Solve the following using De Moivre's theorem, pascal triangle and binomial expansion. Show all your solution. a. sin' 0 and cos' e b. sin11 e and cos11 e C. sin12 e and cos12 e

Q: Let a * b = 2ab be defined on Z†. 1. Compute a * (b * c) 2. Compute (a * b) * c

A:

Q: 3. (a) 5e (b) 2e-21

A:

Q: Find the value of b if the complex number is 6 + 4j = 0

A:

Q: Solve each of the following by Laplace Transform: dy -- 4 – 5y = e-34 sin(4t) ; y (0) = 3, y' (0) = ...

A:

Q: 7. (Relations) Consider the set A = (1,2,3, 4, 5}, and a relation R defined by zRy + 2-y is an integ...

A: Note: Our guidelines we are supposed to answer only three subpart . Kindly repost other subpart as t...

Q: r+1 Q5. Graph the function y = by applying the first and second derivative tests. Also discuss the a...

A:

Q: Let B, D be the following two bases of R³: -1 B = D= a) Find the change of coordinates matrix Po-s f...

A: Solution is below.

Q: Eliminate all the arbitrary constants in the equation y = Ae2x + Be-6x + Ce4x

A:

Q: Show that f(x1, x2) = 2 - (x1 - 1)^2 - e^x2^2 is concave.

A: the given function is fx1,x2=2-x1-12-ex22 To find the function is concave we have to show all its se...

Q: 1 1 -3 1. Let A = 2 1 1 -1 -4 (a) Find row(A), col(A), and null(A). Find a basis for row(A), col(A),...

A: Given: A=11-30211-1-4 To find: 1 a) row(A), col(A) and null(A). Also find a basis for row(A), col(A)...

Q: Find the Inverse of Matrix (M).

A: We can compute inverse of matrix as follows

Q: 1. Use Fixed-Point Iteration Method and Newton Raphson Method to obtain a real root of 5a +1 0with r...

A:

Q: Show that if T is an involution, and S is any other transformation, then STS⁻¹ is an involution

A:

Q: What’s 20/5

A: Division value

Q: i (2 + i) z = (-1+ i)*

A:

Q: Suppose you are given equations of two overlapping circles as a. Determine how to find the points of...

A:

Q: 3n3 + 1 Consider the series Evaluate the the following limit. If it is infinite, type "infinity" or ...

A:

Q: Fluid flows into a tank with velocity y. There is a hole in the tank that causes the fluid to flow o...

A:

Q: Use Laplace transforms and the convolution theorem to solve the integral equation t y(t) + / (t – x)...

A:

Q: Let D be the region of the plane bounded by the curve C parameterized by f(t) = [3 cos(t) – cos(3t)]...

A: (a) D is the region of plane by the curve F(t)⇀=[3cost-cos3t]i⇀+sin3t-3sintj⇀,              (1) wher...

Q: State why the system of equations must have at least one solution. (Select all that apply.) 2x + 5y ...

A: We have to find the reasons of having at least one solution of the given system.

Q: Find the volume generated when the area bounded by the curve y2=x , the line x=4 and the x-axis is r...

A: Volume bounded by the curves, about y-axis.using Disk method

Q: evaluate (1 – 2i) – (-3+ 4i) O V13e-0.983i O 2V13e -0.983i A O 2 13e0.983i O 13/2e0.983i

A:

Q: Question 3 What is the equation of a parabola with a vertex at (4,8) and directrix at y 4 Ox+4)^2-16...

A:

Q: Find the simple interest. Assume the rate is an annual rate. Assume 360 days in a year. Principal Ra...

A:

Q: Use Euler's method to solve an ordinary differential equation = 4e0.8x – 0.5y from x= 0 to 4 with a ...

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.THAN...

Q: Q2: Let X and Y have a bivariate normal distribution with parameters µ = H2 = 1, 0} = 16, o = = 25 a...

A:

Q: Find the general solution of the following equations: 1) y" + 2y' + y = e¬x

A:

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the ar...

A:

Q: find two addi n<0<2n. 4,- |

A: In this question, the concept of the Polar Coordinate System is applied. Polar Coordinate System A p...

Q: A particular computing company finds that its weekly profit, in dollars, from the production and sal...

A: The weekly profit in dollars from the sales of x laptop computers is given by, Px=-0.006x3-0.3x2+600...

Q: find the volume under the surface z = f(x, y) over the rectangle R. 1. f(x,y)=4xy, R = [0,1] × [0,1]

A: We can solve this using double integral  

Q: Let XC Rn convex. Prove that x is an extreme point of X if and only if the set Cis convex, where X =...

A: Let X⊂ℝn be convex . To prove: x is an extreme point of X if and only if the set C is convex, where ...

Q: Let B, D be the following two bases of R°: 2 -1 B = 2 4 D = -3 -3 a) Find the change of coordinates ...

A: Given: B=222, -122, -320 and D=4-3-1, 0-3-4, 1-2-2  To find: Change of coordinate matrix PD←B from b...

Q: Find the differential equation of the family of parabolas with vertex at (1, 3) and axis parallel to...

A: To Find: The differential equation of the family of parabolas with vertices at (1, 3) and axis paral...

Q: Solve the congruence x6 ≡ 4mod(23) by using the primitive root a = 5. There are two solutions.

A:

Q: 2. Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inf...

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as...

Q: The Wigner-Weyl transform is given by W (r,p) dy V 2mh a) Proof that |W(2)* = / dp W(r.p).

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly rep...

Q: 1. Sketch the graph of a function f having the given characteristics. f(0) f'(x) > 0 for x 1 f"(x) ...

A:

Q: A horizontal cylindrical tank 4 ft in diameter and 10 ft long is full of water. Find the work done i...

A:

Q: Find the value of xg in 1 decimal places (positive value) using Secant Method (5th Iteration) f(x) =...

A:

Q: Prove that: ā x (B xẽ) = (ã č)b – (ā-B )ë |

A: We have to prove that a→×b→×c→=a→⋅c→b→−a→⋅b→c→. Let a→=a1i^+a2j^+a3k^ b→=b1i^+b2j^+b3k^ And c→=c1i^+...

Q: 1. Use Newton's method to approximate a solution of 4/r = 1+x in the interval [2, 3] to five decimal...

A: The complete solution is in given below  

Q: Determine the simple interest. The rate is an annual rate. Assume 360 days in a year. p= $470, r=7.7...

A:

Q: Express the given the iterated integral as an equivalent iterated integral in the new order dy dx dz...

A:

Q: a stereo is sold for rs 5600 cash or for rs 1800 cash down payment and ten equal monthly instalments...

A: cash price of the stereo = rs 5600 in the instalment plan  cash down payment = rs 1800 balance to be...

Q: Find the magnitude of (5 + 10i)(5 + 107) O 5/10SV10 O 5/55V3 O 10/5105 O 2/52V3

A:

Q: Which of the following is a factor of the polynomial. f (x) = 2x3 + x2 - 7x - 6

A:

Q: +2+n-3 Simpli fy, O -1+ i" O -1+i O1+i O in+1

A:

Q: Use the simple interest formula to determine the missing value. p= $943.66, r= 3.5%, t= ?, i = $198....

A: Given:p = $943.66,   r = 3.5%,   i = $198.17