Find all complex numbers z satisfying z4 -81-81-√3 = 2 2 and give your answer as a comma-separated list of values in the form a+bi. Use the square root symbol '' where needed to give an exact value for your answer. Z = ??? i

Q: Hi there! I need help with math. Could you determine the length of the curve y = x3 1 + 6 2x between…

A: Given curve is ,               y=x36+12x (.) Length of a curve  y(x)  given by ,           L=…

Q: b) F(s) = |NIN S (s+2)²+4

A: Inverse Laplace transform

Q: Find the general antiderivative of f(x) = 3 4 Use C for the arbitrary constant.

A: Given: The given function is fx=3x. To find: We have to find the general antiderivative of the given…

Q: a. Solve the Gompertz equation dy dt =ry In K yini subject to the initial condition y(0) = yo. Hint:…

A:

Q: Prove that any point on the ellipsewhose foci are (-1, 0) and (7, 0) and eccentricity is…

A: The foci are (-1,0) and (7, 0).          The distance between the foci is 2 ae = 8 or ae= 4.…

Q: For a monopolist's product, the cost function is c = 0.004q+20q+8000 and the demand function is…

A: Given that: The cost function is c=0.004q3+20q+8000.  The demand function is p=450-6q. Profit…

Q: Apply the alternative form of the Gram-Schmidt orthonormalization process to find an orthonormal…

A:

Q: 3. If EEP'S FERY zooming in toward the point (1, 1) on f(x, y) = x(x² + y2)-3/2 sin(x²y) find f.(1,…

A:

Q: Let V be the vector space of differentiable functions f: [2, 5] → R. Select the correct statements…

A:

Q: etA = Compute the matrix exponential et for the matrix A = 6e^(-2t)-5€ 10e^(-2t)-1 -3e^(-2t)+3…

A: The given matrix A=-179-3016 We have to find etA.

Q: 2. (a) Find the function P(x) = a + b сos(x) + csin(x), which interpolates the data X y 0 0.5 1 2 5…

A:

Q: Let A and B be non-empty subsets of R such that a ≤ b for all a E A and b € B. Show that sup A ≤ inf…

A:

Q: dx Solve differential equations dt form and then diagonalize the resulting square matrix. dy dt =…

A:

Q: Find a function u(x, y) that is harmonic in R² and that equals f(0) = 4 sin(30) + 5 cos(60) o the…

A:

Q: 1. Solve for u(x, t): 1 3ux+4u=0, u(x, 0) = 1 + x² 11 7

A:

Q: Your friend throws two dice and tells you that one of the dice is a 4. What is the probability that…

A:

Q: Find the Laplace transform of the given function; b is a real constant. f(t) = cos(bt) Your answer…

A: Given: The given function is ft=cosbt, where b is a real constant. To find: We have to find the…

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = 8 x² + y² - 1

A:

Q: The velocity of a falling parachutist is given by ¹ (1 - e-( =)) V= gm C where g = 9.81 m/s². For a…

A: Given: The velocity of a falling parachutist is v=gmc1-e-cmt. Also, given that: g=9.81m/s2 c=15kg/s…

Q: Given the function f(x) = x2/³ (6-x)¹/3 Find the following: (a) the intervals where f(x) is…

A:

Q: 5 4? What is the determinant of the 6 x 6 matrix whose (i, j)-th entry is x₁y₁

A:

Q: c. Evaluate df dx txandaxx-1(2) df = = f , and then compare the results.

A: We are given that          f(x) = (x + 4)/(2 - 3x)   => df(x) /dx = {(2 - 3x)d(x + 4)/dx - (x +…

Q: V = y = x + 1, y = 0, x = 0, x = 5; Sketch the region. y 7 6 CI 5 H

A: To sketch the region,  y=x+1, y=0, x=0, x=5 .

