Solve each system of linear equations by substitution x+y=3 -x+y=5

Parabolas y=−2x^2 and y=2x^2+k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.

Amass weighing 16 pounds stretches a spring 8/3 feet. the mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. find the equation of motion if the mass is driven by an external force equal to f(t)=cos(2t).

This size running track is usually called a 400 meter track. however if a person ran as close to the inside as possible on the track they would run less than 400 meters in one lap. how far away from the inside border would someone have to run to make one lap equal exactly 400 meters