/sci/ - Science & Math

I am very confused /sci/

Doing trigonometric substitutions in Calc II

<span class="math"> \int_{}^{}x^{3}\sqrt{4-x^{2}}dx [/spoiler]

I have it so that:
<span class="math"> x = 2sin(\Theta) dx = 2cos(\Theta) [/spoiler]

<span class="math"> \int_{}^{}(2sin\Theta)^{3}\sqrt{4(1-sin^{2}\Theta)} \cdot (2cos\Thetad\Theta d\Theta) [/spoiler]

do some identities:
<span class="math"> \int_{}^{}(2sin\Theta)^{3}\cdot 2cos\Theta \cdot (2cos\Thetad\Theta d\Theta) [/spoiler]

now as for where I'm stuck at: my book gives an example where X and dX are the same as above.

I don't understand where the d(theta)2cos(theta) comes from. I know its substitution, and I understand that from U-substitution, but I always had to account for the substitution by multiplying/dividing something outside the integral as well as inside (so that they cancel out) but the book doesn't, it just uses d(theta)2cos(theta) as if it magically appeared.

Any suggestions?

Calculate the change in internal energy of the following system: a balloon is cooled by removing 0.653 of heat. It shrinks on cooling, and the atmosphere does 389 of work on the balloon.
Calculate the change in internal energy of the following system: a 100.0- bar of gold is heated from 25 to 50 during which it absorbs 322 of heat. Assume the volume of the gold bar remains constant.
Calculate the change in internal energy of the following system: the surroundings do 1.43 of work compressing gas in a perfectly insulated cylinder.

/sci/ how do I solve AAA triangles? Usually I don't post homework related questions but I'm completely stumped. I know AAA triangles can't be solved, but supposedly they can. I'll post the full questions.

Estimate the distance: When the moon is at its zenith at point A on earth, it is observed to be at the horizon from point B. Points A and B are 6155 mi apart, and the radius of the earth is 3960 mi.

a. Find angle theta in degrees
b. estimate the distance from point A to the moon

I got part a. (~89 degrees) but I'm completely stumped on part B. I don't need a answer, I just need somewhere to start or a hint or something.

kind of an entomology question, but

do ants hivemind? and if they hivemind, do they have the power to literally revive each other?

my cats food was attacked by an ant colony, so I took it outside and started spraying it with kitchen cleaner (lolololol) figuring the bleach and other hazardous chemicals would kill the ants.

literally spent 10 minutes and 1 bottle spraying a 6in by 6in area trying to kill these things. The colony home was nearby so more ants were sent.

But they didn't go for the food, its like they literally touched the downed ants and within seconds the presumed dead ants were alive again, hiveminding their own business to the cat food again.

i also took an ant and put him in isolation, about 6ft away from the food where no other ants were. 1 ant came and saved him. i placed a piece of cat food there, and without even returning to the colony, and shitload of ants b-lined for the food.

what the fuck?

not troll, but I just had a question

the equation:
6/2(2+1)

isn't it really in the form 6/2*3? or c/b*a? (or c/a*b)

I get c/b*a from the fact that c/b=a and a*b=c

which means 48/2(9+3) really isn't possible, since it isn't in the form c/b*a, unless the 2 is distributed.

proof:
d/a(b+c) = 48/2(9+3)
b and c are given values and can collectively be known as "b" = 12, which makes the problem
c/a=b
48/12=4 (this is where it gets odd)
d/a(b+c)=48/2(9+3), and 48/2(12)= the form c/a*b
48/2(9+3) must be equal to c/b*a or c/a*b, since a*b=c, (a*b)/c must equal 1.

so since 48/2=24, 48/(2*12)=2, this doesn't work
c/b=a = 48/2=24, 48/(2*24)=1
which means a(b+c) must happen first in d/a(b+c), because of the form c/a=b, c/(a*b)=1 and (a*b)/c=1.

which proves distribution has precedent over mult/div, as some kind of super mult/div?

or did I already prove something that's been proven, and this has no relevance to the problem?
captcha: form sidina

Tell me this /sci/

When I combine Hydrogen and Carbon Monoxide to create water, am I to understand that the water was always there untill I brought the two gasses together to create it or was it conjured up out of the mixture of the two gasses?

wow this is going to cost them millions, and we have to wait even longer for the higgs boson.

http://www.guardian.co.uk/science/blog/2010/jun/09/large-hadron-collider-setback

pic unrelated