A circular oil spill continues to increase in size. The radius of the oil spillin miles, is given by the function r(t) = 0.5 + 2t , where is the time in hours . The area of the circular region is given by the function A(r) = m ^ 2 where r is the radius of the Circle at time Explain how to write a composite function to find the area of the region at time t

Step-by-step explanation:

r(t) = 0.5 + 2t

A(r) = πr²

= π(0.5 +2t)² or

A(t) = π (0.25 +2t +4t²)

1 is c

2 is a

3 is a

step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3