Find the center of gravity of the region bounded by the x-axis, the curve y = sec x, and the lines x = -π/4, x = π/4.
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Find the center of gravity of the region
bounded by the x-axis, the curve y = sec x, and the lines x =
-π/4, x = π/4.
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- A 93 gm meter stick has two objects attached to it, one of 177 gm at the 15 cm mark and the other of 179 gm at the 81 cm mark. At what mark on the meter stick is the center of gravity of the system?A lamina V of uniform mass density and total mass M kilograms occupies the region between y = l - x 2 and the x-axis (with distance measured in meters). Calculate the rotational kinetic energy if V rotates with angular velocity w = 4 radians per second about: (a) the x-axis. (b) the z-axis.Pat builds a track for his model car out of wood. The track is 3 cm wide (along the z coordinate), 1 m high (along the y coordinate), and 2.7 m long (along the x coordinate starting from x = 0). The runway is cut such that it forms part of the left-hand side of a parabola, see figure below. Locate the horizontal position of the center of gravity of this track in m.
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