Raymond B. answered • 02/08/24
Math, microeconomics or criminal justice
160 = 104t -16t^2
16t^2 -104t +160 = 0
divide by 4
4t^2 -26t + 40 = 0
divide by 2
2t^2 -13t + 20 = 0
factor
(t-4)(2t-5) = 0
set each factor=0 and solve for t
t = 2.5 and 4 seconds when height = 160 feet
after 2.5 seconds it's 160 feet high and going up
after 4 seconds it's again 160 feet high, but going down
check the answers
104(4)-16(4^2) = 416 -256 = 160 feet
104(2.5) -16(2.5^2) = 260- 16(6.25) = 260- 100 = 160
midway between 2.5 and 4 = (2.5+4)/2 = 6.5/2 = 3.25 = 3 1/4 seconds, it reaches max height
104 -32t = 0
t = 104/32 = 26/8 = 13/4 = 3.25 second when max height = 104(3.25)- 16(3.25^2)=338- 169=169 feet high
possibly all you really want as the answer is: 2.5 = 2 1/2 seconds
