Question

In: Advanced Math

if x1= Acos(wt+a) and x2+ Bcos(wt+b), how can I show that x1+x2=C cos (wt+c)? Furthermore how...

if x1= Acos(wt+a) and x2+ Bcos(wt+b), how can I show that x1+x2=C cos (wt+c)? Furthermore how can I express the value of C and c? (using complex exponentials)

Solutions

Expert Solution

Here is the answer.



Related Solutions

Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation. a) Show that...
Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation. a) Show that T is invertible. b)Find T inverse.
Linearize by hand y = a(x1)b(x2)c and determine the coefficients a, b and c, and the...
Linearize by hand y = a(x1)b(x2)c and determine the coefficients a, b and c, and the coefficient of determination using the data below. x1 x2 y 1 1 3.48 1 2 5.87 2 3 27.35 3 2 43.75 4 5 134.92 6 8 377.38
Is the following map linear? a) F(x1,x2,x3)=(0,0) b) L:R2→R2 defined by L(x1,x2)=(3x1−2x2,x2) c) f:R→R defined by...
Is the following map linear? a) F(x1,x2,x3)=(0,0) b) L:R2→R2 defined by L(x1,x2)=(3x1−2x2,x2) c) f:R→R defined by f(x)=2x
For the given function f(x) = cos(x), let x0 = 0, x1 = 0.25, and x2...
For the given function f(x) = cos(x), let x0 = 0, x1 = 0.25, and x2 = 0.5. Construct interpolation polynomials of degree at most one and at most two to approximate f(0.15)
1/Laura's preferences over commodities x1 and x2 can be represented by U(x1,x2)=min{3x1, x2}. She maximizes her...
1/Laura's preferences over commodities x1 and x2 can be represented by U(x1,x2)=min{3x1, x2}. She maximizes her utility subject to her budget constraint. Suppose there is an increase in p1.   There is an income effect but not a substitution effect of this price change. There are both income and substitution effects of this price change. There is a substitution effect but not an income effect of this price change. It is unclear whether the consumer will buy more or less x1...
In a system A-B-C, a ternary alloy of composition 30wt% B and 30 wt % C...
In a system A-B-C, a ternary alloy of composition 30wt% B and 30 wt % C consists at a particular temperature of three phases of equilibrium compositions as follows: Liquid phase: 50% A, 40% B, 10% C Alpha solid solution: 85% A, 10% B, 5% C Beta Solid solution:10% A, 20% B, 70% C (a) Calculate the proportions by weight of liquid, Alpha, and Beta present in this alloy. (b) For the same temperature, deduce the composition of the alloy...
Show linear dependence or independence. Show all steps algebraically. a. let v1= < x1, x2, ......
Show linear dependence or independence. Show all steps algebraically. a. let v1= < x1, x2, ... , xn > and v2 = < y1, y2, ... , yn > be vectors in R^n with v1 not equal to 0. Prove that v1 and v2 are linearly dependent if and only if v1 is a non-zero multiple of v2. b. Suppose v1, v2, and v3, are linearly independent vectors in a vector space V. Show that w1, w2, w3, are linearly...
A continuous signal contains the following two components: x1(t) = 3 cos 20πt x2(t) = 3...
A continuous signal contains the following two components: x1(t) = 3 cos 20πt x2(t) = 3 cos 50πt (a) Find the minimum required sampling rate to avoid aliasing. (b) Draw the discrete time signals obtained after sampling, when sampled with Fs = 100 Hz. Explain the disadvantage(s), if any, of sampling beyond the Nyquist rate. (c) Assume the sampling rate is Fs= 40 Hz, which components are exposed to aliasing effects? Support your answer by showing “Nyquist intervals” and the...
   3. (i) Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf...
   3. (i) Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf                    f(x1, x2) = 4x1(1-x2) ,     0<x1<1 0<x2<1                                       0,                  otherwise (ii) For the same joint pdf, calculate E(X1X2) and E(X1 + X2) (iii) Calculate Var(X1X2)
Let x0< x1< x2. Show that there is a unique polynomial P(x) of degree at most...
Let x0< x1< x2. Show that there is a unique polynomial P(x) of degree at most 3 such that P(xj) =f(xj) j= 0,1,2, and P′(x1) =f′(x1) Give an explicit formula for P(x). maybe this is a Hint using the Hermit Polynomial: P(x) = a0 +a1(x-x0)+a2(x-x0)^2+a3(x-x0)^2(x-x1)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT