SOLUTION: 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 2

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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
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?
Please help!
Answer by amoresroy(361) About Me  (Show Source):
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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