore be 108 * 1.5 = 162.

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RESPONSE -->

12x10=120

self critique assessment: 2

&#

You need to detail the points on which your solution differs from the given solution, and document what you do and do not understand about the given solution.

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15:17:36

`q005. Find the sequence of ratios for the sequence 1, 2, 3, 5, 8, 13, 21... , and estimate the next element of the sequence.

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21+13+34

confidence assessment: 3

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15:19:13

`q006. Without using ratios, can you find a pattern to the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, ..., and continue the sequence for three more numbers?

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55,89

confidence assessment: 3

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?????p?Z?????

Student Name:

assignment #007

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15:22:08

`q001. Note that there are 7 questions in this assignment.

Sketch three points A, B and C forming an equilateral triangle on a piece of paper, with point A at the lower left-hand corner, point B at the lower right-hand corner and point C at the top. Sketch the segments AB and AC.

Now double the lengths of AB and AC, and place a point at each of the endpoints of these segments. Connect these new endpoints to form a new equilateral triangle. Two sides of this triangle will have three points marked while the new side will only have its two endpoints marked. Fix that by marking that middle point, so all three sides of your new triangle are marked the same.

How many marked points were there in the original triangle, and how many are there in the new triangle?

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15:22:19

`q001. Note that there are 7 questions in this assignment.

How many marked points were there in the original triangle, and how many are there in the new triangle?

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the first has 3 and the second has 5

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15:23:25

`q002. Extend the two sides that meet at A by distances equal to the distance original lengths AC and AB and mark the endpoints of the newly extended segments. Each of the newly extended sides will have 4 marked points. Now connect the new endpoints to form a new right triangle. Mark points along the new side at the same intervals that occur on the other two sides. How many marked points are on your new triangle, and how many in the whole figure?

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3 on the first and 6 on the second

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15:26:22

`q003. Continue the process for another step-extend each side by a distance equal to the original point-to-point distance. How many points do you have in the new triangle?

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15 endpoints

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15:26:39

`q004. Continue the process for one more step. How many points do you have in the new triangle?

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15 endpoints

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15:27:35

`q005. The sequence of marked points is 3, 6, 10, 15, 21. What do expect will be the next number in this sequence?

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28,36

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15:28:41

`q006. How can you tell, in terms of the process you used to construct these triangles, that the next number should be 7 greater?

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you add and end point everytime

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&#

You have some correct answers, but many of your responses require more detail in self-critique. Be sure to see my notes. &#

You also didn't always follow the complete sequence of operations for the program.

&#To run the program correctly you click on the Next Question/Solution button (top left), enter your response in the Answer box (the box at top right), click on the Enter Response button (above the top right box), then again on the Next Question/Solution botton (top left) to see the solution, and finally enter your response or self-critique in the Answer box and click on Enter Response.
You then start the process over with the next question, clicking on the Next Question/Solution button at top left, etc.