Amodel rocket is launched with an initial upward velocity of 204 ft/s. the rocket's height h (in feet) after t seconds is given by the following. rest attached ! !

t = .51 sec and t = 12.24 sec

Step-by-step explanation:

This is parabolic.  The nature of the parabola is symmetrical about a vertical line, so when an object going up passes a certain height, it will reach its max height and begin to fall, once again passing that certain height, just at a later time.  Besides that, this is a second degree polynomial so we are expecting to have 2 solutions.

If we are looking for the times that the height, h, of the rocket is 100 feet, then we sub in 100 for h and factor to solve for t:

To factor this, we will move everything over to one side and set the quadratic equal to 0:

Factor this using the quadratic formula to find

t = .51 and t = 12.24 seconds

(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

it could be 1,3 and more others to create a cylinder.

step-by-step explanation: