5. When an object is falling, the air resistance, A varies directly as the square of
the speed, S. At a certain speed the resistance is 60 newtons. What is the
resistance at twice this speed?

240 N

Step-by-step explanation:

Resistance force (A) varies directly with the square of the speed (S).

A = k S²

At a certain speed (S = s), the resistance is A = 60.

60 = k s²

k = 60 / s²

At double the speed, (S = 2s), the resistance is:

A = k (2s)²

A = (60 / s²) (2s)²

A = (60 / s²) (4s²)

A = 240

(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

the answer is a beach is the best place to be