Problem No. 2 From the given diagram, find the centroid of the irregular plate body with respect to the given point of axis. y² = 2x 2 m Given: Fomula to use: JdA JdA 2 m 2 m

Q: QUESTION 4 What is the best description of the surface parametrized as x= 3sinucosv, y=3sinusinv,…

A: The parametric equations for the sphere of radius r unit is x = r sinucosv , y = r sinusinv ,   z =…

Q: Question 4 2). Uze a double integral to fiad the rolume in the first ocyant bonaded by the…

A: Consider the given information: To find the volume in the first octant bounded by the coordinate…

Q: Which of the following is simply connected? a) the horizontal strip Imz <1 b) the annulus 1</z <2 c)…

A: This is a problem of topology.

Q: 7. What region in the ry-plane minimizes the value of [ (42² + 49y² – 196) dA? R A) The ellipse 49x?…

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Q: Problem #8 A region in the xy plane is bounded by the curves {y = 2* and y = 1 and x = 3} Suppose…

A: Volume by disc method

Q: QUESTION 7 If fx.y)=esinx+xy+In(1+y?) then дхду 20х3у 5x4 2y 1+y? QUESTION 8 1 The domain of…

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Q: Question 2. Identify the surface 4y - 4x +z = 4. Is that surface symetric with respect to each of…

A: Given: Equation of surface 4y² - 4x² + z² = 4

Q: Problem 2. Find the value of a > 0 such that the cone 22 = x² + y?, z > 0 is orthogonal to the…

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Q: Question 9 Which surface has the following equation? a2-2y = 32 O Cylinder O Plane O Paraboloid O…

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Q: Eliminate the parameteu, wite your answer in standand for m: A hy pe bola : x = h+ a sec t, y=R+b…

A: To eliminate the parameter and to write the answer in standard form:A hyperbola: x=h+a sec t, y=k+b…

Q: Problem 8: Given a general closed surface S for which the position vector r = 1,e; and normal n are…

A: Given a closed surface S and its position vector r→=xiei and the normal is n→. To derive the formula…

Q: Which of the following is NOT a method for finding volume of solids of revolution? (A) shell method…

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Q: Problem 3. Calculate the surface area, Area (S) = || ds z+ z3 +1 dA, of the part of the paraboloid z…

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Q: For the blue shaded area shown in the image below, if the dimensions are a = 1.2 in., b = 3.6 in., c…

A: For calculating area following formulae will be used: Area of rectangle = length x breadth Area of…

Q: Problem 5 has two parts, (5a) and (5b). 5a. The solid E lies above the cone z = V3/² +y² and below…

A: Hello. Since your question has multiple parts, we will solve the first part (a) for you. If you want…

Q: Given a plane 2y + 4z = 5 intersects the cone z^2 = x^2 + y^2 in an ellipse. Find the points on this…

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Q: Question 4 Use polar coordinates to find the volume of the solid under the paraboloid z =x+y² and…

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Q: 3. Evaluate (sin r +y cos r)dr + (sin r + z cos y)dy + sin ydz), where C'is the ellipse 36.r + 4y =…

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Q: Problem 1. Let E be the solid ellipsoid bounded by the surface x2 y? 22 = 1. a? 62 c2 for positive…

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Q: Question 11 Calculate the surface area of the given surface. The parabolic cylinder with equation z…

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Q: Problem 3.4 Parameterize the following surface. Then, integrate the given function over the…

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Q: 7. Find the principal axes of the ellipsoid x" Ar = 1, and rewrite the ellipsoid in terms of [3 1 07…

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Q: ellipsoid x* + + = 3 z2 n2 q2 r2

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Q: Find the coordinates of the centroid (to the nearest 0.01 in.) of the uniform flat-plate machine…

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Q: 4.1.25 Show that the largest inscribed rectangular parallelepiped x2 y? z2 1 36 on the ellipsoid is…

A: first, we proved the general case.

Q: Question 2: Calculate the coordinates of the centroid for composite shape given. 5cm 3cm r=2cm (0,0)…

A: The centroid of a right triangle is at h3,b3 with respect to the vertex with the right angle. Here,…

Q: 2. Obtain the eccentricity e and centroid a, and y. of the following image. f(x.y)=1 (object: dark)…

A: From the figure, we have to write down all the dark box function, for which f(x,y)=1 x,y=3,2, 4,2,…

Q: 29. A tank full of water has the shape of a paraboloid of revolu. tion as shown in the figure; that…

A: Height is 4 feet and radius at the top is 4 feet So the parabola passes through the point (4,4) The…

Q: What is the size of the largest segment parallel to the y axis inside the ellipsoid

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Q: Chapter 5, Reserve Problem 5/054 Determine the coordinates of the centroid of the shaded area. 1.5"…

A: To determine the coordinates of the centroid of the given shaded region.

Q: 3. The point D is the centroid of AABC. Find the value of the distance DC if : GD = 2x – 8 and GC =…

A: It is known that the centroid of a triangle is the point at which the 3 medians of the triangle…

Q: Question 3 5 st 36. about x-axis is The area of the surface obtained by rotating the curve X = 3t, y…

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Q: Question 1 Consider the solid under the plane Z = x and above the rectangle 0 < x < 1 by 0 < y < 2

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

Q: As an engineer at Ghana Atomic Energy, you have been tasked to design a cooling tower in the shape…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Problem 2. Use spherical coordinates to find the volume of the solid within the sphere r2+y? + z2 =…

A: z=ρcos(ϕ)x=ρsin(ϕ)cosθy=ρsin(ϕ)sinθz=x2+y2ρcos(ϕ)=ρsin(ϕ)cosθ2+ρsin(ϕ)sinθ2…

Q: QUESTION 11 A three-dimensional solid obtained by revolving a region in the xy-plane about a line is…

A: We have to check

Q: 1. What is the area of the region bounded by the ellipse with the equation x^2+9y^2+3x - 18y + 9 = 0…

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Q: b) a dr+(x+yz) dy+(ry- VE) dz, C is the boundary of the part of the plane 3r+2y+z in the first…

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Q: Problems: 1. Find the centroid for the area surrounded by the curve y=x* , y-axis and the line y=8 ?…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: The given curve is rotated about the y-axis. Find thearea of the resulting surface.   x =  1/4 x2 -…

A: If the curve y = f(x) , a≤x≤b is rotated about y axis , then surface area is, A=2π∫abx1+f'x2d

Q: Question 3 Find the surface area of that portion of the sphere x2 +y2 + z2 = 1 inside the zone z =…

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Q: Problem 5 Find the volume of the wedge cut from the first octant by the cylinder z = 12-3y? and the…

A: To Determine: find the volume of the wedge cut from the first octant by the cylinder z=12-3y2 and…

Q: Find the area of the surface generated by removing about the x-axis the upper half of the ellipse…

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Q: 5. Find the volume generated by the equation x2 +y² – 4x - 6y –- 12 = 0 if it is rotated about the…

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Q: QUESTION 2 (a) Sketch the following surfaces. i) z = 5+x' +y ii) z =5-x + +y? iii) = 5-x-y Z =,

A: Explanation of the answer is as follows

Q: Question 2. Let E be the solid region inside the surface x² + y² + z² = 25 and above the surface z =…

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Q: (b) Find the volume and the surface area of the truncated cone made by the rotation of the solid…

A: From the given graph: Now, from the graph given that:    r = 2 unit, R = 4 unit, and h = 3 unit.…

Q: The figure below is a composite body consisting of the following parts: [1] the triangular prism of…

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Q: Question 5 5 st36. about x -axis is The area of the surface obtained by rotating the curve * = 3t, y…

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