Recent content by chmate

Yes gneill, but still that doesn't solve the problem. Does this mean the book didn't give enough data?

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...

Can you explain me why f_y(x-y) = -1\cdot f'(x-y)? I don't get it. What is then f_x(x+y) = ?

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...

Yeah, I realized, after I posted this thread, that author added and substracted cosx in numerator. This was the trick. The problem is solved.

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...

mxm and nxn by the definition gives us 0. That doesn't change anything.

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, Is there any software which solves integrals STEP BY STEP? Thank you.

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.

Hi borek, can you show me an example? Thank you.