Find the centroid when revolved in y-axis: y³ = x² ; y = 4.

Q: 4. Prove that the L{2t²} = 4 S3

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, -12t) (a) If R(0) = (-1,4,-5),…

A: We will use integral to find original position vector and arc length of given curve

Q: Let h be the vector field h(x, y, z) = (2xy +=²)i + (x² − 2yz)j + (2xz - y²) k. (a) Show that h is a…

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Q: Example 1 For the IVP y'+2y=2-e y(0)=1 Use Euler's Method with a step size of h 0.1 to find…

A: It is a fairly simple linear differential equation thus we'll leave it to you to check that the…

Q: p be an irreducible reprsentation of G

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Q: be an open subset in C and f

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Q: Given the dual D of linear program P : D: min z = 16y - 8y +20y -20y 1) 2y1 +2y3 -2y4 >= 2 2) y1…

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Q: Consider the polar curves in the image then answer the ff: a. Find the point(s) of intersection of…

A: If f is continuous and non negative on the interval α≤θ≤β with 0<β−α≤2π. Then area of the region…

Q: 5. Consider the vector-valued function R(t) = (t³ — t, 2t², 2 — 2t²) a. Find ||R'(t)|| (Simplify…

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Q: Find the extremal of the functions using Euler's equation. [²(x² + y² (y2 + y² + 2ye*)dx, y (0) = 0,…

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (b) Reparametrize R using…

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Q: Let X be a normalized space. holds in general for x E X and y EX: ||x*y|| ≤||x|*||yl| Prove or…

A: As per the question we are given a normalized space X with norm ||•|| And we have to either prove or…

Q: Decide, with proof, which of the following form a basis for a topology on R, stating clearly any…

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Q: Let S be the surface with equation 4y2 + 4z2 - x2 - 16 = 0 1) Find an equation of the trace of S on…

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Q: Decide, with proof, which of the following form a basis for a topology on R, stating clearly any…

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Q: Let h be the vector field h(x, y, z) = (2xy + ²)i + (x² −2yz)j + (2xz - y²) k. (a) Show that h is a…

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Q: A = 3 + j4 B = 4-j5 C = 5-j2 D=1-√3 E = 2+j3 F = 4+j1 10 The complex numbers V and W represent two…

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Q: Applying the law of sines, solve the following problems. Round to the nearest hundredth. 3. Solve…

A: We have to find the value of side and angles by law of sines.

Q: The plane through the point (3,-1,2) can perpendicular to the a) x-axis b) y-axis c) z-axis d) non d…

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Q: Determine the volume produced by the region bordered by x² - 4x - 4y + 4 = 0 and y = 1 about the…

A: We will use disk method to find volume of solid generated

Q: Fill in the blanks. Justify your answer. If f has an essential singularity at zo, then for any n EN…

A: If f has an essential singularity at z0, then for any n∈ℕ the function z-z0nf(z) has _______…

Q: The population of a town is decreasing at a rate proportional to its size. In 1980, the population…

A: In 1980 , population was 50,000 and In 1990, population was 44,000 The population of town is…

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

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Q: 3 Let f(2)= (2 + 1)(x - 2) and use this result to evaluate Find the Laurent series expansion of f…

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Q: Q. yrsy fase Jestell 4 cos 3t 24-24-fct) with Zero intiral locations гу чувст ostal 1<t<2 2 <t<3

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Q: A manufacturing company has a production capacity of 600,000 units with an income of 720,000 pesos.…

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Q: How many 13-card hands having exactly 11 cards from any suit can be dealt? Please write out each…

A: Given, How many 13-card hands having exactly 11 cards from any suit can be dealt?

Q: Solve Usiy: Gaux Sied! Meble 500 500 500 1500 ич L43 1000 HU₁ Uz 1000 1000 1000 1000 1000

A: As per the question we are given a grid with temperature distribution u And we have to find the…

Q: التاريخ 202 1 Sourier Transform J2X ft set (² -56f2= D -xt علم the

A: One of the most important integral transformations is Fourier transformation. It is an integral…

Q: Apply the method of Lagrange multipliers to the function ƒ(x, y) = (x² + 1) y subject to the…

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Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

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Q: 2. Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y² - 3x² and…

A: Using trigonometric substitution

Q: The population of a town is decreasing at a rate proportional to its size. In 1980, the population…

A: We find population in year 2000.

Q: Find the complete solution of 2e-2 Note: fe"du=e" + C dy sin²x = 0. dx COS X--

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Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A: Since you have asked multiple questions here, we will solve the first one for you. To get the…

Q: Find a particular solution of ds π = 10csc² 2t determined by s= 2 when t = dt 4

A: The general form of a first-order differential equation is given by dydt=f(t,y). The solution of the…

Q: te Fourier transfor 33 43

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Q: Area of the Region and Volume of the Solid of Revolution Given: The region is bounded by the curves…

A: Volume of the solid formed by revolving the region between curves y=f(x) and y=g(x) from x=a to x=b…

Q: impson's One-Thirds (Use n = 10) 7. S¯½ (5x³ − 2x² + x + 3) dx -24 sin r

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: Evaluate the following: 2 d. L-¹1- + S-3 3s-5 Th

A: Since  you have posted a multiple  question according to guildlines I will solve first  (d) question…

Q: I. Let C be the curve with parametric equations I = 3t-1² t and yIn(t-1) for t = (1, +∞), and let P…

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Q: Using Simpson's method ²x²dx for n = 4 is equal to Blank 1 (use 2 decimal places with proper…

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Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

A: Solution :-

Q: Find the average value of f(x, y) = sin(x + y) over a. The rectangle 0≤x≤,0 ≤ y ≤n b. The rectangle…

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Q: 4. Evaluate the double integral: LL y x² +1 (Hint: Change the order of integration to dy dx.) dx dy.

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Q: Set-up the integral which yields the area of the indicated region R between C1 and C2. Given: polar…

A: Solution:-

Q: Find the exact length of the polar curve described by: 0 r = 4e 5 on the interval 6 ≤0 ≤ 6.

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Q: y = + x²cosx y + x

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Q: Applying the law of sines, solve the following problems. Round to the nearest hundredth. 1. Solve…

A: Since you have asked multiple questions here, we will solve the first one for you. To get the…

Q: 2. Find the Inverse Laplace of the below given equation. 7s-1 F(s) = (s+1)(s+2)(s-3)

A: The solution is given as