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x is every number i think

first 3*6*27*4*81*2 is 314928 then divide that by 9 which is 34992 so y is 34992

check by substituting y as 34992. :)

sqrt(196)  is not 12! Try again!

The solutions are 20 and 40.

12y^4

nvm its correct. i inputed 10^(1/4) instead of just 1/4

Yep, another way you could solve it is by noting that:

tan(8pi/24) = ( tan(pi/24) + tan (7pi/24) )/ ( 1 - tan(pi/24)tan (7pi/24) )

Express the tan's in terms of sine and cosine, and use the sum to product identities :)

i got it thank you for the hint

Before you start begging like some crazy dude, think about the problem. 

Express those terms in the form of sine and cosine, then try to express these terms using half angle identities. If you're unable to do this, you may need to try easier problems and work your way up from there. :)

https://web2.0calc.com/questions/let-be-a-geometric-sequence-with-common-ratio-and

same question

There is definitely no relation to pascal's identity  in this problem. That identity would be used, when there is a sum rather than a product.

50 C 10 = (50 * 49 * 48 * 47 * 46 * 45 * 44 * 43 * 42 * 41)/(10!).

Multiplying 1/5 to 50 gives us:

(10 * 49 * 48 * 47 * 46 * 45 * 44 * 43 * 42 * 41)/(10 * 9 .... * 1). The 10 terms cancel out. 

(49 * 48 * 47 .... * 41)(9 * 8 *... * 1)  = 49 C 9.

That is correct, I don't know what's wrong?

thats incorrect sorry

$x = ((1662243000 - 1662210000) * 800 / (1662246000 - 1662210000))

[100 + n] / [60 + n] ==[260 + n] / [100 + n], solve for n

n== - 46 2/3 - this is the constant.

Your 3-term GP will look like this:

40/3,  160/3,  640/3

[160/3] / [40/3]==4 - this is the common ratio.

simplify      sqrt(10) / (10)^(1/4)

The above can be written as: 10^(1/2) / 10^(1/4)==10^(1/2 - 1/4) ==10^(1/4)

Thanks that was correct! I guess i probably could have just counted myself so no pressure!

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The answer is [200, 540).