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Ok then can you write the correct answer so I can see what your referring to?
So you need help with ALL of them? Sorry I cant do your homework.
Total degrees in a circle is 360. So if that part is 120 and the total is 360 then:
y + 120 = 360
y = 240 degrees
Is the AB line parallel to the CD line? You dont specify it?
I will assume it is.
I dont know how to give a logical geometric proof but this is my logic:
Suppose the AB line keeps going. This angle is 60 degrees because the half circle formed by the line is total 180. Since AB and CD are parallel (?) then the other angle is also 60 degrees and x is also 60 degrees. I do not recall the theorem names but each of this steps I did was because of certain theorems having to do with parallel lines in geometry.
Hope this helps.

I dont understand your question?
You dont find the C unless your told to and in that case then they'd have to provide some function values in order to find the C.
Do you understand what the C means when doing an integral?
I followed all your steps but can you explain what you did to get here:
Anyways:
Now I must say that I wouldnt have got this idea if I didnt see your solution. Anyways, I was just wasting some time with this problem.
Your initial solution had to include a +C as a result to the integral (which you didnt put). You know when you do an integration you always put a +C in the end. However, in this case the +C was part of the ln(y) solution. So when you raise e to both sides, thats how you get e^C
Get it now?
Note: Thats as far as I can get it. I dont know how to solve the series.
Know how to do it now? Partial fractions again ![]()
Partial fractions is very useful, so learn it by all means. In some cases thats the only way to solve an integral.
What Dragonshade used is trigonometric substitutions. Even though it looks daring, a lot of times it proves easier to apply than any other method.
Yes. When I put "..." it implies it goes on and on (to infinity).
See my post #11
Do you mean this?
I also dont fully understand the problem.
Expanding it is the fastest way in my opinion
So coefficient of x^3 is 27, coefficient of x^2 is -18 and coefficient of x is -57.
Now that I read my post again, I realize it was a little bit too dramatic and emo. I certainly didnt want it to turn out like that.
I dont think theres nothing wrong in comparing yourself with other people since it gives you something to work towards (as long as it doesnt include jealousy and the like).
As I said, theres always people better than you in something. But as someone here mentioned, they are probably lacking on other aspects. Such as social life etc.
Yes MathIsFun, im young, im just 18 ![]()
Anyways, thanks all for your posts.
It is the german.
This is how I prepare for my tests, Im not sure they will help you but its how I do it.
I used to read the chapters and try to understand all the concepts, memorize the theorems etc. I made sure I knew everything well. But I found out that isnt enough when taking a test. Even though I knew everything well, I would always lose little points like you said.
What I started doing for every test from then on is I would do the same I used to do, read the chapters 1-2 times, make sure I understand all the concepts, memorize all the theorems etc.
Now I will do ALL the problems on the back of the chapter section. All of them. They are a lot (about 50+ or so) but its worth it in my opinion. When I finished the problems. I would go back to the chapter, read it again and do ALL the problems again. You might say "why again? " Well, I found that if you do the problems once its not enough practice and you will notice this when you try to do them for the second time, you still struggle with some problems which you have already done. This helps to really grind that practice and get used to all types of problems that might pop up on the test.
This is what I been doing for all my tests. I just had a test on monday on the convergence of series, taylor and maclaurin polynomials and series, integration and differentiation of series etc. I got a 100 on the test where before I would get around a 90 for little mistakes etc.
Dont know if this helps you.
Dont you sometimes feel like you have accomplished nothing in your life?
As many of you know im a Sophomore in university doing a mathematics major. Yesterday I went to talk to the professor that is in charge of the math club in my university. I said I'd like to join them etc. He was really happy (apparentally they dont get much new members). He asked me what classes I have taken etc and then he said that I was in the perfect time to start preparing for the Putnam etc.
They meet once a week and sometimes they have some random professor give a little lecture on some topics and when theres nothing like that, they just practice for the Putnam. He told me that last year my university placed 28th accross the nation, which I guess is good. All of which really interests me. So needless to say I was really happy.
I got home and started doing some research on the Putnam, I learned that it was probably one of the hardest math tests out there (how does it compare to the GRE math subject test?) but I also found out about some kid that took the Putnam while being in grade 10 in High School and got like 56 points on it. (median score is 1 out 120...)
I got so depressed, its like, sometimes you feel like you havent done anything compared to other people etc. Do you ever feel like this?
I cant do arithmetic fast without paper as well.
Hehe.
I got a 5 in AP Calc .... ![]()
You will love college way more than High School. Im having a great time.
I just HATED the fact you were treated as a kid when you were 18 years old. Senior year when I wanted to go home because I just felt like going. They had to call my mom every single time and make sure she says its ok...wtf?
I have an awesome mom who trusts me a lot. She says she remembers when she was in school and some days she felt like not going etc. Ever since 9th grade she told me any day i didnt feel like going to school to just tell her and she wouldnt mind since she knew I was smart and responsible and would balance it out. And thats exactly what i did. I was no idiot. Like, I knew if I was absent it was just worst for me but it was good to know that one of those days when you just feel like c-r-a-p or you KNOW that your aint doing s-h-i-t in school, that I could stay home and my mom wouldnt mind. I love my mom ![]()
Anyways, college is awesome. You will love it.
My story is sadder...
First test on Physics I got a 94. Good enough.
My second test was on the SAME stuff as you, torque, collisions, angular etc. I got a 26 on it... I just didnt understand the stuff to be honest. I just dropped the class.
math > physics
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My stepdad has only completed a HS diploma. He never went to college etc. He doesnt know any algebra at all etc. BUT his mathematical abilities just amaze me. Maybe I should say arithmetic?
Anyways, my family is Cuban-Spanish-American, we live in Miami right now and in my house every weekend theres like a family party, you know, they roast a pig every saturday, beer, music etc. And of course, Dominoes.
I have always been amazed by how my stepdad can count the points on the pieces so fast. You can show him like 20 domino pieces and he just looks at them and instantly tells you how many points...WTF? He always jokes around with me because since im a math major he says "How come your a math major and you cant do it? "
Anyways, the dominoes was just an example. My stepdad can do really long calculations in his mind. And the thing that amazes me is not the fact he can do it. But his speed.
You can ask him the percentage x% of any number n and he just tells you instantly...Like if you say to him what is the 7% of 67. He will tell you 4.69 instantly. It really is amazing.
How is this? Also, does this have any relation to mathematical abilities or is it just arithmetic? Also, since im a math major, am I supposed to be like this?
...
I believe you cant simplify anymore.
Yes they are indeed great. My favorites:
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How can I know so many hundreds of digits of pi and not the digits of your phone number?
Come on baby, let's off to a decimal place I know of and I'll take you to the limit.
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im definitively using the pi and limits one for sure! ![]()
Yes you dont need to worry about the negative root.
Trigonometric substitution. I checked all your work and its correct.