A system of pulleys is loaded with 128-pound and 32-pound weights (see figure). The tensions t1 and

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A system of pulleys is loaded with 128-pound and 32-pound weights (see figure). The tensions t1 and t2 in the ropes and the acceleration a of the 32-pound weight are found by solving the system
4 - 212 – 2a = 128 t, + a 32

where t1 and t2 are in pounds and a is in feet per second squared. Solve this system.

t2 32 lb 128 lb

One way to find the least squares regression parabola y = ax2 + bx + c for a set of points (x1, y1), (x2, y2), .., (xn, yn) is by solving the system below for a, b, and c.

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