(4) y=x and y=x if the density is x+1 Find the center of mass of the given region (8,5)=| (5.5)-() a) (15 (7.5)- ) b) 30 8 (7.5)=| 13 27 (2.5)-() 11 15 13
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- Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a lateral area. b total area. c volume.A thin wire is bent into the shape of a line segment from (1, 2) to (−1, 1), and the curve y = x2 from (−1, 1) to (2, 4). Set up the line integral(s) to find the mass of the wire if its density is given by δ(x, y) = 2y.(Do Not Evaluate.)A wire takes the shape of the semicircle x2+y2 =1 y>0 and is thicker near its base than near the top. Find the center of mass of the wire if the linear density at any point is proportional to its distance from the line y=1
- a planet is in the shape of a sphere of radius R and total mass M with spherically symmetric density distribution that increases lineary as one approaches its center . what is the density at the center of this planet if the density at its edge is taken to be zeroFind the center of mass of a thin rectangular plate cut from the first quadrant by the lines x = 6 and y = 1 if the density is δ(x,y) = x + y + 1Find the mass and center of mass of the lamina bounded by the graphs of the given equations with a density equal to kx. x = 16 - y2, x = 0 Answer provided but how do I get there?
- Suppose a thin plate is bounded by y=0 , x=0, x=1, and y=e^-x and has areal density of p(x,y)= xy. Set up the integrals necessary to find the center of mass of the plate.Find the center of mass of a thin plateof density δ = 3 bounded by the lines x = 0, y = x, and the parabolay = 2 - x2 in the first quadrant.Find the center of mass of a thin plate of density δ = 3 bounded by the lines x = 0,y = x, and the parabola y = 2 - x2in the first quadrant.
- A rod with uniform density (mass/unit length) δ(x)=2+sin(x) lies on the x-axis between x=0 and x=π. Find the mass and center of mass of the rod.A pulse (gas) travelling along a fine straight uniform tube filled with gas causes the density at any time t and distance x from the origin where the velocity is u_{0} to become roh_{0}ϕ(vt-x). Prove that the velocity u (at time t and distance x from the origin) is given byFind the center of mass for a thin plate covering the region bounded by the parabola y=25-x^2 and x−axis, with its density given by δ(x)=6+x.