Problem 1SP: Compute the area of each of the three sub-regions. Note that the areas of regions R2 and R3 should... Problem 2SP: Determine the mass associated with each of the three sub-regions. Problem 3SP: Calculate the center of mass of each of the three sub-regions. Problem 4SP: Now, treat each of the three sub-regions as a point mass located at the center of mass of the... Problem 5SP: Assume the visitor center weighs 2,200,000 lb, with a center of mass corresponding to the center of... Problem 6SP: Although the Skywalk was built to limit the number of people on the observation platform to 120, the... Problem 254E: For the following exercises, calculate the center of mass for the collection of masses given. 254.... Problem 255E: For the following exercises, calculate the center of mass for the collection of masses given. 255.... Problem 256E: For the following exercises, calculate the center of mass foi the collection of masses given. 256.... Problem 257E: For the following exercises, calculate the center of mass for the collection of masses given. 257.... Problem 258E: For the following exercises, calculate the center of mass for the collection of masses given. 258.... Problem 259E: For the following exercises, calculate the center of mass for the collection of masses given. 259.... Problem 260E: For the following exercises, compute the center of mass x . 260. =1 for x(1,3) Problem 261E: For the following exercises, compute the center of mass x . 261. =x2 for x(0,L) Problem 262E: For the following exercises, compute the center of mass x . 262. =1 for x(0,1) , and =2 for x(1,2) Problem 263E: For the following exercises, compute the center of mass x . 263. =sinx for x(0,) Problem 264E: For the following exercises, compute the center of mass x . 264. =cosx for x(0,2) Problem 265E: For the following exercises, compute the center of mass x . 265. =ex for x(0,2) Problem 266E: For the following exercises, compute the center of mass x . 266. =x3+xex for x(0,1) Problem 267E: For the following exercises, compute the center of mass x . 267. =xsinx for x(0,) Problem 268E: For the following exercises, compute the center of mass x . 268. =x for x(1,4) Problem 269E: For the following exercises, compute the center of mass x . 269. =Inx for x(1,e) Problem 270E: For the following exercises, compute the center of mass (x,y) . Use symmetry to help locate the... Problem 271E: For the following exercises, compute the center of mass (x,y) . Use symmetry to help locate the... Problem 272E: For the following exercises, compute the center of mass (x,y) . Use symmetry to help locate the... Problem 273E: For the following exercises, compute the center of mass (x,y) . Use symmetry to help locate the... Problem 274E: For the following exercises, compute the center of mass (x,y) . Use symmetry to help locate the... Problem 275E: For the following exercises, compute the center of mass (x,y) . Use symmetry to help locate the... Problem 276E: For the following exercises, compute the center of mass (x,y) . Use symmetry to help locate the... Problem 277E: For the following exercises, compute the center of mass (x,y) . Use symmetry to help locate the... Problem 278E: For the following exercises, compute the center of mass (x,y) . Use symmetry to help locate the... Problem 279E: For the following exercises, compute the center of mass (x,y) . Use symmetry to help locate the... Problem 280E: For the following exercises, use the theorem of Pappus to determine the volume of the shape. 280.... Problem 281E: For die following exercises, use the theorem of Pappus to determine the volume of the shape. 281.... Problem 282E: For the following exercises, use the theorem of Pappus to determine the volume of the shape. 282. A... Problem 283E: A general cylinder created by rotating a rectangle with vertices (0,0),(a,0),(0,b) , and... Problem 284E: A sphere created by rotating a semicircle with radius a around the y -axis. Does your answer agree... Problem 285E: For the following exercises, use a calculator to draw the legion enclosed by the curve. Find the... Problem 286E: For the following exercises, use a calculator to draw the legion enclosed by the curve. Find the... Problem 287E: For the following exercises, use a calculator to draw the legion enclosed by the curve. Find the... Problem 288E: For the following exercises, use a calculator to draw the legion enclosed by the curve. Find the... Problem 289E: For the following exercises, use a calculator to draw the legion enclosed by the curve. Find the... Problem 290E: Find the generalized center of mass in the sliver between y=xa and y=xb with ab. Then, use the... Problem 291E: Find the generalized center of mass between y=a2x2,x=0, and y=0 . Then, use the Pappus theorem to... Problem 292E: Find the generalized center of mass between y=bsin(ax) , x=0 , and x=a . Then, use the Pappus... Problem 293E: Use the theorem of Pappus to find the volume of a torus (pictured here). Assume that a disk of... Problem 294E: Find the center of mass (x,y) for a thin wire along the semicircle y=1x2 with unit mass. (Hint: Use... format_list_bulleted