if the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x - pi / three ), what should be used for xmin and xmax? explain your answer.

try to keep the ans short yet easy to understand >

Xmin = π/3 and Xmax = 7π/3

Step-by-step explanation:

I assume that the function is:

y = 5 + 3 cos² (x − π/3)

cos² x has a period of π, so to graph two periods, you need a domain that is 2π wide, so:

Xmax − Xmin = 2π

You can choose any values you want for Xmax and Xmin, so long as they are 2π units apart.  To make it easy to graph, you'll probably want to choose Xmin = π/3 and Xmax = 7π/3.

Graph:

desmos.com/calculator/9w3pptakde

it would more likely be bald eagle because its has more in the box so about 75%.

step-by-step explanation:

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