Advanced Math

Question : What is Lami's theorem? Give Examples Solution : Lami’s theorem : Lami's theorem states that if three coplanar, concurrent and non-collinear forces of magnitudes F1 , F2 and…

Question 1: Solve the following Homogeneous Linear PDEs with constant Coefficients \[3\frac{\partial^2z}{\partial x^2}+2\frac{\partial^2z}{\partial x\partial y}-5\frac{\partial^2z}{\partial y^2}=0\] Solution : Given PDE\[3\frac{\partial^2z}{\partial x^2}+2\frac{\partial^2z}{\partial x\partial y}-5\frac{\partial^2z}{\partial y^2}=0 \]Is a Homogeneous Linear PDE with…

Question : solve pde r+10s+25t =0 Solution : Given PDEr+10s+25t =0we know the notation\[r=\frac{\partial^2z}{\partial x^2},\ s=\frac{\partial^2z}{\partial x\partial y}\ ,\ t=\frac{\partial^2z}{\partial y^2} \]Hence the given PDE becomes\[\frac{\partial^2z}{\partial x^2}+10\frac{\partial^2z}{\partial x\partial y}+25\frac{\partial^2z}{\partial y^2}=0\]Which…

Question : what is domain and range of 1/x? Answer : Domain : Domain is a set of values of x which is plugged into the function as an input…

Homework Question: prove that sin^2(theta)+cos^2(theta)=1 sin^2(x)+cos^2(x)=1 Answer : Let ABC be a right angled triangle with an internal angle θ and a,b, c be lengths of its sides. Then we have…

How to find Fourier series of sin^2 x cos x on the interval [-π,π] Question : Find the Fourier series of the function f(x)=sin^2 x cos x on the interval…

Question : Fourier series of sin 3x +5 cos 4x on the interval -pi to pi Solution : Given function \[f(x) =sin 3x +5 cos 4x \] is s a…