Use polar coordinates to find the volume of the given solid. Below the paraboloid z = 50 – 2x² - 2y2 and above the xy-plane

Q: Question 2 Given the composite function f (g(k(t)) = 40 e1+20t Identify f(t), g(t) and k(t), given t...

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Q: What could be an integrating factor in solving the differential equation (1 + x²) + (1 – x)² y = xe¬...

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Q: Evaluate the two path limits: 2x + y? lim (x, y)¬(0, 0) æ + y² x=3y2 2.ar + y? =??? lim ??? (x, y)¬(...

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Q: Evaluate 1 dA x² + y² +1 where R is region in the first quadrant bounded by y = 0, y = x and x² + y²...

A: We have to evaluate ∬1x2+y2+1dA The region R is in the first quadrant bounded by y=0, y=x and x2+y2=...

Q: Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x= 22kx2k...

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Q: Determine all the roots of z +1 = 0

A: The given question is related with complex analysis. We have to determine all the roots of z4 + 1 = ...

Q: If F = (2x + y')i + (3y - 4x)j evaluate e F.dr around a triangle ABC in the xy-plane with A(0, 0), B...

A: Given  F→=2x+y2i+3y-4xj  we have to evaluate ∮F→.dr→ around  a triangle ABC in the xy-plane with A(0...

Q: Solve the right triangle below, round to the nearest tenth. 13. В A 19 28

A: Since you have posted multiple questions and we can answer one question. So, answered first question...

Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

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Q: Prove that fdr %3D dSxVf

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Q: 1- z Res z(z + 1). Iz=00 a) 0 b) 1 c) -1 d) 2 ||

A: Res( f, ∞) = - Res 1z2f1z, 0

Q: . y = (x + 1 )3 and y = 0 from x = - 2 to x =1.

A: To determine the area under the bounded curve is obtained by using double integration  The area betw...

Q: Problem 2 Find the QR-factorization of the matrix (1) 2 A = -2 -1 -1 121 2

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Q: Consider the following statements: 1. If A is a square matrix and Av = λv, for some nonzero number ...

A: 1.  If A is a square matrix and Av = λv, for some nonzero number λ, then v is an eigenvector of A.  ...

Q: 4) -10k +7

A: There are four type of polynomial on the basis of degree Zero degree polynomial The polynomial wi...

Q: is: The number of zeros of sin(-) is: `z-1

A: If y=f(z), then the variable z is called the input of the function, and y is called the output of th...

Q: OTfRTRisJifferentible onŢ and gey-y"for nENand yeR whatis (Jof)? OP T RiscifferentibleanI and fras t...

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Q: Which of the following differential equation has a solution of y = C,x³ + C2x ? 4y = 3x?y' – x³y" 3y...

A: To find which option is correct: We first find y' and y'' of  y = C1x3  +  C2 x and then we will che...

Q: Given system of linear equations: х+у—3z %3D 4 2х + 4у — 4z %3D 5 —х + у + 4z %3D —3

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Q: 6. 4. x=/3 2 R. 14. 4. 10 12 -2 -4 -6

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Q: 1 antd the nullspace of the 3 Construct a matrix system Ax = b, who has a particular solution x, mat...

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Q: Prove that for every natural number v ≥ 4 there exists a planar graph with v vertices which has all ...

A: Let v∈ℕ such that v≥4. Therefore there exists a natural number k such that v=4k+r, where 0≤r<4. T...

Q: Sketch the contour map of the function. You may use the graphing calculator. f (x,y) =x²+4y2

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Q: Use Newton's method to get the third approximation x, to the equation e* =x+3 tarting with x, = 2. D...

A: we have given the equation  ex=x+3   we have to use the newton's method to get the third approximati...

Q: Ex5) In an orthonormal system (O , 7,j),given the points A ,B ,C ,1 ,E and G I is the midpoint of [A...

A: Let A(a, b) and B(c, d) the the mid point of the line AB is obtained by using mid point formula a+c2...

Q: dx What is the particular solution to the differential equation + (v² +) dy = 0 and (1–xy)? xy)? y =...

