If a b c are in AP then prove that 1/bc 1/ca 1/ab are in AP
Q: If a b c are in AP then prove that 1/bc 1/ca 1/ab are in AP Proof: a,b,c are in AP \[2b=a+c \] Dividing this by abc both sides…
how to plot exp(t) in matlab
Question : How to plot exp(t) in matlab ? Solution : We shall write the Matlab program to plot exponential function in the interval [-10 10] y=@(t) exp(t) % exponential…
What is the value of Cos(75)?
Question : What is the value of Cos(75)? Solution : We shall write \[75^0=45^0+30^0 \] And apply Cos(A+B) formula \[Cos(A+B) =Cos(A)Cos(B)-Sin(A)Sin(B)\] Therefore \[Cos(75^0) = Cos(45^0+30^0) =Cos(45^0)Cos(30^0)-Sin(45^0)Sin(30^0) \] Now we shall…
What is the value of Cos(15)?
Question: What is the value of Cos(15)? Solution : We shall write \[15^0=45^0-30^0 \] And apply Cos(A-B) formula \[Cos(A-B) =Cos(A)Cos(B)+Sin(A)Sin(B)\] Therefore \[Cos(15^0) = Cos(45^0-30^0) =Cos(45^0)Cos(30^0)+Sin(45^0)Sin(30^0) \] Now we shall substitute…
What is the value of Sin(75)?
Question: What is the value of Sin(75)? Solution : We shall write \[75^0=45^0+30^0 \] And apply Sin(A+B) formula \[Sin(A+B) =Sin(A)Cos(B)+Cos(A)Sin(A)\] Therefore \[Sin(75^0) = Sin(45^0+30^0) =Sin(45^0)Cos(30^0)+Cos(45^0)Sin(30^0) \] Now we shall substitute…
function f(x)=x^3 is a one one and onto or not ?
Question : function f(x)=x^3 is a one one and onto or not ? Solution :
absolute value function is one one and onto or not?
Question: absolute value function is one one and onto or not? Solution :
solved find eigen values of the matrix A=[3 0 0;0 02;0 2 0]
Question : Find eigen values of the matrix A=[3 0 0;0 02;0 2 0] Solution : Given 3 by 3 matrix \[A=\left(\begin{matrix}3&0&0\\0&0&2\\0&2&0\\\end{matrix}\right)\] It’s Eigen values are given by equation \[\left|\begin{matrix}3-\lambda&0&0\\0&-\lambda&2\\0&2&-\lambda\\\end{matrix}\right|=0\]…
Find Orthogonal trajectories to the family of straight lines y=k(x-1) where k in R
Question: Find Orthogonal trajectories to the family of straight lines y=k(x-1) where k in R Solution : Given family of straight lines \[y=k(x-1) \] (1) To obtain Orthogonal trajectories Step…
solved If B is a matrix such that B^2 =B and A=I-B then which of the following is correct?
Question : If B is a matrix such that B^2 =B and A=I-B then which of the following is correct? A^2=A A^2=I AB=0 BA=0 Solution : From the Given matrix…