Let F = Z, [x] (x³ + 3x + 2) and α=x+ (x+3x+. (x³+3x+2) €F. Find a³.

Q: Let S be an oriented surface in R³ with a piecewise smooth closed boundary C whose orientation is…

A:

Q: Find the general solution of the DE: y"+y' + 2y = 0

A:

Q: 2.17. A load cell is calibrated in an environment at a temperature of 21°C and has the following…

A: Solution

Q: Solve the IVP -8 0] *-[× -16 dx dt x(t) = x, x(0) [8]

A:

Q: Find all the sylow 2 subgroup of D5 and show explicitly that they are conjugate

A: Given That : sylow2-subgroup of D5 To find : sylow2-subgroup of D5 and also show that they are…

Q: 3.45. The density (d) of a liquid is calculated by measuring its depth (c) in a calibrated…

A:

Q: Use Stoke's Theorem to evaluate · F · dĩ where F = (xz, xy, 3xz) where C is the boundary of the…

A: Using the Stoke's theorem we have to evaluate  ∮F.→dr→ where F→=xz,xy,3xz=xzi+xyj+3xzk such that the…

Q: (b) Let g(x, y) = 2 + 5x + 6xy + y². Find the degree 1 and degree 2 Taylor polynomials of g at…

A: (c.) Consider a function h that is a degree 2 polynomial in x and y, that is,…

Q: A. Construct a mathematical model for the following real-life situations 1. You have a summer job…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: max f(x, y, z) = -xz-x² + y-yz - y² - 3z² x,y,z ...5] Express V f(x, y, z) = 0 in the form Ax = b…

A:

Q: In the figure, there are infinitely many circles approaching the vertices of an equilateral…

A: Introduction: An equilateral triangle is a triangle which has sides of equal lengths. If we draw a…

Q: a. RM9338 b. RM9385 C.RM 9583 a EXAMPLE 2 2. Johan won an annuity that pays RM1000 every 3 months…

A:

Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

A: A be a matrix 5 * 5  We have to find the matrix A and also find the geometric description of A and…

Q: 2) ∞ και 2- N n=0 α 2-' Σ δ(t - n)dt 1-0 3) | 2-1 Σ δ( - nat n=-

A: A delta function is defined as δ(t-a)=0       for t≠a ∞    for t=a    . The fundamental property of…

Q: Determine the median of the following data set: 51, 29, 94, 77, 50, 77, 76, 10, 39

A:

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A:

Q: Suppose T:R4 R³ is the transformation given below. Determine whether I is one-to-one and/or onto. If…

A:

Q: If sin(x) = (in Quadrant 1), find 10 29 Give exact answers. sin ( )= $ (-²/2) = COS tan (²/²) =…

A: Now, given sinx=1029 Now, we have sinx2=±1-cosx2 Since, sinx=1029 is in first quadrant, therefore,…

Q: Let f: A → B and g:B → C then the condition (gof) (D) = f(g(D)) holds if a) DCB b) DCA c) DCC d)…

A: It is given that,  f : A→B and g : B→C. Then, the condition gof-1D = f-1g-1D holds if ; a) D⊂B b)…

Q: . Consider the partial differential equation u₁(x, t) = KUxx(x, t) + au(x, t), where a is a…

A:

Q: True or false: If A is an eigenvalue of an nxn matrix A, then the matrix A-XI is singular. Justify…

A: Defining Eigenvalues and Their Associated Eigenvectors λ is an eigenvalue of n × n matrix A, and v…

Q: Answer true or false. If f is not piecewise continuous on [0, ∞o>), then {f(t)} will not exist. O…

A: True or false

Q: a. RM9338 b. RM9385 c.RM 9583 a EXAMPLE 2 2. Johan won an annuity that pays RM1000 every 3 months…

A:

Q: Describe the graph of the equation. r = 17 sin 5ti + 17 cos 5t j O It is a circle of radius 5 in the…

A: Given parametric equation r(t)=17sin(5t)i+17cos(5t)j In cartesian expression r(t)=x(t)i+y(t)j

Q: Find the minimal polynomial satisfied by √2 + √5. over Q.

