What is zeros command MATLAB?
What is zeros command MATLAB? Answer : zeros command MATLAB : It is a command to return an array or a matrix with each entry zero. For Example: To print…
How to write Inheritance in python example ?
Question : How to write Inheritance in python example Answer : Base Class class Calculator: def Addition(self,a,b): return a+b def Subtraction(self,a,b): return a-b def Multiplication(self,a,b): return a*b def Division(self,a,b): return…
How to calculate algebraic and geometric multiplicity ?
Question : Calculate algebraic and geometric multiplicity of eigen values of the following matrix? \[\left(\begin{matrix}2&0&1&1\\1&2&5&-5\\0&0&3&0\\0&0&1&3\\\end{matrix}\right)\] Answer : Algebraic multiplicity of an eigen value :Algebraic multiplicity of an eigen value k…
What is general solution of ode cos(y)y’=x/(x^2+1)sin(y) ?
Question : What is general solution of ode cos(y)y'=x/(x^2+1)sin(y) ? Answer : Given ordinary differential equation \[cos\left(y\right)y^{'}=\frac{x}{x^2+1}sin(y)\]We can write this as\[\frac{d\left(\sin(y)\right)}{dx}=\frac{x}{x^2+1}\sin{\left(y\right)}\]Dividing by sin(y) \[\frac{1}{\sin{\left(y\right)}}\frac{d\left(\sin(y)\right)}{dx}=\frac{x}{x^2+1}\]\[=>\frac{1}{\sin{\left(y\right)}}d\left(\sin{\left(y\right)}\right)=\frac{x}{x^2+1}dx\]Integrating \[\log(\sin{\left(y\right)})=\log{\left(c\sqrt{x^2+1}\right)}\]where c is an arbitrary constant.\[=>\sin{\left(y\right)}=c\sqrt{x^2+1}\]\[=>\…
What is the value of 1/2df/dx+1/3df/dy+1/4df/dz ? If u=
Problem : What is the value of 1/2df/dx+1/3df/dy+1/4df/dz ? If u=f(2x-3y,3y-4z,4z-2x) Answer : If \[u=f\left(2x-3y,3y-4z,4z-2x\right)\]Substituting P=2x-3y, Q=3y-4z, R=4z-2xThen \[\frac{\partial u}{\partial x}=\frac{\partial f}{\partial P}\frac{\partial P}{\partial x}+\frac{\partial f}{\partial Q}\frac{\partial Q}{\partial x}+\frac{\partial f}{\partial…
What is the value of xdf/dx+ydf/dy+zdf/dz ? If u =
Question : If u=sin^(-1){(x+2y+3z)/(x^8+y^8+z^8)} then find the value of xdf/dx+ydf/dy+zdf/dz Solution : If \[u=sin^{-1}\left(\frac{x+2y+3z}{x^8+y^8+z^8}\right)\] then=>\[ sin{\left(u\right)}=\frac{x+2y+3z}{x^8+y^8+z^8}\]Differentiate with respect to x\[cos{\left(u\right)}\frac{\partial u}{\partial x}=\frac{\left(x^8+y^8+z^8\right).1-\left(x+2y+3z\right).\left(8x^7\right)}{\left(x^8+y^8+z^8\right)^2}……….(1)\]Similarly differentiating with respect to y and z \[cos{\left(u\right)}\frac{\partial…
What is the work done by the vector field F on the particle that moves along C? For each of the following
Homework Problem : Compute the work done by the vector field F on the particle that moves along C for each of the following F(x, y) = (xy) i +…
how do you Evaluate surface integral of a sphere ?
Example of evaluating surface integral of a sphere Question : Evaluate the surface integral ∬ 𝐹. 𝑛𝑑𝐴 𝑆 for 𝐹 = [𝑥 3 , 𝑦 3 , 𝑧 3 ]…
Find Laplacian of the following field
Question : Find Laplacian of the following field 𝑓 = 𝑒^2𝑥 𝑠𝑖𝑛(2𝑦) Solution : Laplacian of a scalar field\[f\ =\ e^{2x}\ sin\left(2y\right)\]is given by \[\nabla^2f=\frac{\partial^2f}{\partial x^2}+\frac{\partial^2f}{\partial y^2}\]differentiating it partially with…
Solved Find velocity and acceleration vectors of the satellite
Question : Find velocity and acceleration vectors of the satellite moving in an elliptical orbit given by varying position vector 𝑎𝑐𝑜𝑠(𝑡)𝑖̂+ 𝑏𝑠𝑖𝑛(𝑡)𝑗̂. Solution : Given that the motion of the…