Here's my final proyect, check it out if you want to learn more about this topic
http://www.freewebs.com/riroman/
Monday, May 21, 2007
Friday, May 18, 2007
Final Project
Final project done. I guess this is it, besides the final. Good luck and enjoy my project.
http://www.freewebs.com/jcsp88/
http://www.freewebs.com/jcsp88/
Monday, May 14, 2007
Trigonometric Techniques of Integration
My final project was on Trigonometric Techniques of Integration and can be found in any of the following links. I apologize if you get any pop-ups. I understand they can be quite annoying. Drawings and graphs shouldn't take long to load. Either way, if you come up with any spelling mistake or other type of error while looking at it, please let me know so I can fix it. Enjoy!
Lina Garcia
www.trigint.741.com
trigint.741.com
Lina Garcia
www.trigint.741.com
trigint.741.com
Test
I was just testing to see if the built in blogger function microsoft word has could be used to publish equations. Well, it doesn't work
Friday, May 11, 2007
Luis DP's FP Solutions
1. Jim reaches the point (5, 10) after t = 5 seconds. Bob will reach the point (5, 10) after t = 1 second. Bob will win the race.
2. The orientation of the first curve is counterclockwise. When the functions for x and y are exchanged, the curve's orientation becomes clockwise.
3. (r, θ) = ( √98, 5 pi/4) (-√98, pi/4)
4. (x, y) = (-.5, (√3 )/2)
2. The orientation of the first curve is counterclockwise. When the functions for x and y are exchanged, the curve's orientation becomes clockwise.
3. (r, θ) = ( √98, 5 pi/4) (-√98, pi/4)
4. (x, y) = (-.5, (√3 )/2)
Problems Posting Answers
I'm having two major problems posting the answers. The first one is that they are to big to post on bubble share, so I don't know how to post them atm, the second one is that I'm having trouble working out one problem. I'll present the annotated answers on monday, in hopes of getting some partial credit, or maybe just some corrections on my answers.
Wednesday, May 9, 2007
MAC's Beauty Post
I recently received a forward called "La Simetria de los Numeros" and I was really amazed by it. Mathematics can sometimes be beautiful... I wanted to share this with all of you and that is why I'm making this post. Look at the patterns.
1.
1 x 8 + 1 = 9
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
2.
1 x 9 + 2 = 11
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111
3.
9 x 9 + 7 = 88
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
4.
1 x 1 = 1
4.
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321
Amazing... check the answers if you want, they are real. I like them all, but my favorites are numbers 1 and 4, which are yours?
Tuesday, May 8, 2007
AP TEST
The AP Exam is finally here. I just wanted to say, good luck to everyone that is taking the exam. Hope you all get a 5.
Friday, May 4, 2007
Final Draft: Problems
This are my final Problems. I change the very much from my first problems and I add a word problem. If a problem is not well elavorated or needs something please add a comment and tell me. Thanl You.
Differential Equation Problems
1. A new sport called kiteboarding gets to Cartagena. Initially 10 persons starts doing kiteboarding. After 2 years passed the number of persons that are now doing kite boarding is 120. Find the equation at any time. What would be the number of people doing kiteboarding in 50 years?
2. Solve the equation.
Differential Equation Problems
1. A new sport called kiteboarding gets to Cartagena. Initially 10 persons starts doing kiteboarding. After 2 years passed the number of persons that are now doing kite boarding is 120. Find the equation at any time. What would be the number of people doing kiteboarding in 50 years?
2. Solve the equation.
3. Solve the IVP.
4. Make a slope field with the next equation. 
Problems Final Draft
Well this is the final version of my problems. However I'm still open to suggestions on how to incorporate some word problems into the mix, since this compilation of problems seem quite plain and boring
Thursday, May 3, 2007
Tuesday, May 1, 2007
Monday's Slides 4/30/07
Today, we solved a few more inverse trig problems. A couple of interesting topics arose.
The first slide shows an integral that required an inverse secant and substitution. Don't forget to change the limits of integration when you make your substitution.
The second slide shows a derivative of an inverse cosecant function that also requires the chain rule. Anto's solution involved inserting an x^4 inside a square root. (To explain this step, he showed an example of the technique in the upper right corner.) Can you see another way forward that avoids inserting x^4 inside the radical?
The last slide shows a definite integral of a rational function with trigonometric expressions in both the numerator and denominator. Juan used the wise step of doing some algebra before doing the calculus. This step avoids using any inverse trig functions. The problem is that he forgot to extract both the negative and positive roots. It turns out we only needed the negative root because in the interval [3,4], cosine is negative.
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Then we looked at the answers to the multiple choice questions from review sheets 1 & 2.
Be prepared on Wednesday to ask questions on any problems for which you have confusion or doubt.
The first slide shows an integral that required an inverse secant and substitution. Don't forget to change the limits of integration when you make your substitution.
The second slide shows a derivative of an inverse cosecant function that also requires the chain rule. Anto's solution involved inserting an x^4 inside a square root. (To explain this step, he showed an example of the technique in the upper right corner.) Can you see another way forward that avoids inserting x^4 inside the radical?
The last slide shows a definite integral of a rational function with trigonometric expressions in both the numerator and denominator. Juan used the wise step of doing some algebra before doing the calculus. This step avoids using any inverse trig functions. The problem is that he forgot to extract both the negative and positive roots. It turns out we only needed the negative root because in the interval [3,4], cosine is negative.
This album is powered by BubbleShare - Add to my blog
Then we looked at the answers to the multiple choice questions from review sheets 1 & 2.
Be prepared on Wednesday to ask questions on any problems for which you have confusion or doubt.
Finding squares of numbers ending in 5
I came across this website showing how to easily compute, in your head, the squares of numbers ending in 5. The formula is:
(n)* (n+1) + 25
Now, the trick is that the 25 isnt "added" it is just the last two digits of the number you find computing the first part of the formula.
Example
1. 85*85
In this case n = 8, therefore
8*9 + 25 = 7225
2. 135*135
In this case n = 13, so
13*14 + 25 = 18225
(n)* (n+1) + 25
Now, the trick is that the 25 isnt "added" it is just the last two digits of the number you find computing the first part of the formula.
Example
1. 85*85
In this case n = 8, therefore
8*9 + 25 = 7225
2. 135*135
In this case n = 13, so
13*14 + 25 = 18225
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