Question 366737
1. A rocket is fired upward at an initial velocity of 1008 ft/s from a tower that is 120 ft high. When will the rocket reach a height of 3896 ft above ground level? H=VT-16t^2

Let t =  the number of seconds the rocket will reach a height of 3896 ft above ground level after it is fired upward 


3896 - 120 = 1008t - 16t^t
16t^2 - 1008t + 3776
Divide both sides by 16
t^2 - 63t - 236
Solve for t by factoring
(t-4)(t-59) = 0

t-4 = 0
t = 4 

The rocket will reach a height of 3896 ft above ground level 4 seconds after it is fired upward 

2. The length of a rectangular table is 1 ft more than twice the length of a side of a square rug and the width of the table is 3 ft less than the length of a side of the rug. If the area of the table is 81 ft^2 greater than the area of the rug, what is the area of the rug? 

Let L = length of table
    W = width of table
    R = side of square rug

1st equation
L = 2R + 1

2nd equation
W = R - 3

3rd equation
WL = R^2 + 81

Substitute the values of L & W in terms of R 
(R-3)(2R+1) = R^2 + 81
2R^2-6R+R-3 = R^2 +81
Combine like terms
R^2 -5R - 84 = 0

Solve by factoring
(R+7) (R-12)
R = 12

Area of rug is 12^= 144 ft^2