Hm, I think I get it. (Vectors are fairly new to me so forgive me if I misunderstand and misuse these operations.)
knowing c = (v.w)/(w.w)
in my expansion I had
v.v - 2*(v.w)*c + (w.w)*c^2 >= 0
a vector times itself must be the magnitude of itself squared, right? So knowing that and plugging...
How come (v+cw).(v+cw) >=0? And after finding that value of c, I'm still not sure how that relates back to the original question. Sorry if I'm missing something obvious!
Homework Statement
Given vectors v and w, show that |v*w| =< |v|*|w|
Homework Equations
I know that |v| = sqrt((x1)^2+(x2)^2+...+(xn)^2)
and that |w| = sqrt((y1)^2+(y2)^2+...+(yn)^2)
also |v*w| = x1y1 + x2y2 + ... + xnyn
We were also told
Hint: use |v+c*w|^2
and (v+c*w)(v+c*w)...
Oh, sorry, for my last question I meant regarding the step where I integrated
integral of (-1-(dx/dy))dy
I integrated by "distributing" the dy and "cancelling" it out on the right side to get
int(-dy - dx)
-y - x
The step where I simplified (dx/dy)*dy to dx is what I was asking...
Oh, I think I know what to do then. I can flip my strategy around and solve for x instead:
(y^2 +1)*dx + (2xy + 1)*dy = 0
dividing by dy, distributing, and rearranging:
dx/dy + 2x/y = - 1/y^2 - (1/y^2)*dx/dy
therefore u(y) = e^(2*lny) = y^2
so
(d/dy)((y^2)*x) = -1 - dx/dy
integrating with...
that's interesting. We haven't done exact differentials as far as I know, but since I don't know what that means perhaps we have!
dy/dx + y/2x = (-1/(2xy))(dy/dx) -1/(2xy)
using u(x) = x^(1/2)
integral of ((d/dx)(y*x^(1/2))dx) = integral of (-1/(2*x^(1/2)*y)(dy/dx)(dx)) - integral of...
Homework Statement
Solve this differential equation:
(y^2 +1)*dx + (2xy + 1)*dy = 0
Homework Equations
dy/dx + P(x)*y = Q(x)
u(x) = e^(integral of P(x)dx)
(d/dx)(u(x)*y) = Q(x)*u(x)
y = (integral of (Q(x)*u(x)dx))/(u(x)
The Attempt at a Solution
I tried dividing by dx then...
I understand how to get the question right, but my friend posed an alternate method that is wrong and I was wondering why his method doesn't work.
Homework Statement
The coefficient of static friction is 0.75 between two blocks stacked on one another. The coefficient of kinetic friction...
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