```Question 36691
Janice tosses a softball upward with an intinal veolicty of 100 feet per second. Use the formula h=vt-16t^2
H=100T-16T^2
A. When the ball hits a height of 84 feet?
H=84=100T-16T^2
16T^2-100T+84=0...DIVIDE BY 4
4T^2-25T+21=0
4T^2-4T-21T+21=0
4T(T-1)-21(T-1)=0
(T-1)(4T-21)=0
T-1=0....T=1....
4T-21=0......T=21/4....
HENCE IT WILL BE AT 84 FEET AT T=1 SEC WHEN IT IS GOING UP AND AT T=21/4=5.25 SEC.WHEN IT IS COMING DOWN.

B When will the ball hit the ground.
WHEN THE BLL HTS THE GROUND H=0..SO..
0=100T-16T^2
4T(25-4T)=0
4T=0......T=0...THAT IS BEFORE IT IS THROWN UP
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A box is to be formed from a rectangular piece of sheet metal by cutting squares measuring 5in on a side and then folding the sides. The piece of sheet metal is twice as long as its width.
LET WIDTH =B
LENGTH =2B
5" CUT AT EACH CORNER.HENCE
REMAINING LENGTH OF BOX =2B-2*5=2B-10=2(B-5)
REMAINING WIDTH OF BOX =B-2*5=B-10
HEIGHT OF BOX =5"

If the volume of the box is to be 1760in^3, what are the dimensions of the origional piece of metal.

VOLUME = 5*2(B-5)(B-10)=1760.........(B-5)(B-10)=176
B^2-15B+50=176
B^2-15B-126=0
B^2-21B+6B-126=0
B(B-21)+6(B-21)=0
(B-21)(B+6)=0
B-21=0....B=21........THE OTHER ROOT IS NOT TENABLE AS IT GIVES NEGATIVE VALUES.
HENCE ORIGINAL SHEET HAS
LENGTH = 2*B=2*21=42" AND
WIDTH = 21"```