invitational b q

[smeag]

questions: 11, 40, 46, 60, 66.
also, please show me a few examples on approximating and finding the exact values of square roots. Also please help me on the arithmetic sequences. Thanks for your efforts!

[smeag]

c'mon please help more capable people!

[PokémonMaster]

For #11, take the average of the terms and multiply by the number of terms. To clarify, (((Term 1-Term 2)/difference between terms)+1)*((Term1+term 2)/2). Sorry if that is confusing, i still can't figure out Latex.

For 40, I would just approximate the square roots by splitting the number up. Ex. sqrt(21347) split to sqrt(213) and throw the 47 away. Then just add in a zero and voila!, you have a good approximation.

#46.Dividing bases isn't my thing, so nsguy1350 will probably explain it for you. :P

On #60, you should recognize that (9^2)/(3^4) cancel out, and if you memorize your numbers to the fifth power (or just multiply), you should get a very good estimate. #60 is normally easy(ish) to do because you can cancel out.

Multiplying 2 numbers that are the same distance apart is the middle # squared minus the difference between the numbers/2 squared. In this case, it is 100^2(10000) minus 12 ((112-88)/2) squared, which is 9856.

I know of a trick, no, a method, rather to find exact square roots, but it takes way too long to be practical, so I can't really help more than I have.
If anything is unclear, just tell me.

[nsguy1350]

What year is this?

[PokémonMaster]

O.O ... oops, I didn't check the year. If this isn't this year's Invitational B, I am sorry.

[smeag]

no worries guys, you are doing the right test 2010 invitational B. And can nsguy (wherever you are) please help me on dividing bases? and showing me examples on finding square roots?

[DentonKnight]

Amazingly enough, nsguy is not the only one on this forum who knows how to divide bases.
Work long division as you normally would.
4 goes into 1 0 times, so carry the 1 into the next column (it becomes a five because this is base five). Then you have 8 in the fives column. 4 goes into 8 2 times, with no remainder. So write 2.
4 goes into 4 1 time with no remainder, so write 1.
Ans: 21 base 5
I hope this is clear.

[PokémonMaster]

I'm sorry, DentonKnight, it's just that he's normally the one who answers things.

[smeag]

sorry if any offense was taken DentonKnight. By the way how did you get your username?

[DentonKnight]