Show that the area A of a bounded region R of the surface z = f(x, y) is A = [[₂√¹ + S² + S² dx dy. where Q is the normal projection of R onto the xy plane.

Q: Solve the following differential equations Use variation of parameters. (D²+1) y sec ¹x

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Q: Absolute extrema on open and/or unbounded regions If possible, find the absolute maximum and minimum…

A: The given function is f(x,y)=x+3y, and the region is R=x,y|x<1,y<2. To Find: Maximum and…

Q: The Taylor series for f(x) = ln(sec(x)) at a = 0 is Σen(x)". n=0 Find the first few coefficients.…

A: Given fx = lnsecx            f'x = 1sexx sexxtanx                     = tanx         f''x = sec2x…

Q: Let S\index{1} be a circle passing through A(0,1) and B(-2,2) and S\index{2} be a circle of radius…

A: The equation of line AB is             y-2=2-1-2-0(x+2)                 =-12(x+2)or       x+2y-2=0…

Q: - Consider the ODE y() (t)- y(t) = 0. (a) What's one solution of this ODE? (b) ISuppose n is even.…

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Q: A company is planning to manufacture wheelchairs that are light, fast, and beautiful. The fixed…

A: (a) To find: The cost function. Given information: The fixed cost is $500,000 and variable cost is…

Q: Mary Stahley invested $3500 in a 48-month certificate of deposit (CD) that earned 7.5% annual simple…

A: Sol:- For the first part of the question: The simple interest formula is: I = P * r * t, where I is…

Q: singular value decomposition of a matrix -0.5 0.5 0.5 -0.5] [10 0.5 0.5 0.5 0.5 0 -0.5 -0.5 0.5 0.5…

A: with the help of svd we find matrix A  then we find its norm

Q: Using the product rule differentiate the following (show all working): a) y = 2x6 cos 5x b) y = e³x…

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Q: 2. Prove the following: For any simple graph G = (V. E), V can be partitioned into X, Y, Z such that…

A: The objective is to prove that for any simple graph G=V,E, EX,Y,Z≥2E3. A simple graph is a graph…

Q: For each of the following statements, if the statement is true, then give a proof, and if the…

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Q: Sketch the level curve z = k for the indicated values of k. N z = k = -4,-1,0, 1, 4

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Q: 3. There are three distinct cube roots of any nonzero real number c. (a) Set up an algebraic…

A: Sol:- (a) To find the three distinct cube roots of a nonzero real number c, we can set up the…

Q: Exercise 6 Find a (real) general solution. Show each step of your w y" + 3y + 2y = 12x²

A: We will find general solution.

Q: Find the following. (Round your answers to the nearest cent.) Finance Number of Charge Payments…

A: a)Unearned finance charge = (m * (m+1)) / (n * (n+1)) * F = (6 * (6+1)) / (12 * (12+1)) * $9.20 = (6…

Q: 1-3 2 Exercise 3.8.102: Compute eta where A = -2 12 e¹A [ -1-3 4

A: Given: A matrix A=1-32-212-1-34 To Find: Compute etA

Q: 7. Represent the following number in base 5 by sketching a 17 manipulative.

A: To represent the number 17 in base 5 using a manipulative, we can use a set of base 5 blocks. We'll…

Q: II. Using Transform of Integral 1 a.) F(s) = s² (S-1)²

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Q: 2. Let T: M2,2 (R) → R be defined by T(A) = det(A). Show that T is not a linear transformation.

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Q: www Find the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) 10 -4…

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Q: 3. f(x, y) = x² x+y + y²-1 -; (1, 1), (-1, 1).

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Q: Please have someone else check if this answer is right

A: The area of the washer is equal to the area of the outer disk minus the area of the inner disk.…

Q: Find an equation of the plane with the given characteristics. The plane contains the lines given by…

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Q: Suppose fertilizer A is 25-2-5 (amount of nitrogen, phosphoric acid and potash, respectively) and B…

A: Suppose x pound of fertilizer A and y pound of fertilizer B needs to be produced for the mixture.…

Q: Find the general solution of the given higher-order differential equation. y"" - 9y" + 15y' + 25y =…

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Q: You are in charge of purchases at the student-run used-book supply program at your college, and you…

A: Let, x1: represent number of Calculus books x2: represent number of History books x2: represent…

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y…

A: The given bounded by y=x2, y=0, x=6. We have to find the volume to the solid.

