Recent content by Supernova123

If 50kg of salt is mixed with 100 kg of water to form a 1500kg/m^3 solution, can I find the concentration of salt by subtracting the density of water which is 1000kg/m^3, or do I have to equate it like this: 50/((50+100)/1500)=500kg/m^3 ? Is the volume of salt negligible so that the volume of...

Ax=a(1,2,-3)+b(-4,-4,4)+c(6,2,-8) and V contains Ax. So wouldn't de1+fe2=(1,2,-3) or (-4,-4,4) or (6,2,-8)?

Homework Statement How would one determine if a vector space is a subspace of another one? I think that the basis vectors of the subspace should be able to be formed from a linear combination of the basis vectors of the vector space. However, that doesn't seem to be true for this question: Let...

I found my mistake. I wrongly assumed that (sinθ)^n=sin(nθ). Here's my solution: Σcos(2n-1)θ=Re(Σz2n-1) =Re(eiθ(1-e2Niθ)/(1-e2iθ)) =Re((1-e2Niθ)/(e-iθ-eiθ)) =Re((1-cos(2Nθ)-isin(2Nθ)/(-2isinθ)) =Re((i-icos(2Nθ)+sin(2Nθ)/(2sinθ)) =sin(2Nθ)/2sinθ

Okay, so I got: Σcos(2n-1)θ = ∑z2n-1 - Σsin(2n-1)θ =z(1-z2N)/(1-z2) - isinθ(1-(isinθ)2)/(1-(isinθ)2) =(z-z2N+1)/(1-z2) - (isinθ - isin(2N+1)θ)/(1 - isin2θ) =(z - izsin2θ - z2N+1 + iz2N+1sin2θ - isinθ + isin(2N+1)θ + iz2sinθ - iz2sin(2N+1)θ)/(1 - z2 - isin2θ + iz2sin2θ) =(cosθ + isinθ -...

Homework Statement By considering ∑z2n-1, where z=eiθ, show that Σcos(2n-1)θ=sin(2Nθ)/2sinθ. (Σ means summation from 1 to N)Homework Equations Just a guess. S=a(1-r^n)/(1-r) The Attempt at a Solution I was thinking this but it doesn't seem to work very well...

Oops, that was a typo sorry. What I meant was insulated spherical conductor.

So it says here that a conducting sphere of radius R with a charge Q uniformly distributed over its surface has V = Q/4πεR , using infinity as the reference point having zero potential,,V (∞) = 0. This gives C = Q/|ΔV| = Q/(Q/4πεR)=4πεR. Does ,V (∞) mean that you are taking the potential of a...

Alright, thanks for the input. I'm guessing that since sin(x)=cos(π/2-x), then: sin(x)=u, cos(π/2-x)=u arcsin(u)=x, arccos(u)=π/2-x So arcsin(u)+arccos(u)=x+π/2-x=π/2 Since they differ by a constant ,then arcsin(x/a)+c=-arccos(x/a) arcsin(x/a)+arccos(x/a)=c=π/2

I was wondering if there is a convenient way of checking if a substitution is correct or not. For example, I tried solving for ∫(1/(a^2-x^2)dx using two different substitutions, x=acosu and x=asinu giving different solutions. I got the integral as arcsin(x/a) using x=asinu and -arccos(x/a) using...

I think I understand now. Thanks for your time :)

I have trouble understanding the internal resistance experiment in which potential difference decreases as current increases because I thought they are usually directly proportional to each other. Is there any concept that I am missing? I know that the lost voltage will be greater as current...