Q4: Find the centroid of the next shaded area. 1m Im 1 Y 1.5m 1m re1

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in the first…

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Q: Compute the surface area of the cone generated by revolving c(t) = (8t + 5, 7t) about the x-axis for…

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Q: What is the x centroid position for the shape below? Center:D, 2m 10m 3.4m 3.9m 4.4m 4.9m

A: Formula for centroid, C C=∑Ax∑A

Q: given ∫∫s (x2z) dS and S is the part in z = sqrt(x2+y2), which lies in x2+y2 = 1 calculate the…

A: we have to evaluate ∬Sx2zdS Now, we have z=x2+y2 ⇒z2=x2+y2∂z∂x=xz and…

Q: Q5. Consíder y = e+3 on [o,s]. Set up the surface area obtained by rotating The corve about y= 1 Ca)…

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Q: Find the area and centroid bounded by the curve 5y? = 16x and the curve y2 = 8x – 24.

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

Q: Q3: Find the centroid of the next shaded area. 4m

A: Solution :-

Q: Ex4: Find the centroid of the region that lies inside the cardioids r = a(1+ cos8) and outside the…

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Q: Determine the x-component (m) of the centroid of the given figure if the cut portion is a semicircle…

A: Given, a=39 m, b=16 m and c=2 m To find the x-component of the centroid of the given figure.

Q: Q4: Find the centroid of the next shaded area.

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Q: Jff v² av where D is the tetrahedron in the first octant bounded by the coordinate planes and the…

A: Let us consider the given integral I=∫ab∫f(x)g(x)∫p(x,y)q(x,y)F(x,y,z)dzdydx To solve the triple…

Q: Q5] [3M] Find SR 4xe* ((x² + y)*)dA, where Ris the region enclosed by y – axis and the two parabolas…

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Q: Locate the centroid x̄ of the area.

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Q: Q2 (a) Find the volume under the surface z = 3x3 + 3x²y and over the rectangle R = {(x,y):1 < x <…

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Q: The region in the first quadrant is bounded by the curve y = 2 - x^2 and y = x^2. How far is the…

A: Given- The region in the first quadrant is bounded by the curve y = 2 - x2 and y = x2.  To find- How…

Q: Determine the distance h for which the centroid of the shaded area is as far above line BB' as…

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Q: Evaluate II Væ² + y? dV, where E is the region that lies inside the cylinder æ2 + y² = 16 and…

A: E is the region that lies inside the cylinder x2+y2=16 and between the planes z=-5 and z=4 Change…

Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x-axis. A…

A: Area of surface generated by rotating a curve y=f(x) from x=a to x=b about x-axis  A=∫ab2πydsWhere…

Q: Q4(a) Find the area of the surface generated by revolving the curve, x = /6y – y2 ; 2<y<5

A: Given the curvex=6y-y2    , 2≤y≤5we need to find the area by revolving the curve about y axis from…

Q: 4. Locate the centroid (x, y)of the following composite areas: -3 ft 3 ft I 1.5 ft 1 ft

A: Consider the given composite area and divide then into four areas as shown in diagram below,

Q: Q3: For the shaded area below determine: a)The centroide (X.Y) of the area, b) the second moment of…

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Q: Evaluate fff (3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0…

A: ∫∫∫(3x + 2y) dV=∫∫∫(3x + 2y) dxdydz = ∫z = 04∫y = -13∫x =-11(3x + 2y) dxdydz = ∫z = 04∫y = -134y…

Q: Determine the y-coordinate of the centroid of the shaded area. bl x=y²/b 0.62b b Answer: y = i b

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Q: 24. Round to the nearest tenth if necessary. 1 13. Point P is the centroid for AMNO. Calculate RP if…

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Q: Y 5 m 1m 1.50 m 1 m 4) What is the y-coordinate of the centroid, y of the given figure in m.? 3.50 m…

