Find the mass of a thin funnel in the shape of a cone z =√x² + y2, 1 ≤ z ≤ 3, if its density function is p(x, y, z) = 7 - z.

Q: Evaluate • [[ ₁ ² ² + ₁ x² + y² - z dS where S is the part of the cone z² = x² + y² that lies…

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Q: Questions 1-10 are concerned with the equation: +6+9y=9x 1. What is the order of the equation? a. 0…

A: 1) The order of the equation is 2 2) the degree of the equation is 1 , since highest term has power…

Q: Given the tables for g & m below, find the following: r g(r) m(r) 0 8 7 1 4 9 2 6 6 3 0 3 4 7 5 5…

A: Given: Table showing the values of gr and mr with respect to r.To find: Average rate of change of m…

Q: Calculate the flux of the vector field (³, ³), out of the annular region between the x² + y² = 9 and…

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Q: Find the equation of circle at the osculating sphere and osculating point (1, 2, 3) on the curve x =…

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Q: 7. It is known that for any function f(x) continuous on [0, 1] the Bernstein polynomials satisfy…

A: Given: Function f(x) is continuous.           maxx∈0,1f(x)-Bnx→0 , n→∞ is satisfied by Berstein…

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Q: An input-output analysis of a national economy has the following input-output tableau. Agriculture…

A: Given, An input-output analysis of a national economy has given in the table.   Agriculture…

Q: you have spotted a new pair of shoes that you really want to buy, but they are too expensive. The…

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Q: 9. Ŵ Let U = (1, 4, 3), V = (2,1,1), W = (1,0,0). What is the dimension of the span of {U, V, W} ?…

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Q: Find the intercepts of the graphs of each equation, test for symmetry about x- axis; y-axis & origin…

A: Note: “Since you have posted multiple questions, we will provide the solution  only to the first…

Q: With the set of basis vectors on R³ which is complemented by the following inner multiplication: u1…

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Q: Let H be a subgroup of a group C. Prove that Ha = H if and only if a ∈H. Also show that HH = H. More…

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Q: Perform the Gram-Schmidt process on the following sequence of vectors to find an orthonormal basis.…

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Q: 1. For the matrices A and B given: -3 5] 2 1 A = - 3 (a) Find the determinants of A and B

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Q: ∑ sin2(3n+2) / (2n2-3) ii. ∑ 1 / (n - 2π) iii. ∑ (n + 1) / (n3 + 2)

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Q: Solve the following partial differential equation with the given conditions: 8² u Ju Əx² Ət' u(-1,…

A: We are given the following partial differential equation with the given conditions.…

Q: 6. Let the n x n matrix A have real, distinct eigenvalues. Let (t, xo) be the solution of the…

A: Given: ϕt,x0 is the solution of the initial value problem x˙=Ax, x0=x0           A matrix of n×n has…

Q: pay less than $150$150 per square foot. The price of one 1,8001,800 square foot house is…

A: Question is based on simple geometric properties. Square is a figure with equal sides and all angkes…

Q: Calculate two iterations of Newton's Method to approximate a zero of the function using the given…

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Q: Find the general solution u (x, y) to the PDE = 0. Ux =

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Q: Let R denote the ring of integers modulo 48 and S denote the ideal (0, 16, 32). The order of the…

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Q: Prove that for all z € C, |z| = |2|.

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Q: Find the extremum of​ f(x,y) subject to the given​ constraint, and state whether it is a maximum or…

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Q: Consider the following matrix: 1 -6 -6 -6 -4 -2 -2 8 -60 0 12 -1 -3 -3 0 A = a) Find the distinct…

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Q: 5) Consider the following weighted graph: 11 6 H 5 6 A 10 E 9 14 8 3 16 4 B 3 12 C Use Kruskal's…

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Q: If I were to find the general Fourier Series expression for a function that is defined for example…

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Q: Let V be the group of vectors in the plane, with vector addition as the binary operation. Show that…

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Q: f(x) = 2 ai 02 1 Pi bi 3 Suppose you want to determine √25 on the in- terval [2,3] by using the…

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Q: For given data (xi,yi), i = 1, 2..., n, the solution of equations a ac Σlyi - (cx; + d)]² = 0 i=1 od…

A: Look inside the summation its like summing up square of distances of y to some fixed cx+d.Least…

Q: Use the vectorized Euler method with h=0.25 to find an approximation for the solution to the given…

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Q: Find the flux of the vector field = (y, z, x) across the part of the plane z = rectangle [0, 4] x…

A: A vector field F = (y, -z, x) is given. One has to find the flux or surface integral of the vector…

Q: 9.) The Inverse Laplace tra (A) In(s² - 2-3 (C) //e+ + 3/e³1

A: Inverse Laplace transform of the function

Q: Which of the following are true regarding the second derivative of the function f(x) = cos √xatx=2?…

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Q: Prove the statement using induction. (1+2+3+...+n} = 1³ +2³ +3³ +... n³ for every n € N.

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Q: Let -2 2 4 Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R³…

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Q: 7x/4 Evaluate the integral (sinx + cos x) dx using the fundamental -x/4 theorem of calculus. Discuss…

A: The given integral is, fx=∫-π/47π/4sinx+cosxdx. To Evaluate: The above integral. Also,  To Explain:…

Q: . ACB iff P(A) CP(B). . ACB if and only if AUB = B . (A x B) U (C x D) C (AUC) x (BUD)

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Q: Let F = . Use Stokes' Theorem to evaluate curlF. ds, where S S is the part of the paraboloid z = 9x²…

A: We Know that  The Stoke's theorem statement is  "The surface integral of the curl of a function over…

Q: 4. The following function f(x) = { 1²,1≤0 -²,0 ≤ ≤1 1-2x, 1≤x

A: Definition is given below.

Q: Using Reduction of Order: (D2-1)y = 2e2x

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Q: Intersections in England are often constructed as one-way "roundabouts," such as the one shown in…

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Q: Find the inverse Laplace transforms of the following functions: (10) (ii) (iii) 3s-2 (s-2)(s+1)² 3s…

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Q: Consider the matrix A. B. A = 2-2 0 0 11 1 021 002 Find the eigenvalues and eigenvectors of A. Why…

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Q: Divergence Theorem for more general regions Use the DivergenceTheorem to compute the net outward…

A: Divergence Theorem for more general regions

Q: Find all limit cycles of system x₁ =−x₂ + x₁(1-x² - x²) (2 - x² - x²), x₂ = X₁ + X₂(1 − x² − x²)(2 −…

A: As per the system we are given a 2d nonlinear dynamic system and we have to find : The limit cycles…

Q: Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two…

A: Newton's method: It is an iterative technique used to find the approximation of the root of a…

Q: 3. From results obtained in Secs. 21 and 23, determine where f'(z) exists and find its value when…

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Q: Let x, y, z be (non-zero) vectors and suppose w = 10y - 5x + 4z. 03 Using the calculation above,…

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Q: Compute an analytic expression, by hand, for the real and imaginary parts of the following complex…

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