J.branco

yeah sorry. mixed the expressions Just shoot me and rape my skull!

as you said before the potencial is a caracteristic of the source charge right? so being the distance double, the potencial of the second charge is a quarter of the first (2r)^2=4r. So supposing the potencial of the first is -1, the other's will be-1/4. Now -1/4 is bigger than -1 but |-1| is bigger than |-1/4| so i'm not sure. Would choose between D and E. Being the signals only a case of convention, I would choose D.

now referring to the rocket, the same apllies. Suppposing the second burn of fuel will give the rocket the same amount of energy, the variation of velocity will be smaller : (10000^2 - 0) ≠ (20000^2 - 10000^2) so the final velocity, in the frame of the buoy A won't be 20000mps. Now in the frame of buoy B, im not sure but since the inicial velocity is 0 i suppose the final will be 10000mps. ANy mistakes in what i've said?

the problem of the train: for someone outside the train the ball has kinetyc energy corresponde to 50J. equivalent to the 10mps, the it's travelling. When you throw it, you give it more 50 J. ΔE = 1/2m (vf^2-vi^2) ↔ 50 = 1/2 (vf^2-10^2) ↔ ↔ 100 =1/2 (vf^2) ↔ ↔ 200^(1/2) =vf so the final velocity of the ball wont be 20mps but 14,14mps aproximatly. in order to achieve the variation of speed of 10mps, you'd have to give it aditional energy

ok, assuming that it does damage your brain. compared to other drugs it will be at a really lesser extension right? can't the effect be insignificant if we think that it can be compensated by better "using" your brain cells? I mean, the more you use your brain, the smarter you will be right? so if you take a mentaly active life, won't the effect of smoking pass unnoticed?

ok, but my refering to the axis of symmetry of a fuction and its inverse.

i'm trying to prove that a funtion f(being f injective, and it's inverse are symmetric to the line y=x i can prove that the any segment defined by the points (fx,x) (x,fx) is perpendicular to that line, which also contains the midpoint of the segment. SO the line is the perpendicular bisector to any segment (fx,x)(x,fx) however i realy don't know where to go next? is this enough?whats is the definition of symmetry axe?

right, while the air does'nt reach the end of the straw, it will push the liquid, this being pushed up in the cup. when it reaches the end of the strw it will always bubble. Not sure but I think that the condition for a bubble to appear is that the gas inside the liquid is at a higher pression that the one at the surface. as this is the case, the air will always bubbles!

yeah, it's reallymuch easier that way;)

Imagine you're immerging a shpere, with a diameter d, in a liquid. What will be V(x), where: x is th height of the immerged part of the sphere V(x) the volume of the part that is immerged for x=d, V(x)=4/3πd^3 and for x=d/2, V(x)=4/6πd^3

sum for geometric progressions being u1*(1-r^n/1-r) and r= 5/6 for the first and r=35/36 for the second

as the probability of getting a 6 in a roll is 1/6, with 6rolls it's: 4 ∑ (5^p-1)/(6^p) = 1/6 + 5/36 + 25/216 + 125/1296 p=1 following the same idea, ifthe probability of getting a double 6 in a roll with 2dies is 1/36, in 36rolls it's: 36 ∑ (35^p-1)/(36^p) p=1 right? as they are geometric progressions, for the first one the probabilty is (1/6)*(1-(5/6)^4)/(1-5/6) =.5177 for the secnd the probability is (1/36)*(1-(35/36)^36)/(1-35/36)=.6373 so you get better chances with the double 6:D