3. Use the divergence of the vector field to compute F(x, y) = (tan-1 (2x)) ₁ + (xy-2 +²8²) J j 4 fo tan-¹ (2x) 4 where is the cardiod r = = 1+ sin 0. dy - (zy - 2+8²) dr,

Q: u²(x) = -x + = - = √(x - 1)' u(t)\dt, u (0) = 0,u (0) = 1. n

A:

Q: 3 "(x) = -x + x ²₁² = 1 √ ₁ ( x −t)³u(t)dt, u (0) = 0,u'(0) = 1.

A:

Q: Find the solution of the initial value problem 1 6y" - 7y + y = 0, y(0) = 6, y'(0); 6 Then determine…

A:

Q: The consumer price index (CPI) rose from 106.7 to 124.9, while Helen's net salary didn't change at…

A: Percentage relative change in a quantity is calculated as the the ratio of the change in quantity to…

Q: Find z = f(x, y) and use the total differential to approximate the quantity. (2.04)^2(1 + 8.8)^3 −…

A:

Q: Show that the set of all rational numbers is not complete

A:

Q: Consider the following statements: (i) There exists a function f: R → R which is discontinuous at…

A: Note : A function f is said to be continuous at a point c if lim f(x) x→c = f(c) .

Q: Find the Fourier series up to second harmonic from the following data X Y 0 0 T - 6 T - 3 2 T 2T ST…

A: Here consider θ=2πxT Here the last value is the mere repetition of the first .Therefore we omit that…

Q: QUESTION 5 Consider the following statements: (i) there is a function f: R → R that obtains every…

A:

Q: Using Simpson's Rule, with n = 10, approximate the integral below. Give the error of approximation π…

A:

Q: 3. For each of the functions below, decide whether the function is injective and surjective (i.e.,…

A: 3.  (d) Given f:P([5])×P([8])→P([5]×[8]) by f(S1, S2)=S1×S2   (e) Given…

Q: the local maximum and minimum values and saddle point(s) of the function. If you have…

A: According to guidelines we solve one question. Thanku

Q: d. positive c. zero a. negative b. cannot be determined with counterclockwise orientation is The Fd7…

A: Solution:-

Q: Real numbers with right ray topology is T2-space. Real numbers with right ray topology is T1-space.…

A: We have to choose the correct statement from the following ; (a) Real numbers with right ray…

Q: Expand f(z) = f(2)=...+ eBook 1 (z-1)(z-2) |z>2 Z 1 2 in a Laurent series valid for the indicated…

A:

Q: b. For each of the following, show that G is a group using the operation of S4, and determine how…

A:

Q: The figure shows a semicircle with radius 1, horizontal diameter PQ, and tangent lines at P and Q.…

A: As per the question we are given a circle of radius 1 and a horizontal line above the x-axis. Now we…

Q: QUESTION I 1.1 Thembi flies out from O.R. Tambo International Airport and needs to park her car at…

A: The various tariffs for parking at an airport are given in the table. 1.1.1 To Find: Cost of parking…

Q: u²(x) = -x + ² = f (x −1 ) 'u (1)dt, u (0) = 0,.u '(0) = 1.

A:

Q: Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = y - y' = -x…

A:

Q: The san sebastian brewery produces beer. The annual fixed coat is $150000, and the variable cost per…

A: The annual fixed coat is $150000, and the variable cost per barrel is $16.

Q: 3. Find the general solution of the differential equation y(4) - 4y" = t² + et.

A:

Q: 201 12 20 -1 0 3

A: We have to find the eigen values of the given Matrix.

Q: Consider the initial-value problem (x² − 1)y"+y' + y = ex y(1) = 1 y' (1) = -1 Does the Existence…

A:

Q: Evaluate the line integral f y(tan x + x sec² x) dx + x tanæ dy + dz once around the circle x² + y²…

A:

Q: What is the number of solutions to the congruence in Z125? x³ + x² + 3 = 0 (mod 125)

A: In the question we are given the following polynomial congruence equation : x3 + x2 + 3 ≡ 0 (mod…

Q: ANSWER ALL PARTS: Part A: Select the negation ofNo dogs are cats. a. All dogs are cats. b. Some…

A: Given: The statements, Part A: Select the negation of No dogs are cats. Part B: Select the negation…

Q: -B-Let f:( M, (Z).+-)-(M, (Z). +..) be a function define by such that g[]=[ EM₂(2). Is f is…

A:

Q: 1. Given data x 0 0.1 f(x) 1.0000 1.0000 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0003 1.0024 1.0102 1.0313…

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

Q: Determine all values of a for which the following set of polynomials is dependent or independent.…

A:

Q: Use partial fractions as an aid in obtaining the Maclaurin series for the given function. f(z) 71…

A:

Q: Show your solution: Given: y'' + 3xy' + 7y = 0 Question: The indicial equation for the given…

A:

Q: Determine the longest interval in which the given initial value problem is certain to have a unique…

A:

Q: 10. Find an equation of the plane that passes through the points (x, y, z) = (1, 2, −1), (x, y, z) =…

A:

Q: It costs c dollars each to manufacture and distribute backpacks. If the backpacks sell at x dollars…

A: The maximum profit is obtained by equating the profit function to zero.

Q: 8. (Fourier transformation and Dirac delta-function) Use Fourier transform to solve Poisson's…

A:

Q: Let U₁, U2, U3 – be the following subspaces of Rª U₁={a, b, c, d)=R4| ²b=c; a=d=0}; U2={(a, b, c,…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: (a) (b) W₁ = 4x1 + 5x2 W₂ = x1 - 8x2 W₁ = 5x1 - 7x2 W2 = = 6x1 + x2 W3 = 2x1 + 3x2

A: Given that (a)             w1 =4x1 + 5x2            w2 = x1 − 8x2   (b)            w1 = 5x1 − 7x2…

Q: Solve y" + 2y + 2y = e cos(x) with y(0) = y(0) = 1.

A: Given differential equation is y'' + 2y' + 2y = e-xcosx

Q: 2. Use the solution to the previous problem to solve the following initial value problem. Describe…

A:

Q: 36. Malik will spend a total of $30.00 before sales tax on x bags of marbles and y cars purchased at…

A:

Q: a. Let g be the piecewise linear function 0, g(t)=(t-5), 1. t = [0,5) t≤ [5, 10) t> 10. Express g…

A:

Q: 5. Find the two square roots of -5 + 6i.

A:

Q: 4. What is the most general unifier of the following pairs of wff's? If none exists, report "fail."…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: The image of the house in Figure 1 under the linear map R: R2 → R2 defined by R( R( ((1)) = (-²) is…

A: This is a question of Linear Transformation.

Q: 4. A thin homogeneous bar of thermal diffusivity 9, length 2 cms and its left end maintained at…

A: Given that a thin homogeneous bar of thermal diffusivity 9, length 2cms and its left end maintained…

Q: 1 Determine the measure of an angle whose measure is The angle measures (Simplify your answer.) of…

A:

Q: Show your solution: Given: y'' + 3xy' + 7y = 0 Question: For the given differential equation, x = 0…

A:

Q: 4. Given A= 83 and B = [9] what transformations are induced by A, B, AB, and BA. And what are the…

A:

Q: Instructions: Solve the following word problems. 1. Three couples have reserved seats for a concert.…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…