Evaluate f (x² + y² +2²) do over the portion of the cone z = √x² + y²,0 ≤z≤4.

Q: In rectangle, ABCD, point E lies halfway between sides AB and CD and halfway between sides AD and…

A: The area of triangle= 1/2 (base)*(height)  The area of rectangle= length*width .

Q: Let x and y be positive reals such that 3 3 x³² + y² + (x + y)³ +30xy 3 = 2000. Show x + y = 10.

A: x3+y3+x+y3+30xy=2000 We have to show x+y=10

Q: 3. Write the integral as the limit of a sum. 16 6 -Ź³ (5+46) (8) n-x n i=1 n B. Write lim3 5+: as a…

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Q: Decide whether the argument is valid or a fallacy, and give the form that applies. If she wears…

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Q: Write the equations in cylindrical coordinates. (a) 4x² + 4y² (b) 5z = 4x² 3x² + 3y² = 4y

A: The given equations are: (a) 5z=4x2+4y2 (b) 3x2+3y2=4y We have to convert the given equations into…

Q: x = -2x+3y + xy y = -x+y=2xy²

A: a) x'=-2x+3y+xyy'=-x+y-2xy2 To find the equilibrium point with Jacobian matrix . Further we need to…

Q: The characteristic polynomial of the matrix A= 1 4 -1 is (A-2)(X - 5)². -1 -1 4 a) Find the…

A: As per your request I have solved first subpart.

Q: Find the work done by the force field F(x, y) = y² 7 + (x²-4) j to move a particle along the portion…

A: We shall plot the curve over which we have to perform the integration.

Q: For the given matrix and eigenvalue, find an eigen vector corresponding to the eigenvalue. 11 -2] A…

A: In the given question 12 and 13 we have to find the eigen vector for given eigen value.

Q: Find the general solution of the differential equation y" - 3y + 2y = ln r.

A: 1) if the roots of the auxilary equation are real and distinct i.e., a&b then solutions are…

Q: Problem 8. Let CCR" be a closed convex set, and suppose that X₁,..., XK are on the boundary of C.…

A: Ans- To show that P_{\text{inner}} \subseteq P_{\text{outer}}, let x\in P_{\text{inner}} be an…

Q: Fill in the following table. (Enter vectors in the form ) 4xyi + 8yzj + 4zxk 10xyi + (5x² +10yz)j +…

A: 1)If F=fi+gj+hk then curl F=ijk∂∂x∂∂y∂∂zfgh2)If F=fi+gj+hk then div F=∂f∂x+∂g∂x+∂h∂x3)If curl F=0…

Q: f(x) = x² 50x² Enter the critical points in increasing order. (a) Use the derivative to find all…

A: To find the critical points of f(x) = x4- 50x2 we need to find the values of x for which the…

Q: Objective Function: x + 3y x ≥ -23y + 2 x ≤ 32y+ 2 x ≥ -5y + 15 What are the vertices of the…

A: The common region determined by all the constraints including non-negative constraints x,y>=0 of…

Q: 7.3 (#39) Find either F(s) or f(t), as indicated. L {tU(t-2)}

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Q: Laplace Transforms Use the integral definition (and show all integration steps) to find £{te-t}

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Q: 4. Let y = [ }]. and the origin. i) Compute the orthogonal projection of y onto the line through x =…

A: Let y=17. To Find: Orthogonal projection of y onto the line through x=-42 and origin.

Q: A projectile starts at time t = 0 at the point (6, 6, 15) with the initial velocity of (8, 10, 10).…

A: Equation of motion and initial conditions:

Q: 1. Solve the following second-order ordinary differential equation using fourth-order Runge-Kutta…

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Q: Suppose the presence of phosphates in certain waste products dumped into a lake promotes the growth…

A: The group measures the length across the algae growth and obtains the data in the table. x Length…

Q: Let f(x, y) = xsiny+ysinx + xy be given. In part (a)-(d), determine which partial derivatives the…

A: fx,y=xsiny+ysinx+xy

Q: 1. Let I(u) = F(u'(x), u(x), x) dx. Find the first variation and Euler-Lagrange equation for each…