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Q: a) find eigenvalue/eigenvalues and the corresponding eigenvector/eigenvectors of A. A = ( ) -1 -1 b)...

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Q: Select the best answer to each question. In your solution sheet, write the letter of the correct ans...

A: Answer: The given differential equation is                                          y4-4y3+4y2=3e2x+...

Q: 1-z Let C: z-il=9. Then ſ. dz = z(z+1) а) 0 b) 2ni с) —2лі d) 4ni e) — 4пі f) 2п

A: Multipart:    We have , gz = 1 - zzz + 1 gz = 1zz + 1 - zzz + 1 g(z) = 1zz + 1 - 1z + 1 We need to f...

Q: 2. Find the maximum and minimum of the function f(x,y) subject to the x² +2y² constraint x* +2x²y² +...

A: This is a problem of multi variable calculus.

Q: Determine the values of a, if any, for which all solutions of the differential equation y" – (2a – 1...

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Q: 4. 4 of 8 The graph shows data points representing the voltage of an electric curren v(t)-147 12 10-...

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Q: Construct a matrix system Ax = b, who has a particular solution x, = 1 and the nullspace of the {}} ...

A: This is a problem of linear transformation.

Q: a. f(x) x-2 x-7 b.f(x) = r2+1

A: (a) the given function is f(x)=1x-2 the function is continuous in interval [a,b] if it is continuous...

Q: Let M and N be 3 x 3 matrices with det(M) = 64 and det (N) = 81. Calculate det Also show whether NT ...

A: Let M and N be are 3×3 Matrices. We have given that ,  detM = 64  and  detN = 81 We need to find ,  ...

Q: 2. Determine if the following series are convergent or divergent. ( a) Σ n(ln1) 1 (Use the Integral ...

A: The given series converges.

Q: Evaluate the integral 1 ;dz. aD(0,1) Z(2z² + 3)²(7ª + 2)3

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Q: Given the differential equation x*dy – tan(y) dx – xsec²ydy + 2xydx = 0 then what is y(x + y) = tan(...

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Q: nd the flux of the vector v=⟨x,y,z⟩ along the surface of the right tetrahedron below.

A: Flux of the vector

Q: Consider the traffic flow diagram that follows, where a1, a2, a3, a4, b1, b2, b3, b4 are fixed posi-...

A: The complete solution is in given below  

Q: First, gently shade this area in on your curve, then calculate your z scores for X = 47 and for X = ...

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Q: What could be an integrating factor in solving the differential equation 2(х — у)dx + (3x? — 2х — бх...

A: We have given differential equation ,  2x - ydx + 3x2 - 2x - 6xydy = 0  This is of the form ,  Mdx +...

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1...

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Q: Find the QR-factorization of the matrix 1 0 2 2 1 1 A = 1 1 -2 -1 -1

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Q: Show that 1 -2 = R³. span 3 1

A: In R^3 if three vectors are linearly independent then they span the whole space R^3.

Q: If you are given a matrix M such that M = [p 4 5 q 5 4  r 0 5] , define the vector [p q r] th...

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Q: -3x1 + x2 + 12x3 = 50 6x1 – x2 – x3 = 3 6x1 + 9x2 + x3 = 40

A: Here we consider X1=x,  X2=y, X3=z (for Easier to solve) .  So, 

Q: Nesto hypermarket sells three brands (A, B, and C) of laptop computers. The monthly sales of the thr...

A: Given: The monthly sales of the three brands are: Brand A = 15 units; Brand B = 9 units and Brand C ...

Q: Maximize P= 2x, + 5x2 subject to x1 +2x2 s20 X, + 3x2 s 17 X1 + 4x2 s 16 X2 514 X1, X2 2 0 (A) The f...

A: Given that Maximize P=2x1+5x2subject to x1+2x2≤20                x1+3x2≤17                x1+4x2≤16 ...

Q: 4. Let S = {v1, V2, V3, V4, V5} where, 3 3 3 9 2 Ea 1 Sa 4 -3 -3 la 6 Find a basis for the space spa...

A: Here  v1 = 13-12,   v2 = 39-36, v3 = -121-2,  v4 = 21-20,v5 = 31-34The matrix is 13-12339211-1-31-2-...