Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 9(x² - a²) is revolved about x = 0 from y = 0 to y = 3a.

Q: find for y dy dx x sinx (x-1) (x²+1) Evaluate f(u² + 2u + 3)7 (u + 1)du

A: To find the derivative of a composite function and the integration by substitution method.

Q: Let vector field F=(xz,-y,z) and surface, S is a cylinder x² + y² = 4 for 3≤z≤0 with the outward…

A: According to Stoke's theorem If S is a smooth surface  bounded by a closed, smooth boundary curve C…

Q: Exercise 3. Let M = {1+ x,-1+x².2 + x³). Then M is a basis for a. P3 b. P₂ c. PA d. None of the…

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Q: III. Consider the parabola C: 2 - 4 = -(x - 2)² on the xz-plane. 2. Sketch the portion of the…

A: Given,  Parabola :C: z-4=-(x-2)2 on xz-plane We have to draw or sketch the portion of cylinder…

Q: Consider the following differential equation. dy =y6/7 dx Let f(x, y) = y6/7. Find the derivative of…

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Q: Q4- Solve the following differential equation: (1 + x²) dy + -(y- tan ¹(x)) dx = 0

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Q: Consider

A: We find the general solution by finding roots of equation.

Q: Q2:(a) In Euclidean metric space (R, 1. 1),if A = {y € R: y = 2 cos (2x); x € R} then fined the…

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Q: Find a plane containing the point (-4,4,2) and the line of intersection of the planes -3x + 8y + 2z…

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Q: Find the flux of the vector field F = [x,y,z] through the oriented surface S: z= x^2 + y^2, z <= 1…

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Q: Q3- Sketch the region of integration and evaluate the integral: In8 Iny ex+y dxdy

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Q: A food store surveyed 50 of its shoppers as to whether they had purchased bacon or steak during the…

A: Note: Hi! Thank you for the question, As per the honour code, we are allowed to answer three…

Q: Q5- Find the Maclaurin series generated by the following function: f(x) = sinh(x)

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Q: Using Laplace transform, solve the following simultaneous equations: y₁+3y1 - y2 u(t-1)et, Yo…

A: We solve given simultaneous equation by using Laplace transform.

Q: 9: Check Euler's Theorem for the Function

A: We checked Euler's theorem for function.

Q: dC₁ = -k₁C₁ + k₂C₂ dt dCB dt B = k₁C₁-k₂C₁ Solve this ODE-IVP system in Excel up to 2 min with a…

A: We are given the following information.           k1=1 min-1k2=0.5 min-1CA0=1  (gmol/L)CB0=0…

Q: Solve the cariccal equatins using the Souhin gov en y₁cx) _you? = y²cx² +12ycxp²² , усхрдо C 22 x

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Q: Let E be the region bounded below by the cone z 7- (2²+ y²) and above by the sphere 2² = 10²-2² -…

A: Given- Let E be the region bounded below by the cone z = -7·x2 + y2 and above by the sphere z2 = 102…

Q: 4 18 D B W

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Q: EXERCISE 2.2 Derive the expression of the Bezier curve for the four points Po = ( = (0, 0, 0), P₁ =…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: AS the moon revolves around the earth, the side that faces the earth is usually just partially…

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Q: III. Consider the parabola C: 2-4 = -(x - 2)² on the xzz-plane. 1. Find the center-radius form of…

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Q: generate new members at a rate of 2 member: h member is expected to stay a club member f the number…

A: Given: Club started with 5 members. To find: Total new members in Week 2

Q: 3.0 Let T: R³ R be a temperature function defined as T(x, y, z) = x² - y² + 2xyz. Find the heat flux…

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Q: 3. Verify Stokes' Theorem for the vector field F= 2zi +3xj+5yk, taking S to be a portion of the…

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Q: Write the Mayan numeral as a Hindu-Arabic numeral. 2. 4 5 6 8 9 *** **** BE L www **** - 13 14 15 16…

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Q: Evaluate the indicated line integrals in the complex plane by direct integration. Siz dz along the…

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Q: A unicycle wheel has diameter 36 in. Determine the distance that the wheel will roll when it turns…

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Q: Find the flux of the vector field F = [x,y,z] through the oriented surface S: z= x^2 + y^2, z <= 1…

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Q: 3. An amusement park is planning a new roller coaster. Part of it is to have the shape of the cosine…

A: We need to use given data to sketch the graph . Use relation between degree and radian to get angles…

Q: The Denham Motel in Leduc has 90 rooms. If $300 per room is charged the owner will rent 40 rooms per…

A: Given that The Denham Motel in Leduc has 90 rooms. If $300 per room is charged the owner will rent…

Q: 2. Show that the following functions are harmonic, that is, that they satisfy Laplace's equation,…

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Q: Question 1: a) What is the equation for curvature for the curve y=sin(x)? b) What is the curvature…

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Q: Q4- Solve the following differential equation: (1+r)dy + (y-tan-¹(x)) dx = 0

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

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Q: Let C be the parametric curve with parametric equations [x=t(t² + 1)-¹/2 te [-3,3] y = 2t - 2…

A: The slope of the tangent to the curve: y=f(x) at x=a is f'(a). If a line is horizontal, then the…

Q: Find the spectral decomposition of the matrix 可

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Q: What is the maximum profit of this pure strategy game: 6 4 2 -1 Select one: O a. -1 O b. 6 O c. 4 O…

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Q: in fuzzy graph

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Q: A partial differential equation has A. one independent variable B. two or more independent variables…

A: Definition of the  partial differential equation :  A partial differential equation is a…

Q: Consider the market for lollies where if the price per lolly is $4, total market demand for lollies…

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Q: GIVEN: f(x) = 2x³ − 2x¹ +10x² -2=0 Using NEWTON'S METHOD, determine new estimate after 2nd…

A: We have to determine the new estimate after second iteration by Newton’s Method. Newton's  Method…

Q: B.) Convert the following function to standared form Min Z = 2x₂ + 5x3 S.t: x1 - x₂ ≥ 2 2x₁ + x₂ +…

A: Given  Min z= 2x2+5x3 x1-x2&gt;=2 2x1+x2+6x3&lt;=6 x1-x2+3x3=4 x1,x2,x3&gt;=0

Q: Write the given function as a power series and give the interval of convergence. a.) f(x) = 3x²…

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Q: Transportation Model (Optimal Feasible Solution) Minimize: C = 15x₁a + 24xıb + 12xic + 19x1D + 10x2A…

A: The following steps are used to obtain the optimal solution of the given transportation problem.…

Q: Is the given differential equation =etty separable? If so, how does the equation separate? A. This…

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Q: 6) A biologist monitoring an infestation of grubs has an initial population of 400 grubs per hectare…

A: Sol

Q: Use the Cauchy-Riemann conditions to find out whether the following functions are analytic. b.…

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Q: The Ferris Wheel Al and Betty have gone to the amusement park to ride on a Ferris wheel. The wheel…

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Q: Numerical Analysis 1. Consider the function f(x) = e-* sin(x). a) Calculate the degree 2 Taylor…

A: Sol