Q: Find all critical points of h(t) = t³⁄4 − 2t¹4 and identify them as local maximum points, local…

A:

Q: Compute the eigenvalues and eigenvectors for the matrix 2-3 0 2-30 3 -5 1

A: The given matrix 2-302-303-51. We have to find the eigenvalues and eigenvectors of the matrix.

Q: Solve the system of linear equations using Gaussian elimination with back-substitution AND…

A: Given system of linear equation is ,              x+y+z+w=132x+3y-w=-1-3x+4y+z+2w=10x+2y-z+w=1 (.)…

Q: Find the power series centered at 0 for the function f(x) = ln(x2 + 1) / x2 .

A:

Q: (b) Find the adjacency matrix for one of the following directed graphs: (i) V1 e3 e2 803 V3 02 (ii)…

A: 5. (b) To Find: The adjacency matrix for the directed graphs.

Q: Calculate the area of the parallelogram with the given vertices. (0,0), (4,7), (11,11), (7,4) OA. 33…

A: I have explained everything with in the solution. Please go through that.

Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y=-x²-2x+8…

A:

Q: Two insects are crawling along different lines in three-space. At time t (in minutes), the first…

A:

Q: Describe the increasing, decreasing, and constant behavior of the function. (Enter your answers…

A:

Q: If the population of Quokkas on Rottnest Island in 2007 was estimated at 9700 and in 2017 it was…

A:

Q: (e1,e2, e3} be the standard basis of R³. If T: R³ R³ is a linear transformation such that 3 3 men T(…

A:

Q: Find all the local maxima, local minima, and saddle points of the function f(x,y) = x² + xy + 3x +…

A:

Q: 2. For which value of a is u(x, y) = x³ + xy² harmonic in R². ?

A: Given ,           u(x,y) = x3+αxy2 (.)  A real valued function  f(x,y) is harmonic in ℝ2  if ,…

Q: Consider strings of length n,n ≥ 1,over the set {a, b, c, d}. a. How many such strings contain at…

A: (a). Total strings that contains at least one pair of adjacent characters that are the same = Total…

Q: A street light is mounted at the top of a 15ft tall pole. A man 6ft tall walks away from the pole…

A:

Q: Find the particular antiderivative F(x) of f(x) = 2 that satisfies F(4) = 5.

A:

Q: 5) Solve the following system of ODES: x'+y'+x=-e-t x+2y'+2x+2y=0 and x(0) = -1 and y(0) = 1 HINT:…

A:

Q: Let A = {1, 2, 3} and B = {1, 3, 5}. Let A × B denote the Cartesian product of A and B. Indicate if…

A:

Q: f4(t) = costu(t-1) F4(s) = s² + 1 [s(cos 1") sin 1"]

A:

Q: Using the Chinese Remainder Theorem Solve the following: Here is the theorem first: Chinese…

A: Introduction: The Chinese Remainder Theorem (CRT) is a theorem in number theory that provides a way…

Q: Use the method of reduction of order to find a second solution to ty" (6t+3)y'+(9t+9)y= 0, t>0 Given…

A:

Q: 2. A soda can holds 354 cubic centimeters (12 ounces), and its top and bottom are twice the…

A: Sol:- Let's start by defining some variables: Let r be the radius of the can. Let h be the height of…

Q: a) Min x2dt Subject to constraint "x²dt = 1, x(0) = x(n) = 0

A:

Q: Find a real root of x³2x-1=0 which lies between 1 and 2 by using Bisection method correct to 2…

A:

Q: d. ajbj = [5 0 61(2) (16) 1:30-13 1 3 4 = 13 4 0 (18)

A: Given that  aij = 506313140    and   b = 241                 aijb = 506313140241…

Q: A farmer has 380 feet of fencing to construct a rectangular pen up against the straight side of a…

A: Let, the dimension of the rectangular pen is x ft by y ft.      Length (parallel to the barn) = x ft…

Q: Write a minimization problem with objective function f(x1, x2) = (x1+x2²)2. Find the solution. Draw…

A: