Ahalo jumper with a mass of m parachutes from a gas balloon at time t = 0. under certain assumptions, the distance, s(t), that he has fallen in time t is given by s(t) = m2 g k 2 ( kt m + e −kt/m − 1) for some positive constant k. (a) find s ′ (0) and s ′′(0) and interpret the quantities in terms of the halo jumper. (b) relate the units of s ′ (t) and s ′′(t) to the units of t and s(t).

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

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