A large flea market is held at a local fairgrounds on the first Saturday of each month. The rates at which people enter and leave the flea market are recorded for a three hour period beginning at 12 noon. The rate at which people arrive is modeled by the function A(t) 42 sin (0.03 t-07) + 71. The function L(t) = 42 sin (0.034 t-1.52) + 42 models the rate at which people leave the fairgrounds. Both A(t) and L(t) are measured in people per minute and t is measured for 0 t 180 minutes, when the count begins at t 0, there are already 1572 people in the flea market area of the fairgrounds. Answer all parts in complete sentences including units a) How many additional people arrive for the flea market during the 3-hour period after it opens to the public?
b) Write an expression for P(t), the total number of people at the flea market at time t.
c) Find the value of P (75) and explain its meaning.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

according to egenuity the answer is

step-by-step explanation:

d. 344.22