A point starts at the location (1.5,0) and moves counter-clockwise along a circular path with a radius of 1.5 units that is centered at the origin of an x-y plane. An angle with its vertex at the circle's center has a measure of θ radians and subtends the path the point travels. Let x represent the point's x-coordinate. (Draw a diagram of this to make sure you understand the context!) Complete the following statements.

As θ varies from 0 to π/2, xvaries from  to  units.

As θ varies from π/2 to π, x varies from  to  units.

As θ varies from π to 3π/2, x varies from  to  units.

As θ varies from 3π/2 to 2π, x varies from  to  units.

c is the correct answer

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is