Use cylindrical coordinates to evaluate the triple integral □ لاا √² + y²dV, where E is the solid bounded by the circular paraboloid z = 9 -9 (x² + y²) and the xy-plane.

Q: For what values of x does the graph of f have a horizontal tangent? (Use n as your integer…

A: First of all we have to find the derivate of the given function then for the horizontal tangent we…

Q: The indicated function y(x) is a solution of the associated homogeneous equation. Use the method of…

A: Please see the below picture for detailed solution.

Q: Find a basis {p (x), q (x)} for the vector space {f(x) = P3[x] | ƒ' (−1) = ƒ (1)} where P3[x] is the…

A: We have to find p(x) and q(x).

Q: 3. Find the area of the region bounded by the curves y = x² and y = cos(x). Give your answer correct…

A: The region bounded by the curves y=x2 and y=cos x

Q: 2. Determine the parent function and equation of the transformed function of the graph shown below.…

A: Let's find function equation.

Q: Find the first four nonzero terms in a power series expansion of the solution to the given initial…

A: Let's solve power series.

Q: Find the general solution of the differential equation. y (4) - y = 8t+cost. NOTE: Use C₁, C2, C3,…

A: We need to solve D.E.

Q: Find the maximum and minimum values of the function f(x, y, z) = 3x - y - 3z subject to the…

A: The given function is;  f(x,y,z)=3x-y-3z Constraints x2+2z2=144 and x+y-z=3.

Q: 3. An air ambulance is travelling from Barrie to Toronto. Toronto is located 90 km [S5°E] of Barrie.…

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Q: dy 2x = (3y + x)- dx

A: Given, 2x=(3y+x)dydxdydx=2x3y+xPut y=vxDifferentiate…

Q: 2 Solve the following ODES by Inverse Operator method. 2X (D²³ +1) y = 3 + x +52x Ans : y = C₁ 2²+…

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Q: Given the initial value problem 2 y y' + = 0, y(0) = 28, y'(0) = b, 5 25 Find the solution as a…

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

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Q: Determine whether the following statement is true or false. ƒ(x) − ƒ(1) x - 1 If lim- x→1 O True…

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Q: Evaluate the following expression. Your answer must be in exact form: for example, type pi/6 for DNE…

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Q: Consider the differential equation y" - 2y + 17y= 0; ex cos(4x), ex sin(4x), (-∞o, co). Verify that…

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Q: 5. Determine whether 3x 4 is a factor for each polynomial. Show all your work! 3 a. 6x 6x³ - 26x²…

A: Solution is given below:

Q: Determine the intervals on which the graph of y = f(x) is concave up or concave down, and find the…

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Q: Find the volume of the solid of revolution formed by revolving the region bounded by y = f(x) = 2x -…

A: Given problem:- Find the volume of the solid of revolution formed by revolving the region bounded by…

Q: Replace the Cartesian equation x² + y² equation. OA) r sin² 0 = 4 cos 0 B) r = 4 sin 0 Oc) r = 4 cos…

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Q: 74 +82-16-0

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Q: Hnd an equation in spherical coordinates for the rectangular equation x² + y² = z² = 0 - Do not…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = y In(x), (1,…

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Q: Find the points at which the following polar curve has a vertical or a horizontal tangent line. r =…

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Q: Get the:  1. Revenue function  2. Demand function

A: To find out the revenue function and demand function by using the marginal revenue function.

Q: Use spherical coordinates to evaluate the triple integral [[[ 2² + 3² + 2²dV, where E is the ball:…

A: We will first change it into spherical coordinate and then solve it.

Q: A circular plate with radius 7 m is submerged vertically in water as shown. Express the hydrostatic…

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Q: Determine whether the given set of functions is linearly independent on the interval (-00, 00). f(x)…

A: Follow the procedure given below.

Q: Solve the differential equation by variation of parameters. 1 4 + e* y" + 3y + 2y = Step 1 We are…

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Q: √√(y - 3), 1 ≤ y ≤9

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Q: I 44. Solve the initial value problem: EL y""-2y"-y' + 2y = 0; y(0) = 2, y'(0) = 3, y"(0) = 5.

A: The solution is given below

Q: Consider the following. U = 7i + 6j, v = 2i + 4j (a) Find the projection of u onto v. (b) Find the…

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Q: Find the general solution of the given differential equation. dy dx y(x) = = 3y 3y² 2 + Cx Give the…

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Q: 5. Find the 6th term of the recursive sequence defined by a₁ = 0, an+1=2a₁ +3.

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Q: 16 Q4- Solve the following system of ODE dx dt Eaux"> dy dt = y + 1 =x+1

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Q: Solve the following ODES by Undetermined Coeff 11 4X y - 16 y = 19.2 € + 60e, y(a) = Y(u) -4X HO 4X…

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Q: et a = = = ci + j and b = 4i + 20j. Find c so that a and b are orthogonal. i

A: Please refer to the image below

Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy - + y = f(x),…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: If $500 is invested at 4% interest, compounded annually, then after n years the investment is worth…

A: We need to find out that after 6 years what will be the invested amount become.

Q: Write an equation for the transformed logarithm shown below, that passes through (-2,0) and -5-4-3-2…

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Q: 2. Find the area of the region enclosed by the parabola y = 2x² and the line y = -x-1

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Q: Evaluate the indefinite integral using Substitution. (use C for the constant of integration.) 3 ln z…

A: Substitute ln(x)=t

Q: Find the area of the triangle with vertices P(1,5, −2), Q(0, 0, 0) and R(3, 5, 1). NOTE: Enter the…

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Q: Convert the point (x, y, z) = (4, 5, 1) to spherical coordinates. Give answers as positive values,…

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Q: Find the moment of mass from the x-axis for y = x ln(x) - 3x and y = 1 bounded by x = 3 and x = 6.…

A: Given : two curve y=x ln x - 3x and y=1            bounded by x=3 and x=6

Q: Find a general solution (implicit if necessary, explicit if possible) of the differential dy…

A: The given differential equation is dydx=2xy

Q: The graph shows a city's daily rate of use of electricity (in millions of kilowatts). Estimate the…

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Q: 7πT 6' expressions, or decimals to at least one decimal place. (x, y, z) = Convert the point (p, 0,…

A: x=ρ.sinϕ.cosθy=ρ.sinϕ.sinθz=ρ.cosϕ

Q: Solve the following ODES by Inverse Operator method An- (D²-2D +1) y = xe sinx Anse y tết xếể…

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