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Q: Determine the y-coordinate of the centroid of the shaded area shown. 12" Parabolic 5" Answer: y = i…

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Q: Determine the y-coordinate of the centroid of the shaded area. y Ix= y2/b 0.48b b Answer: ỹ =

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Q: Determine the y-coordinate of the centroid of the shaded area. bl. | x=y²/b b Answer: y = i 0.48b MI…

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Q: Q1. Locate the centroid of the shaded area shown in the Figure (1). y = 4vx -27 2 mm 9 mm 6 mm…

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Q: Q3. With respect to the coordinate axes X and Y locate the centroid of the shaded area as shown in…

A: As according to given diagram: Area of trapezoid is: A=100×220+12×220×50A=22000+5500A=27500 mm2…

Q: Determine the y-coordinate of the centroid of the shaded area. y b Ix= y2/b 0.48b b Answer: y = the…

A: Consider the elemental strip of thickness dx at distance x from y axis.

Q: Determine the centroid of the following Fig from X and Y axes. Y, 30 centT1 2 CentQ1 -4 -3 -2 -1 1 2…

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Q: Find the moment of inertia of the plane area generated by the equations y = 8x³, y = 0, and x = 1…

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

Q: Consider the figure below, point D is the centroid of △ABC with DF = 4x − 1 and BD = 6x + 4. Use the…

A: Figure of triangle is given, where point D is centroid with DF=4x-1 and BD=6x+4.

Q: Find the Centroid tor the Shaded area. [Q2] 120 r=5 150 6 30 90 130

A: Solution to Question (1) Given a shaded area with dimensions,we have to find the centroid of that…

Q: Which of the following equals to the area of the plane region bounded by the ellipse 4x²+y² = 4.…

A: Here we find area for given ellipse.

Q: Find the centroid of the third quadrant area bounded by the following curves y2+ 2y + 8x = −1 and y…

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Q: Find the centroid of the third quadrant area bounded by the following curves y? + 2y + 8x =-1 and y…

A: According to question given:y2+2y+8x=-1y=-5We have to calculate the centroid of the third quadrant…

Q: 3 m 7) Determine the location of centroid (x, ỹ ) of the cross-sectional area shown (P9-69) 1.2 m 3…

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Q: Use Cartesian coordinates to evaluate y²2 dV D where D is the tetrahedron in the first octant…

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Q: 1F M is the centroid of BC, AM= 44, CE= 54, and DM =23, find each missing measure.

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Q: =+ x²y) ds part of the cylinder y² + z² = 9 that lies between the planes x = 0 and x = 3 in the…

A: See the details solution in below

Q: Y 5m 1m 3) What is the x-coordinate of the centroid, X of the given figure in m.? 1.50 m 1 m 3.50 m…

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Q: The region in the first quadrant is bounded by the curve y = e^x and the lines x = 0 and the x = 1.…

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Q: Find the centroid of the fourth quadrant area bounded by the following curves y? + 2y + 8x =-1 and y…

A: We will use double integration to solve this

Q: 2. Find the area of the ellipse S on the plane 2x + y + z = 2 cut out by the cylinder x2 + y? = 2x;…

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Q: Use Cartesian coordinates to evaluate y² dV D where D is the tetrahedron in the first octant bounded…

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Q: Use Cartesian coordinates to evaluate Jff v² av D where D is the tetrahedron in the first octant…

A: Let us consider the integartion I=∫ab∫f(x)g(x)∫p(x,y)q(x,y)F(x,y,z)dzdydx To solve the integral…

Q: Find a parametrization of the curve x^(2/3)+y^(2/3)=8^(2/3) and use it to compute the area of the…

A: Finding the parameters:

Q: Evaluate ||/ Væ² +y? dV, where E is the region that lies inside the cylinder æ² + y² = 16 and…

A: Given :  The integral ∫ ∫ ∫E x2+y2 dV , where E is the region that lies inside the cylinder  x2+y2 =…