A Few Questions

[Englandude]

Can someone please explain to me how to do these :

The number of terms in the expansion of
[unparseable or potentially dangerous latex formula] is _____ The answer is 6.

I have no clue how to do the following questions:

[unparseable or potentially dangerous latex formula] The answer is 1/4

[unparseable or potentially dangerous latex formula] The answer is -1/4

[unparseable or potentially dangerous latex formula] The answer is 1/4

Forgot how to do the following:

Change .44 base 8 to a base 10 fraction.

Change .44 base 5 to a base 10 decimal.

That's all. I'm just trying to get as much as i can before regionals. Good luck to everyone! I wanna see 400s in numbersense!

Oh, one more thing...how do i make the pi symbol with latex?

[bradp]

sin75cos75 = A
2sin 75 cos 75 = 2A
sin(2*75) = 2A
sin 150 = 1/2 = 2A

A = 1/4

I remember taking the A test and staring at that question for like a minute after I finished everything else... and still not figuring it out. I guessed 1.. which was ingenious because obviously two numbers less than one could multiply together to be one! :\

[Michael T]

I remember taking the A test, getting it right, and you missing it. Considering we had like just reviewed our identities in precal on friday, it was funny.

[zefuri]

changing base you do 4/8+4/64

[Michael T]

If it's a repeating decimal, such as:

.444... base 7

then it equals (the repeating number)/(the base - 1)

(If anyone wants to Latex that for me in a nicer way, please do.)

The expansion problem you simply add the two exponents and then add 1, IIRC.

3 + 2 + 1 = 6.

The next two...I think that's just knowing what each term equals to, but stephen/brad might know some secret trick.

[zefuri]

basically a geometric series is:

sum=a/(1-r)

where r is the common ratio and a is the first number of the series.

[Michael T]

I feel stupid now. I thought it was different that a geo. sequence somehow...I dunno. I think strangely sometimes.

[zefuri]

for the first one you can clearly see that there are no terms that will cancel so just pretend its binomial expansiona nd you know its 6 terms

[stupidityismygam]