QUESTION 8 Let g(x, y, z)=x. Let S the solid bounded by the surfaces x = 3²+3² and x = 6. SSSx.av. g Using cylindrical coordinates I can be rewritten as iterated integral as "S'h(0. r. x) dx dr de where Consider the integral /= b= c= e = (= h(0,r.x) = The exact value of 7 is

Q: 3. Consider the problem of finding the point (s) on the plane 2x - 2y-z = 36 closest to the origin.…

A: The point is on the plane 2x-2y-z=36

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A: In this question,  we solve given homogeneous system by elimination method.

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Q: A pool of 9 semifinalists for a job consists of 7 men and 2 women. Because all are considered…

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Q: Use the Washer Method to find the volume of the solid obtained by rotating the region bounded by y =…

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Q: 44 If x = a[cost +-log tan² t dy T and y = a sint, then find at t= - dx 4

A: x=acost+12logtan2ty=asintt=π4

Q: Let A = {9k +7 ke Z} and B = {3j+1 je Z}. Show that AC B. :

A: Let, x ∈ A    => x = 9k + 7 for some k ∈ Z.

Q: 5. Solve 2y" - 3y' - 2y = 0; y(0) = 1, y'(0) = -1.

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Q: Find two linearly independent solutions to the Cauchy-Euler equation ²y" - 3xy' + 3y = 0. (ii) Use…

A: Cauchy Euler's differential equations

Q: 2. Solve the Ordinary Differential Equations (ODE) by the Series method. (x²-x)y"-xy'+y=0

A: The given ordinary differential equation is x2-xy''-xy'+y=0. The objective is to calculate the…

Q: Let T = (tij) be the 7 × 7 matrix with (i, j)-entry tij given by 1,1 ≤ i ≤6, tij 0 for all other i,…

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Q: 3. |If x1 = [1,2,3,4]'; and x2 = [2,2,2,2]'; then what is y = x1¹*x2?

A: The given vectors are, x1=1,2,3,4' , and x2=2,2,2,2'. To Find: y=x1'*x2.

Q: Let P be the vector space of polynomials of order less or equal to n. Let sub-space of P such that…

A: This is a question of vector space.

Q: Question 30 Calculate the flow or line integral in the field F along the path C. F = y²i+ + zj + xk;…

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Q: a. Find y. dx ex b.y=x() c. y = (arctan (cos x)² + 1)

A: We have to find the derivative of given function.

Q: Find the work done by F over the curve in the direction of increasing t. F = ti + = j + k ; C: r(t)…

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Q: (i) Find a particular solution to the differential equation y" - 5y + 6y=c²t. (ii) Use the…

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Q: 1. Let = 27-33+ k, (a) Normalize ü (find the vector that points in the same direction as u, but has…

A: We are given the vector v→=2i-3j+k. Our aim is to normalize the vector v, to find a non-zero vector…

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Q: Problem II Consider a linear transformation L₁ R4 → R³ given below and a linear operator L₂ R³ R³…

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Q: Solve the given initial-value problem. X(t) = -1-2 × = (-¹-²)× + (2), ×(0) - (-²) X' X 3 4

A: X'=-1-234X+44, X0=-24

Q: The amount of money in the account after 2.5 years is ​ ​(Round to the nearest cent as​ needed.)…

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Q: Given the first order initial value problem, choose all correct answers dy 2x-3y y(-1)=2 dr 4y + 3x…

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A: The given problem is to find the Fourier series representation for the given periodic function…

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Q: our team is preparing a variety of pastries for a brunch event this weekend. You anticipate that…

A: 25%of the pastries will have 2 ounces of lemon filling.  Anticipate that each of the 400 guests will…

Q: Let p be a prime number. Prove that for any natural number n we have   | GL (n, Zp ) | = (pn -…

A: To Prove:  GLn,ℤp=pn-1pn-ppn-p2....pn-pn-1, where p is a prime.

Q: If the arithmetic progression whose common difference is nonzero, the sum of first 3n terms is equal…

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Q: Current Attempt in Progress If f (x) x² and g(x) = (x + 2) (x - 1)(x − 3), find all x for which f(x)…

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Q: 6.1 (3) Sketch the region enclosed by the given curves. Draw a typical approximating rectangle and…

A: Area bound by the curves

Q: Cn Let A = a₁ + a₂ + ... +an, B₂=b₁ + b₂ + b3 + ... + b₂ D₂ = C₁ +C₂2+...+c, and cn=a₁bn +…

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Q: Topic: Time Rates: Inverse trigonometric functions Suppose a car is traveling along a straight road…

A: The car is traveling in a straight line. The position of the car at time t can be measured using the…

Q: + = The region formed by y revolved around the y-axis. 3x - x³, y = 2, and y-axis is Find the…

A: A region R is given which is bounded by y=3x-x3 and y = 2. One has to determine the volume of the…

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Q: Calculate the circulation, SF. dr, in two ways, directly and using Stokes' Theorem. The vector field…

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Q: If Zhang has 3 times as many nickels as dimes and they have a combined value of 200 cents, how many…

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Q: What percent of people who donated Time also donated Money? What percent of people who donated Money…

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Q: Question 14 The augmented matrix is given for a system of equations. If the system is consistent,…

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Q: Determine the solution of the following differential equations. a) (D² +9) y = 81x² - 14cos3x b) (x…

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Q: Consider the following model: Max 6x + 2y S.T.: 1) x + 2y ≤ 60 2) 3x + 2y ≥ 70 3) y ≥ 5 4) x,y ≥ 0.…

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Q: (i) Find all eigenvalues of the matrix A. (ii) For each eigenvalue of A, find an associated…

A: The given matrix is 040100010. The objectives are to calculate the eigenvalue of the given matrix.…

Q: Find the gradient field F of the function f. f(x, y, z) = x4e9x +y6₂⁹ OF = (4 + 9x)x3e9xi + 6y5z9;…

A: Given function f  f(x,y,z) = x4e9x + y6z9  We need to find the gradient field F for the given…

Q: Use the Divergence Theorem to compute the flux of the field 1 5ye², 36xz, arctan (√)) x² + y² x² +…

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Q: Consider the differential equation y' = (y² + 3y + 2) ln(1 + y²). (a) Find the equilibria and…

A: The given differential equation is y'=y2+3y+2ln1+y2. To find the equilibria and determine their…

Q: 4. Solve dy d.x. 3y² - x² XU . Note: your solution may be left in implicit form.

A: Use variable separation method after y substitution to solve.

Q: 1) A particle moves in a velocity field (²xy + 10, x²) starting from point (0, 1) at t = 1. Where…

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Q: Question 2 a) Evaluate L{est}. b) Evaluate L {(t− 3)² + sin 7t + cos 8t}

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