simplify: i^1997 + i^1999 (in complete and detailed solution please thank you!)

Q: Use the Gauss-Seidel method to solve the following system. Compute the errors. [10 2 -1] [X1] X2 =…

A: Given: 102-1-3-62111x1x2x3=4125105 To find the solution using Gauss -seidel method.

Q: 041] Solve the following complex number problems. Solutions for compl asformation is reauired in…

A:

Q: Find the Laplace transform of 4 sin(3t)+2 cos(9t).

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: 1. Which of the following is the product of complex conjugates? a? - b? O a² + b²) O Va? + b² )(a² –…

A:

Q: Verify by direct substation that y = > Cn x", is a solution of this linear differential equation n=0…

A:

Q: If 2100 square centimeters of material is available to make a box with a square base and an open…

A:

Q: 1. Determine the amount of money invested today at 12% interest can provide the following…

A: Given that, We need P312,000 for 6 year, P227,000 for the next 6 year and P89,000 thereafter. Now…

Q: Let B be the surface with equation x = -1+ /y. (a) Provide a hand-drawn sketch of B. Label the…

A: We are given that B as the surface with equation x=-1+y2. For (a), Let us sketch the surface B. It…

Q: For the matrix A, find (if possible) a nonsingular matrix P such that P'AP is diagonal. (If not…

A:

Q: -2x jika x > 0 jika x <0 f(x) =

A:

Q: Solbing linet differential equartions X dy 24

A:

Q: Use a graphing calculator to determine the linear, quadratic, or exponential equation that best…

A: For Linear equation  y = ax + b Here a = slope and b = Y-intercept  By graphing calculator  a =…

Q: Find the Laplace transform of f(t) = sin(2t) cos(2t). 2 g2+4 g2–16 g2+16 2.

A:

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A:

Q: Use (5) in Section 8.4.

A: Given,         X'=0110X+sinhtcosh(t)

Q: Find the Laplace transform of f(t) = cos(2t) + 7 sin(2t). s+1 s2+4 _s+14 g2+14 s-14 s2+4 s+14 s2+4

A:

Q: @ Determine the directional derivative of F(x,y.z)= e*co5 ly) (1-2)² at the origen in thé directio…

A: This is a problem of vector calculus.

Q: Evaluate the following (Express all answer in Rectangular Form): a. cotlog(1 – 4i) i b. (2e) C. z2 +…

A:

Q: Find the value of x in the following figure. Assume that lines m and l are parallel. 25° (5x-54)° m…

A:

Q: Find a parameterization for the hyperbolic paraboloid z = z – y².

A:

Q: Consider the following differential equation: (2x + 3)?y"(x) – 3(2x + 3)y'(x) + 4y(x) = 8 ln(2x + 3)…

A:

Q: 4. The point H (-1,-6)is translated 2 units up. Find the coordinates of the resulting point, H? Type…

A: We want to find coordinates of point H'.

Q: Find the point S so that ray (PQ) and ray (RS) are each of the same vector where P = (2, 5), Q = (1,…

A: For two vectors to be equal, their magnitudes and directions must be the same. The formula to…

Q: ||r(t) x r"(t)|| Use the formula k(t) to find k(t). r(t) = 11 cos(t)i+ 11 sin(t)j + 6tk K(t):

A: Given :  r(t) = 11 cos(t)i + 11 sin(t)j + 6tk To find :  We have to find k(t),   where   k(t) =…

Q: 2. Answer and show the Solution in parametric vector form. a. x, + 3x2 - 3x3 = 7 c. x, + 2x;- 3x3 =…

A:

Q: The point G (-6, 4) is translated 2 units left. G'? What are the coordinates of the resulting point…

A: Given point G is (-6, 4)

Q: the outward FIax Through the surtace OE 25 니 3. 1)

A:

Q: Triangle A is mapped onto triangle -8 -6 -5 -३ -2 1. -2 Which of the following transformations is…

A: We want to find applied translation on triangle.

Q: The shaded region between the graphs of y = – 2x+ 20 and y = 3z- 15 is displayed below in 25 -6 + Ax…

A:

Q: 808 Find the initial value of the transfer function X(s) : s(s²+2s+101) 4 1 8

A:

Q: 4. Solve the systems of linear equation below 2a + b + 5c + d = 5 a + b – 3c + 4d = -1 3a + 6b – 2c…

A:

Q: Reading Question 5.2.2. Consider the map o : C* → C*, x + xt, where C* denotes the group (C -…

A: We have given function ϕ: x→x4 and ϕ: C*→C*, where C*=(C-{0}, ·) and four option. We need to choose…

Q: 5. Let C = {x ∈ Z|x ≡ 7( mod 9)} and D = {x ∈ Z|x ≡ 1( mod 3)}. (a) If C ⊆ D? Justify your…

A:

Q: Consider the polar curves C1 :r = 2 – cos 0 and C2 :r = 2 + 2 cos 0, 0 E [0, 27). (a) Show that both…

A: Given the curves C1:r=2-cosθ and C2:r=2+2cosθ, θ∈[0,2π). (a) The graph has symmetry with respect to…

Q: By using variation of parameters. what is a possible value for u for the differential equation y" +…

A:

Q: Determine the volume generated by rotating the region bounded by the curves given below about the…

A: Introduction: Apart from disc method and washer method, there is another method to determine the…

Q: f. f(t) = eat cos² b t.

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 7. Prove that the vector length is preserved by orthogonal matrix multiplication. That is , if x E "…

A:

Q: Prove that for a diagonalisable square matrix A, the determinant is the product of the eigenvalues…

A:

Q: Prove that a natural number (an-1an-2a1ao)10 is divisible by 9 if and only if the sum of the digits…

A:

Q: The point D (-4, -2) is rotated 180° counterclockwise around the origin. 7 What are the coordinates…

A: We want to rotate the given point D 180 degree counterclockwise.

Q: Obtain the X-value of vertex for the parabola defined by y = x2 +8x - 5

A:

Q: 9. Find at least the first four nonzero terms in a power series expansion about x = 0 for a general…

A:

Q: There are 100 students at a swim meet. Every 3rd finis in the race receives a medal. Every 5th…

A:

Q: Evaluate (x+y² + z?) dS, where S is the porti on of the paraboloid x=5+y² + =? contained within the…

A:

Q: Rectangular

A:

Q: 7. solve the following differential equation. (16y - xy) dx +x dy = 0

A: To solve the given differential equation.

Q: Determine the supremum of the following set with full justification, if it exists. = (-1)" (","). n…

A:

Q: Evaluate In(3 + j4)

A:

Q: .Use the De Moivre's Formula to show that if z = (cose + isine), then z" + ; ÷= 2cos (n8) and (금) 3…

A: