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i will change it
sorry, i think i saw another problem's answer
combination{x}{y} means x combination y
In class we studied the identity combination{r}{r}+combination{r+1}{r} +combination{r+2}{r} + ... +combination{n}{r} = combination{n+1}{r+1} We also took a glimpse at combination{r}{0}+combination{r+1}{1} +combination{r+2}{2} +... +combination{n}{n-r} = combination{n+1}{n-r}. We will now take a closer look at this second identity.
(a) Confirm that the second identity works for n=5, r=2 and for n=7, r=3.
(b) What is the relationship between the first and second identities?
(c) Prove the second identity above algebraically without using what you learned in Part b. (In other words, prove it without the help of the hockey stick identity we studied in class).
(d) Prove the second identity above with a block-walking argument.
srry, i used latex, i will change it to regular english
For no. 3 its not 20/3, but 6 because i tried it yesterday and got it correct
In class we studied the identity \displaystyle\binom{r}{r}+\binom{r+1}{r} +\binom{r+2}{r} + \cdots +\binom{n}{r} = \binom{n+1}{r+1} We also took a glimpse at \displaystyle\binom{r}{0}+\binom{r+1}{1} +\binom{r+2}{2} + \cdots +\binom{n}{n-r} = \binom{n+1}{n-r}. We will now take a closer look at this second identity.
(a) Confirm that the second identity works for n=5, r=2 and for n=7, r=3.
(b) What is the relationship between the first and second identities?
(c) Prove the second identity above algebraically without using what you learned in Part b. (In other words, prove it without the help of the hockey stick identity we studied in class).
(d) Prove the second identity above with a block-walking argument.
1. For some positive real number r, the line x + y = r is tangent to the circle x^2 + y^2 = r. Find r.
2. Find the center of the circle passing through the points (-1,0), (1,0), and (3,1). Express your answer in the form "(a,b)."
3. A line with slope 3 is 2 units away from the origin. Find the area of the triangle formed by this line and the coordinate axes.
4. Find the maximum value of y/x over all real numbers x and y that satisfy (x - 3)^2 + (y - 3)^2 = 6.
thank you
Prove your relationship using a block walking argument.
Prove your relationship using a committee-forming argument.
did you get it?
got it
thanks
yes, but i started math early and i skipped a few grades in math
i'm only 12
sorry, i mean no.3
i am doing geometry and algebra 2 and will be starting trig soon
for no.2 i tried it but its wrong
they suggest using any sort of probability
thanks, i solved the questions
I'm in 8th grade and this is a question for my AOPS Counting and Probability Hw.
i solved no.2 but i need some hints on 1 and 3