Physicist in Training

I am part way done with this problem.... I don't know how to solve part e or part f. Any help or clues would be greatly appreciated. I have been trying to figure this out for a couple days now.

W={<x,y,z>, x+y+z=0} is a plane and T is the orthogonal projection on it.

a) Find the basis of {v1, v2} for this subspace.

I found the basis of W to be v1=<-1,1,0> and v2=<-1,0,1>

b) These basis vectors are basis vectors for what eigenvalue?

I found the eigenvalue to be zero after multiplying W with v1 and v2.

c) Show that n=<1,1,1> is orthogonal to {v1 ,v2}

I just took the dot product of n*v1 and n*v2 and both were zero

d) Show that n is orthogonal to all of W

My reasoning is that n is orthogonal to all of W because W is a linear combination of {v1 ,v2}

e) n is an eigenvector for T for what eigenvalue

??????

f) Using matrix with eigenvectors and one for eigenvalues, find the standard matrix of T.

??????

I am part way done with this problem.... I don't know how to solve part e or part f.

W={<x,y,z>, x+y+z=0} is a plane and T is the orthogonal projection on it.

a) Find the basis of {v1, v2} for this subspace.

I found the basis of W to be v1=<-1,1,0> and v2=<-1,0,1>

b) These basis vectors are basis vectors for what eigenvalue?

I found the eigenvalue to be zero after multiplying W with v1 and v2.

c) Show that n=<1,1,1> is orthogonal to {v1 ,v2}

I just took the dot product of n*v1 and n*v2 and both were zero

d) Show that n is orthogonal to all of W

My reasoning is that n is orthogonal to all of W because W is a linear combination of {v1 ,v2}

e) n is an eigenvector for T for what eigenvalue

??????

f) Using matrix with eigenvectors and one for eigenvalues, find the standard matrix of T.

??????

The problem is...

Initially, there are 60 squirrels and 60 raccoons in an ecosystem. r(t) = raccoon population in t years, s(t)= squirrel population in t years.

r'(t) = 5/2r(t)-s(t) and s'(t)= -1/4r(t) +5/2s(t)

solve for s(t) and r(t)

************************************

My answer....

r(t)= 90e^(2t) - 30e^(3t)

s(t)= 45e^(2t) +15e^(3t)

Now obviously if t=0 then they both equal 60 so it looks right, but I would like some confirmation.

The problem is...

Initially, there are 60 squirrels and raccoons in an ecosystem.

r(t)= raccoon population in t years

s(t)= squirrel population in t years

r'(t)= 5/2r(t) - s(t)

s'(t)= -1/4r(t) +5/2s(t)

solve for s(t) and r(t)...

I am completely lost. I have looked in many books and I can hardly find any information on this topic.

So I am reading my textbook and I come to the problem...

(x-L)/(x)=1/2

the answer is

x = 2L

I do not see how they came to that answer. Can you please explain it to me?

Like I asked. I went to the garage to give my mechanic the clip for the wipers when he said, "they just pulled the truck out and the power steering line blew." Do I have to pay for this repair?

Hello,

I am taking German this semester and I will be taking it next semester also. I would like to find a German pen pal so I can increase my understanding of the german language and not forget what I have learned. I have found websites that can connect people, but they look sketchy at best. Does anyone know any good websites to find a German pen pal?

Thanks.

I am trying to write a computerized test so I can study for my German class, but I don't know how to import the German language or use umlauts or other special characters. I googled this several different ways but I just don't know where to go for this info.

I was looking up offenders in an Ohio offender database and found that a guy that was charged with 151 felonies (most come from robberies).

Is there anyone that has had more?

I tried to google this and find the answer, but I cannot. My guess is that it comes from subscriptions to their service from media sources such as Fox News, CNN, MSNBC, etc.... Then I am sure that some of the revenue comes from advertisements on their site. However, I am not sure if politicians spend money on the polls eventhough I am sure that they are quite interested in the results.

I am not on here so people can do my homework so, I would appreciate if you didn't give me a full answer. I am stuck on the following problem and I do not know where to begin or what to do.

A cylinder is inscribed in a right circular cone of height 5 and radius (at the base) equal to 6. What are the dimensions of such a cylinder which has maximum volume?

2 asks for the critical points of

f(z)=(1+4z)2(4−z2)4

I came up with the derivative as being....

f'(x)=2(1+4z)(4)(4-z^2)^4 + (1+4z)^2*4(4-z^2)^3(-2z)

I then factored out (1+4z)(4-z^2)^3

I solved for these and got (-1/4) & (+/- 2)

After that I had gotten

(32-8z^2)+(8z+32z)

factored out the eight and then used the quadriatic formula to obtain..... (-1) and (4)

so that leaves me with the following answers which I believe are right, but they may not be.

2,-2,-(1/4),4,-1,0

The equation is

f(z) = (1+4z)^2 (4-z^2)^4

I have without simplifying at all......

f'(z) = 2(1+4z)(4)(4-z^2)^4 + (1+4z)^2*4(4-z^2)^3(-2z)

The chain rule has been driving me mad and I just want to make sure I have this correct before I continue with the algebra.

The question is the to differentiate with respect to y (or find y').

The question...

sin(6x+y^6) = 3y-x^5

My answer.... (I am sure that it is wrong)

dy/dx = (3-5x^4)/((6+6y^5)cos(6x+y^6))

ln(19x^4)-8y^5=x^4e^y

So far I have

(1/19x^4)-(40y^4)*(dy/dx)= ?

I am stumped as to what to do with the x^4e^y