i know how to do this one... since 9 is a perfect square and the other side is (2x+1)^2, take the square root of 9 (which is 3 OR -3), the smallest root is usually the negative, so do 2x+1= -3, solve for x, you'll get -2 ----------------------------------------- i learned about ellipse but forgot all about it...(that's a sin), but..sorry. ------------------------------------------ i know how to do this, but since i am chinese...i am having trouble putting my thoughts into words...However, there is a good explaination in the trig section of the website, here is the link: http://www.math-magic.com/trig/basic_memorizations.htm it really has nice explainations to it.
i hope i helped at least a lil. I am sure the Webmaster will be here in a short time to help you too.
Hey. Let me guess. You are Michael from Midlothian, Ragin'? The Sin = 3/5 problem doesn't require trig or being Chinese (Although it does help to be Chinese).
Sin = Opposite over hypotenuse. Cos = Adjacent over hypotenuse. Tan = Opp/Adj.
Sin= 3/5;
The 3 is the length of the opposite side and 5 is the length of the hypotenuse. Using our knowledge of special right triangles (Or just flat out knowing 3,4,5 forms a right triangle) we can figure that the adjacent (or unknown side) is 4.
since Tan = Opp/Adj, (Or you can use Sin/Cos = Tan) so we put in the 3 that we had at first from Sin = 3/5, and divide it by the 4 from when we concluded that the Cos = 4/5. That gives us 3/4.
quote: Originally posted by: "Hey. Let me guess. You are Michael from Midlothian, Ragin'? The Sin = 3/5 problem doesn't require trig or being Chinese (Although it does help to be Chinese). Sin = Opposite over hypotenuse. Cos = Adjacent over hypotenuse. Tan = Opp/Adj. Sin= 3/5; The 3 is the length of the opposite side and 5 is the length of the hypotenuse. Using our knowledge of special right triangles (Or just flat out knowing 3,4,5 forms a right triangle) we can figure that the adjacent (or unknown side) is 4. since Tan = Opp/Adj, (Or you can use Sin/Cos = Tan) so we put in the 3 that we had at first from Sin = 3/5, and divide it by the 4 from when we concluded that the Cos = 4/5. That gives us 3/4. "
lol, i thought about 3,4,5, right triangle for a moment when i was typing, but i thought it'd be better to tell him about the trig part because similary problems will not always be a easy to identify like this 3,4,5, triangle...
Okay, nice name. Since you are a freshman I will try to explain ellipses as easily as possible. I think Quincy and Sam did a good job of explaining the "trig" problem and the "algebra" problem. If you want me to try to explain either of those differently, let me know.
BTW, you were right about the pentagonal numbers page. Sorry. The formula is right, the examples are not. That is what happens when you cut and paste to save time. I will get that changed. Thanks for pointing that out to me.
Okay, lets see if we I can explain a crash course in pre-cal on ellipses. First, you always want to get the formula in this form:
(x-x_o)^2/a^2 + (y-y_o)^2/b^2 = 1.
So in your example we can divide by 27 and get:
x^2/9 + y^2/(27/4) = 1.
To find the length of the major axis, you have to find out if b or a is longer. In this case a = 3 (notice I just took the square root of 9) and b = sqrt(27/4). In this case a > b, so the major axis is defined as 2a or 2(3)=6. The minor axis is defined as 2b or 2(sqrt(27/4)). If b had been greater than a, then the major axis is 2b and the minor axis would be 2a. Did this help?
Sometimes the question asks for the area or for the center. The area of the ellipse is defined by ab/4*pi. The center of the ellipse is (x_o, y_o).
There are some other things the question can ask. For example, it can ask for the focus. That is a little more complex and I can explain it if you really need me to.
Webmaster
A freshman at state???? You are from Midilothian aren't you?
Hey thanks to all of you this really helped. Ya penguins are awesome - don't ask. And yes I'm Michael from Midlothian - podunk town no one has heard of. Hopefully I can get some more precal experience so that these sort of problems can come easier to me. But alas I have to take algebra 2 next year due to the school though I could easily test out of it. I'm looking forward to state with all of yall, thanks again
Well Michael from Midilothian, podunk town no one has ever heard of,
I remember what it was like being so far ahead in NS and not being able to advance because my current high school math level was not where I needed to be. I had to go in after school so my coach could teach me the basics of trig, pre-cal, and calculus. If you need to, this is the place to ask. I really enjoy my current status of online coach, so don't hesitate to ask. I will tell you whatever you need to know, even if it is giving lessons in calculus.