A: According to Bartleby guidelines I have solved first part

Q: Current Attempt in Progress Use the table to estimate 12 ef X f (x) dx. x0369 12 f(x) 32 22 15 11 9…

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Q: (a) Find given that x² + y² - 9x + 10y = 2. dy dx dy NOTE: Differentiate both sides of the equation…

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Q: Find the equation of the plane that passes through (-2, 1, -1) is perpendicular to: x (t) = 3 - 2t…

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Q: Exercise 4.3 Prove equation (4.7), that H(A, B) = H(B) + H(A | B). What interpretation of the…

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Q: Definition 13.1.1 generalizes to linear PDEs with coefficients that are functions of x and y.…

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Q: Determine which of the following statements are true for all sets A, B, C, and D. f a double…

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Q: Suppose f: R → R is continuous and periodic with period P >0. That is, f(x+P) = f(x) for all XER.…

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Q: How many distinct partitions are there of {1, 2, 3, 4, 5}?

A: For the given set { 1,2,3,4,5} To find the total no of distinct partition of the set. Here, we…

Q: 9. For each of the following relations on N, determine which of the five properties are satisfied.…

A: We have to determine properties based on the given relations on ℕ

Q: Use the Simpson's Rule to approximate the value of the definite integral. 3 [/dr Simpson's Rule dx,…

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Q: Assume there is a certain population of fish in a pond whose growth is described by the logistic…

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Q: Find the prime factorization of each of the following numbers. a. 14^4 22^22.25^11 b. 400 50 4500^23…

A: According to the guidelines 'first 3 parts should be solved' I am answering first 3 parts (a), (b),…

Q: 7. For what value(s) of k will the function f(x) = kx² - 4x + k have no zeros?

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Q: Determine the interval of definition for the solution of the initial-value problem

A: Since the given problem is system of differential equation of order 1. we have to find the interval…

Q: Write the system of equations as an augmented matrix. 5r+ 3c = -1 4c = 6 -2y y -7y +4r +3c 14

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Q: a) b) Find the square roots of 10 (mod 31). Find the square roots of 134 (mod 217).

A: The given problem is to find the square roots of 10 (mod 31) and square roots of 134 (mod 217).  x =…

Q: → R is continuous and let ro E R. Prove that {x: f(x) = i

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Q: An investor has $60,000 to invest in a CD and a mutual fund. The CD yields 9% and the mutual fund…

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Q: The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the…

A: Below we have presented given data along with matrix form of given data.

Q: Task 4. (2p). Iterate towards a minimum value of the function A(x) using the Golden Section [-(42).…

A: To iterate (two iterations) towards a minimum value of the function Ax using the Golden Section…

Q: Save Determine the direction in which f = x²y√z has maximum rate of increase from P = (8,5,3).…

A: The given function is f=x2yz. Consider, f=x2yz                   .........1 On differentiating…

Q: Please explain why  If V� is a vector space and u� and v� are vectors in V�, then according to the…

A: V is a vector space and u and v are vectors in V.

Q: (4) Show that L[u(v — 2)](s) = −²³. -38 +386

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Q: Let G-D6 be the dihedral group of order 12, H be the subgroup of G generated by R120 rotation of…

A: Given ,              G= D6 D6 =  e, R60 , R120 , R180 , R240 , R300 , L , R60L , R120L , R180L ,…

Q: f(y) - f(z) = [²√ 1 (² + 1 dt = So f(z+t(y-2)) dt = ₁ Df (z+t(y-2)) dt (y-2).

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Q: A tank is leaking at an increasing rate as indicated by the data below. Use the table to answer the…

A: (a) Find the upper limit estimate for the amount of material leaked after 4 hours.  (b) find the…

Q: (2) Show that L[r²e²](s) = (s-1)³ ·

A: Laplace transform of f(x) is defined as below.       L{f(x)} = 0∫∞ e-sx.f(x)dx

Q: 7. Determine whether the vector field F(x, y) = (eª² co vative. If it is, find its potential…

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