Math Questions

adri · Last edited by adri on Fri Jul 24, 2009 11:29 am; edited 3 times in total

Well like Metalfreek, I'm starting a topic with some "math questions". Not all of them require a lot of work, some of them well you just have to see those to solve them...

Question 1:
Well because I had to use a table for this one, I created a webpage to display the table properly. Smile

--> Link

Question is simple, what's the number that should replace the Questionmark.
Skills needed: + - * /

Question 2:
http://www.frihost.com/forums/vt-108646.html#905508

Question 3:
http://www.frihost.com/forums/vt-108646.html#905707

PS: Also check this topic: http://www.frihost.com/forums/vt-106519.html, some nice and tricky questions there too...

Adri

metalfreek

Is 5 the answer?

fx-trading-education

answer is 7 because (8 + 13) / 3 = 7

adri

fx-trading-education got it right, you had to add up the first to numbers and divide them by the third number and then you get the fourth number.

adri

Question 2:

They asked the baker, Mr. Wis, how many breads he had sold on monday. The baker answered:

My first customer bought half of the stock + half a bread. My Second customer, bought half of what was left + half a bread. The third customer asked for half of the stock that was still available + half a bread to feed the ducks. The last Customer, Mr Salomon, wanted to buy a bread, but there were no more breads.

Mr Bread didn't sold any half breads. Can you tell me how many breads he sold?

Adri

Hogwarts

Pretty shonky baker if he only bakes 7 loaves o_o

adri

Question 3:

Prove that:

sin(a+b)*sin(a-b)=cos²b-cos²a
cos3a = 4cos³a-3cosa

*Those two have nothing to do with eachother, they are two seperate things. Smile

Adri

_AVG_ · Last edited by _AVG_ on Sat Jul 25, 2009 9:42 am; edited 1 time in total

The first one:

TO PROVE: sin(a+b)*sin(a-b)=cos^2b-cos^2a

sin(a+b)*sin(a-b)=(sinacosb+sinbcosa)(sinacosb-sinbcosa)
=sin^2acos^2b-sinasinbcosacosb+sinasinbcosacosb-sin^2bcos^2a
=cos^2b(1-cos^2a)-cos^2a(1-cos^2b)=cos^2b-cos^2acos^2b-cos^2a+cos^2acos^2b
=cos^2b-cos^2a

And the second one:

TO PROVE: cos3a = 4cos^3a-3cosa

cosa+isina=e^ia
cos3a+isin3a=e^3ia=(e^ia)^3=(cosa+isina)^3=cos^3a+3icos^2asina-3cosasin^2a-isin^3a
=cos^3a-3cosasin^2a+i(3cos^2asina-sin^3a)
Equating Real parts, cos3a=cos^3a-3cosasin^2a=cos^3a-3cosa(1-cos^2a)=cos^3a-3cosa+3cos^a
=4cos^3a-3cosa

metalfreek

Knowledge=$$$ (9 more players needed!)
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