So to all: Keep the questions coming. I try to check this forum out several times a day, at least until state is over.
Ha I guess we aren't too podunk being 4A and all, but still. Oh ya and it must have been fate because my UIL coach(also my future algebra 2 teacher) just suggested that I test out of her class and take calculus next year. ITS SO AWESOME!!! I've been trying forever to have a teacher let me test out. So hopefully next year I'll be more successful in the 4th column. And ya I love coming here, I used to go to academicmeet.com for tricks but I've grown to like this site a lot better. Thanks for putting it together, and count on me posting some more questions .
To learn the number sense questions you don't really need to take precal or calculus. I've only taken through Algebra 2. The questions can be learned quite easily. Just in January of this year I rarely made it past 40. By March I was finishing tests. You just have to learn how to do the problems. I'm still horrible with the precal questions. I always forget the identities. To help with precal my teacher gave me a circle chart. I just looked at this, and it all seemed to come together. The calculus isn't bad at all. You can learn how to do most of what you will see on a test in several minutes. Make sure to sit down and practice some example problems after you learn it. It'll stick much better. Cya at STATE!
Ya I know that you coud know the tricks very quickly, but I'm looking to understand the mathematics behind it deeper so I can know what I'm doing as well. I mean it takes the fun out of number sense for me if I'm just pluggin in formulas. I like to be creative and do different things when I recognize a unique situation. Plus next year I want to take the number sense, computer science, and math. And in order to advance in math I'll need at least pre cal. Thanks for the input.
I totally agree with penguin. Sure you can memorize formulas, but if you don't know the background or why it works you are stumped if they change it a little. Formulas are good, but only to a certain extent.
Computer Science is an AWESOME competition. I loved it. Almost more than NS, but only because you also have a hands-on section where you get to really program. If you are good at NS you will do well in CS.
The Math tests I always thought were stupid. It's funny because on the TCM forum, most people like the math better. But I found that on a multiple choice math test you can use the answers to find out which one is correct without even having to know how to do the problem. Here's an example from the District 1 Math Test:
This is problem 10:
Simplify: sin(A)tan(A) + cos(A)
a) 2cosA b) sin^2 A c) secA - cscA d) secA e) csc A
Let's say you don't know trig. You can still do this problem. Pick an arbitrary value say A = 1.12 and plug into the question. Now plug 1.12 into each answer. Compare the expression from the question to the answers. Only one should work. The only one that works is D, so the answer is D. You don't even need to know how to do it.
I was able to get first MANY times as a freshman, beating many of the upperclassmen. People thought I was a math genius. They were wrong. I didn't know how to do half of the problems on the test that I got right. That's why I like NS. It takes more skill. Which is why I never cared about the math test. I probably could have done much better than I did, but I had no desire to.
That's my opinion. I am sure other people think very differently.
quote: Originally posted by: "Ya I know that you coud know the tricks very quickly, but I'm looking to understand the mathematics behind it deeper so I can know what I'm doing as well. I mean it takes the fun out of number sense for me if I'm just pluggin in formulas. I like to be creative and do different things when I recognize a unique situation. Plus next year I want to take the number sense, computer science, and math. And in order to advance in math I'll need at least pre cal. Thanks for the input. P.S. what school are you from?"
I was the anonymous above, Sam. I feel the exact same way as you do Penguin. I know the tricks and the basics of the subjects, but I want to be able to apply them. It drives me carzy knowing so little. I also really want to do both computer science and general math next year. I especially want to do the computer science. Do you have any suggestions on what books to read or how to learn the java language for the test?
Ya computer science is a real fun test but there's a catch. You have to have a good team to take you through regionals. I'm not totally sure on the individual policy, but I know that without three strong team members, the programming portion will be horribly difficult. Java is a complex language, but made to be learned easily. You can get some cheap books off Amazon if your a self learner (you probably are), but there's nothing better than taking the AP class. Also, being a computer nerd like myself never hurts. You just need to program a lot so you can get used to the logic. And I feel just as you do about when I don't know something. I think its my competitive nature (can't stand it that there's knowledge out there that someone else knows and I don't) I'm pretty sure this is a good thing to have in number sense though
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