Recent content by zabumafu

Homework Statement Find the general solution of the given differential equation: y''+y'+4y=2sinht Homework Equations I believe sinht=(e^t-e^-t)/2 The Attempt at a Solution I tried to find the general equation if it were homogenous however I get the roots are r=[1+-...

Homework Statement t^2y''-4ty'+6y=0 t>0, y1(t)=t^2 find the 2nd solution using method of reduction of order.Homework Equations The Attempt at a Solution Let y=v(t)t^2 y'=2tv+v't^2 y''=2v+2tv'+v''t^2+2tv' put in back into eq and solving reduces to (checked it twice) t^4*v''=0 v''=0 Then I...

I was just asking trying to think ahead for part b but I think I might get it now. And no they switched it up for part be its not -2 its (4,2,1). I assume I'd do something like this (let vectors be v1,v2,v3 to save time) c1v1+c2v2+c3v3=0 and if it does =0, then that implied c1=c2=c3=0 and...

Okay that makes much more sense I think I have it: (1)4c1-3c2=6 (2)-2c1+c2=-4 (3)c1+2c2=7 ->(3) becomes c1=7-2C2 -> into (2) -2(7-2C2)+c2=-4 C2=2 C1=3 3(4,-2,1)+2(-3,1,2)=(6,-4,7) (12,-6,3)+(-6,2,4)=(6,-4,7)? And these are linearly dependent since c1 doesn't equal c2 correct? For part B. I...

So would I need to find the same c1,c2,c3 that satisfy it for both? The only equation my teacher gave us was V=c1v1+c2v2+CnVn

Homework Statement express the vector (6,-4,7) as a linear combination of (4,-2,1) and (-3,1,2) Homework Equations The Attempt at a Solution I am not quite sure how to go at it but this is what I am assuming to do: (C1*4,C2*-2,C3*1)=(6,-4,7) C1=3/2 C2=2 C3=7 and the...

Okay so for a) if f(a)=f(b) and g(a)=g(b) then f(a)+g(a)=f(b)+g(b) so a is a vector space? Then it'd be the same for b) since f(a)=f(b)=0 then g(a)=g(b)=0 so f(a)+g(a)=f(b)+g(b)=0 and therefore b is a vector space also? then for c it shouldn't be a vector space since f(a)=f(b)=-1 and if...

Homework Statement Let I = [a,b], a closed interval. With addition and scalar multiplication as defined for all real-valued continuous functions defined on I, determine which of the following sets of functions is a vector space. a) All continuous functions, f, such that f(a)=f(b) b)...

Perfect so dV=-λ/2πεo[ln(a)/(b)] =[-(4.0*10^-6)/2π(8.85*10^-12)]*ln(.048/.012) dV=-99725V dV=U/q U=K=-.598J which was correct

My book (the source I was using) says the potential due to a continuous line of charge is V=(λ/4∏εo)ln[(L+(L^2+ d^2)^.5)/d] however what confused me is if L is infinitely long and ignored, that turns the natural log portion of the function into +-d/d

I am not sure, I used the only equation involving lambda provided by our book. If your hinting that there is, I'd say by a factor of 1/2 but can't explain why other than by basing it off of other derived equations.

microCoulomb sorry should have noticed that before and just noticed I did nano, so let me rework that however I only have 1 more attempt at the problem so I want to make sure its right. I corrected it to .299J I believe using microCoulombs

Homework Statement A very small sphere with positive charge 6.00uC is released from rest at a point 1.20cm from a very long line of uniform linear charge density 4.00uC/m.What is the kinetic energy of the sphere when it is 4.80cm from the line of charge if the only force on it is the force...