Q: DETAILS The terminal side of 8 lies on the given line in the specified quadrant. Find the exact…

A: Given Data. 35x + 12y = 0 in quadrant iv Ang relation of the farm Ax+ By = C has Slope (tan) of -A/B…

Q: Let H be a normal subgroup of G and K a subgroup of G that containsH. Prove that K is normal in G if…

A: Assume that H is a normal subgroup of G, and that K is a subgroup of G containing H. Then, we need…

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A: The given differential equation is y''-10y'+25y=0; y1=e5x We have to find second solution y2.

Q: Given the information below, determine we (0,0). w (s, t) = F(x (s, t), y(s), z (2 sint)) x (0,0) =…

A: The given function is ws, t=Fxs, t, ys, z2 sint. Also, we have  x0, 0=2, y0=4, z0=1, xs0, 0=-1, xt0,…

Q: The Laplace transform of y(t) = e-2t . t

A: By first shifting property of Laplace transform; L[e-at.f(t)]=F(s+a) where…

Q: Find an equation of the tangent line to the graph of the function at the given point, (a) use a…

A: Given: y=4x3+32   . . . (1) We have to find the equation of the tangent line to the graph of the…

Q: Vx(av) = Vaxv+a (Vxv) V (aT) = Va T+a(V.T) V(v⋅w) = (Vv). w + (Vw). v

A: ∇×αv=∇α×v+α(∇×v) Proof: ∇×αv=∑i∂∂x×αv=∑i∂∂x×αv…

Q: Let A is nonnegative irreducible matrix such that I -A is invertible and (I -A)-1 >= 0. Let λ1…

A: Given: A is nonnegative irreducible matrix such that I-A is invertible and I-A-1≥0.To prove: a)…

Q: Marcus and Sylvio are watching whales.  Marcus spots a whale N55°E from his position on the…

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Q: a. If T(vi) = v, for each i, show that T = ly.

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Q: (a) Tell about the convergence (conditionally/absolutely) of alternative series, which for an=1/n…

A: (a)   Alternative series ,for which an=1n                          ∑n=1∞(-1)nan≡ ∑n=1∞(-1)nn…

Q: Let B be the solid bounded by the surfaces z=3x^2+4y^2,   x^2+y^2=25, and the xy-plane (distances in…

A: Sol:- (a) The axis of rotation passes through the point (-3, 4, -4) and is perpendicular to the…

Q: The economic dimension (diameter and height) of a cylindrical overhead storage tank for a capacity…

A: The capacity of a cylindrical tank is 125,000 gallons. Firstly convert the capacity into ft3. It is…

Q: An indoor physical fitness room consists of a rectangular region with a semicircle on each end. The…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub…

Q: (f) y" - 4y' + 5y = 0, y(0) = 1, y'(0) = 0

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Q: Exercise 5H. Let X be a square matrix with real entries such that XTX = I. Argue that det(X) = +1.

A: Clearly X is orthogonal matrix . And the determinant of orthogonal matrix is 1,-1

Q: What are the dimensions of the garden with the largest area she can enclose? length for cedar side…

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Q: Simplify: -(108)/(63). Write your answer as an improper fraction.

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Q: The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then…

A: The Rate at which a body cools down is given by, dTdt=kST-Tm where k < 0 and Tm is a constant.…

Q: Twins graduate from college together and start their careers. Twin 1 invests $1500 at the end of…

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Q: T: R² R² rotates points (about the origin) radians (in the counterclockwise direction). rough 37

A: This problem is from linear algebra.Since e1=1,0,e2=0,1 is standard basis of R^2.

Q: The graph to the right shows a region of feasible solutions. Use this region to find and minimum…

A: Given: (a) z=6x+8y. We have to find the maximum value of the function in the feasible region.

Q: 4. Prove each of the following statements: a). If a,b,r € R and a² + b² ≤r², b). If S={(x,y) = R²…

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