A: We have to find the minimal polynomial which satisfied by 2+5 over Q.

Q: 8. (e sin y + 3y) (3x - e" sin y)y' = 0

A:

Q: 1. Calculate the uncertainty of the result of: Show working. (10.1 ± 0.7) (22.6 ± 0.1) x (13.2 ±…

A: We have to calculate uncertainty. Firstly we solve without uncertainty,2ndly we solve uncertainty…

Q: What are the largest steps you take to solve -4y, y(0)=1 dt (without getting an overflow!) using the…

A: (a) Given the IVP dydt=-4y, y0=1. The solution to this equation is given by yt=e-4t---1. The Forward…

Q: Which of the following is Eulerian graph? a. Graph F b. Graph E c. Graph B d. Graph C O a Ob

A:

Q: Question 2: a) A manufacture of truck producer needs 4 truck tires (x) for 1 frame (y). The demand…

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: Example 1 The Maclaurin series expansion for e* is i=0 -x². Find the Padé approximation to e* of…

A:

Q: Assume a function such that Y = (2x410)/(6x² + 5x). Obtain the first derivative. O f'(X) = (8x³ -…

A:

Q: Correct. If y, and y₂ are linearly independent solutions of ty" + 4y + tey = 0 and if W(y₁, y₂)(1) =…

A:

Q: (b) A linear system has the form dy dt = Ay, y(0) = (1,0,0) and 23 = -1/2-2i. What is the largest…

A: Given: A linear system, dydt=Ay, y0=1,0,0T. The eigen values of A are λ1=-1, λ2=-12+2i and…

Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

A:

Q: Determine the y-coordinate of the centroid of the area under the sine curve shown. y Answer:y- Mi…

A:

Q: 43. If f is differentiable and is periodic with period T, show that f' is also periodic with period…

A: First we prove that f'(x) is periodic by definition of derivative. Then we give an example to prove…

Q: Problem 3 to have a unique solution: .. Find the largest interval where the following IVP is…

A: I have given the answer in the next step. Hope you understand that

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A:

Q: Answer true or false. F(s) = s²/(s² + 4) is not the Laplace transform of a function that is…

A:

Q: Q.3 If f(x)= √x-2 2 (x² − x + 1)² Find (a) The intervals on which f is increasing, (b) The intervals…

A: Note: Given function is fx=x-2x2-x+12 The domain is 2,∞ a. Differentiate both sides,…

Q: x² y² 9 Let C₁ be the ellipse + = 1 traced counterclockwise and C₂ be the paral- lelogram with…

A: Given, C1 : x29+y24=1 C2 : Parallelogram with vertices at (2,1), (1,-1), (-1,-1) and (0,1)C =…

Q: Answer true or false. The function f(t) = (et) 10 is of exponential order. O True O False

A: We have to determine that whether the function,  f(t) = et10 is of exponential order or not.

Q: Question - and V let Let "M" be an R-Module A, B are sub-Modules of M², then prove that the Quotient…

A: Given : M be an R-Module and A and B are submodules of M. To prove :  AA∩B ≅ A+BB

Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

A:

Q: A firm faces the following total revenue and total cost functions: TR = 150 - 0.20² and TC = 60+…

A:

Q: Which of the following is/are  non-Eulerian graph? a. Graphs B C D ONLY b. Graphs B C D E c.…

A:

Q: Show the final answers using EXACT values only, not calculator-based values. Show complete…

A:

Q: (10) Write a summary (unit frame, scale factors, gradient, arc length, volume element, and…

A:

Q: Find an integrating factor and solve the given equation. (15x + ²) + (5²+ 15y dy X dx

A: