Homework Statement
Dielectric medium inside capacitor consists of two types (check the pic). Capacitor's plates are connected to a source of constant tension U. Distance between the plates is d and their area is S. Find the electric charge of capacitor's plates.
Data given: U=500 V, d=2cm...
Homework Statement
If z=\frac{1}{x}[f(x-y)+g(x+y)], prove that \frac{\partial }{\partial x}(x^2\frac{\partial z}{\partial x})=x^2\frac{\partial^2 z}{\partial y^2}
Homework Equations
The Attempt at a Solution
I don't know how I'm supposed to find the partial derivative of z with respect to...
Homework Statement
Find \lim_{x \to 0}\frac{1-cosxcos2xcos3x}{1-cosx}
The Attempt at a Solution
Actually my book gives this continuation \lim_{x \to 0}\frac{1-cosx+cosx[1-cos2x+cos2x(1-cos3x)]}{1-cosx} but I don't know how author arrived there. Can anyone explain it to me?
Thank you
Homework Statement
Find the equation of plane which contains the line l:\left\{\begin{array}{l} x=t+2 \\y=2t-1\\z=3t+3 \end{array}\right., and makes the angle of \frac{2\pi}{3} with the plane \pi:x+3y-z+8=0.
The Attempt at a Solution
My attempt was to find the normal vector of plane which...
Hi tinytim,
I see now that the vectors are lineary dependent so 0 is the right answer.
I just want to have this question answered, are these operations I did legal?
Thank you
Hello Ray,
I did these operations: (-11\vec{m}\times\vec{n})\cdot(2\vec{m}+7\vec{n})=(-11\vec{m}\times\vec{n})\cdot2\vec{m}+(-11\vec{m}\times\vec{n})\cdot7\vec{n}=
=-22(\vec{m}\times\vec{n})\cdot\vec{m}-77(\vec{m}\times\vec{n})\cdot\vec{n}
So, according to definition, the vector...
Find (\vec{a}\times \vec{b})\cdot \vec{c} if \vec{a}=3\vec{m}+5\vec{n}, \vec{b}=\vec{m}-2\vec{n}, \vec{c}=2\vec{m}+7\vec{n}, |\vec{m}|=\frac{1}{2}, |\vec{n}|=3, \angle(\vec{m},\vec{n})=\frac{3\pi}{4}
This is my approach...
Homework Statement
Given \pi: \begin{cases}l_1: \frac{x-2}{4}\ = \frac{y-1}{2}\ = \frac{z+5}{-4} &\\l_2: \frac{x+4}{-2}\ = \frac{y+1}{0}\ = \frac{z}{1} & \end{cases} and the point M=(1,2,3) outside the plane. Find the projection of the line M_1P on plane \pi where P is the intersection point...
Hello!
I've solved my problem. I've been looking for this part of code:
srand(time(NULL));
random = arr[rand() % (sizeof(arr) / sizeof(arr[0]))];
Thank you.