hey mr.jones, it's quincy here, i have some questions about the problems i came across on the ns test
1. the sum of the coefficients of the 3rd and 5th terms in the expansion of (x-y)^5 is
(i don't have the answer for that one)
2. the product of the coefficients of the binomial expansion of (x+2y)^4 is
(i don't have the answer for that one either)
i am pretty sure those has to do w/comb. and perm. and the formula is derived from the pascal triangle somehow...but i don't know the exact formula, so i figured it'd be better to ask you since you can use your software to derive some formulas.
thanks
quincy
p.s. btw my ns scores in competitions are going up, now all i do is look @ the problem and do them in my head(haven't actually wrote on a test for so long)...but i still can't finish the test though...and still need to learn the tricks left on the 4th column..but i think i can handle it. Also...anatomy is so boring!!!! i hate that class...lol
i was flipping through your probability section and somewhere in there it said that 4C4 is 1, but i think it's undefined because the denominator is (4-4)!4!, can you explain to me how you got 1? thanks
don't quote me on it, but I'm pretty sure 0! is evaluated to 1, despite it just being 0 times nothing. Don't know why but that's just how I'm always worked it and it hasn't failed.
Yep, Pengiun is correct. 0! is always evaluated as equalling 1. It's set as a predefined value.
I am sorry that I haven't had very much time to work on this site. Now that I know you are looking at it again I will be more enthusiastic about checking it more often and answering your questions.
I think I made a couple of pages on your questions. On the 1st question you have to evaluate the coefficient of each of the terms (the 3rd and 5th). See this link:
*I can't make this a link because I am using a very old computer right now so sorry, but you can cut and paste*
As for the second question I guess I forgot to add this to the website. I thought I did but after looking at it I guess I didn't.
First of all, I can't believe that Mr. White would take this to the 4th power. I thought for sure he would stick to just 2 and 3. This makes me think I am missing something. But here is what I came up with based on a previous thread from last year:
We were talking about the formula (ax + by)^n. To find the product of the coefficients use:
For n = 2, use 2*a^3*b^3
For n = 3, use 9*a^6*b^6
For n = 4, use 96*a^10*b^10 (This is why I think I am missing something)
So for your example, which I think is crazy to begin with we are going to get 96*2^10 = 96 * 1024 which is not easy but comes to 98304. And just to check we are going to have the expansion:
You might want to check on that to make sure you read the problem right. It is not very fun. I thought for sure that Larry would stick to n=2 and n=3.
If you need me to explain either of these in more detail I can. I want you to do research on the first and see if you can get the answer. (Just for your info though you should be able to come up with 15)
Thanks! i went to your binomial expansion page and read about it again, i now know how to do it :). But personally i think it's really a pain to do those operations in my head under limited time and w/out any guarentee of getting it right, because you have to find the 3rd term, remember the number, and add it to the 4th term...if i was doing a test i'd skip that and come back if i have spare time...I recheck "the product of the coefficients of the binomial expansion of (x+2y)^4" problem and it was right, and yeah...that multiplication is insane, i am wondering if you did 96*2^10 = 98304 in your head...
I did in fact do it in my head. Think of this as 96 x 1024 as being (100-4) x 1024. It's not exactly a cinch but you get 102400 - 4096 which is not too terribly hard. It is just hard to think of it without looking at it. But I did do it in my head.
I talked to Larry white and he told me that he had planned to only use (ax + by)^2. So you really should not worry about raising it to any other power.
Leo Ramirez
Visit my website at www.rammaterials.com for Number Sense workbooks.
