16) I have -3x + 12.25=the square root on 15.25. I think that I subtract 12.25 to the 15.25 making it the square root of 3 so then I would divide that by -3x. Hopefully you understand this enough to help
96) 2X2 – 5X -3 = 0 First divide everything by 2 X2 – (5/2)X -3/2 = 0 Divide the “b” coefficient (5/2) by 2 and then square it ((5/2)/2)2 =(5/4)2= (25/16) This is going to be what you want for the c, so convert the c to the same denominator X2 – (5/2)X – 24/16 = 0 Just changed (3/2) to (24/16). So now, how do we get 25/16? X2 – (5/2)X – 24/16 + 49/16 = 49/16 We added49/16 to both sides so that we could get 25/16 for the c coefficient X2 – (5/2)X + 25/16 = 49/16 Simplified by adding – 24/16 + 49/16 to get 25/16. (X – (5/4))*( X – (5/4)) = 49/16 Factored! (X-(5/4))2 = 49/16 Simplified X-5/4 = sqrt (49/16) Square root of both sides X – 5/4 = +- 7/4 Simplified the sqrt (49/16) X = 5/4 +- 7/4 Solved X = 3 OR -1/2 Solutions are both rational solutions!
In this problem (116) they are giving you the equation h= -16t2 +120t -106. This means the initial height is -106 (cavern is 106 feet deep) and the initial velocity is 120 ft/sec. Since the height is measured down from the top of the canyon wall, they are telling you that the top of the canyon wall is 0 feet. So h = 0! This gives us the following equation: 0 = -16t2 +120t -106; where h = 0. So we solve like we would any non-factorable equation, either with the method used in 96, or with the quadratic formula. Let’s use the quadratic formula this time: (-b +/- sqrt (b2 – 4ac))/2a where a =-16; b= 120; c=-106 Putting those into the equation, we get that t= 1.02 seconds, I leave the exact form for you!
16) I have -3x + 12.25=the square root on 15.25. I think that I subtract 12.25 to the 15.25 making it the square root of 3 so then I would divide that by -3x. Hopefully you understand this enough to help
ReplyDeletesorry that was 96) not probelm 16)
ReplyDelete116) I got to 16t squared - 120t + 212=0, and I'm stumped after that.
ReplyDelete96)
ReplyDelete2X2 – 5X -3 = 0 First divide everything by 2
X2 – (5/2)X -3/2 = 0 Divide the “b” coefficient (5/2) by 2 and then square it
((5/2)/2)2 =(5/4)2= (25/16) This is going to be what you want for the c, so convert the c to the same denominator
X2 – (5/2)X – 24/16 = 0 Just changed (3/2) to (24/16). So now, how do we get 25/16?
X2 – (5/2)X – 24/16 + 49/16 = 49/16 We added49/16 to both sides so that we could get 25/16 for the c coefficient
X2 – (5/2)X + 25/16 = 49/16 Simplified by adding – 24/16 + 49/16 to get 25/16.
(X – (5/4))*( X – (5/4)) = 49/16 Factored!
(X-(5/4))2 = 49/16 Simplified
X-5/4 = sqrt (49/16) Square root of both sides
X – 5/4 = +- 7/4 Simplified the sqrt (49/16)
X = 5/4 +- 7/4 Solved
X = 3 OR -1/2 Solutions are both rational solutions!
Hope this helps
NS
In this problem (116) they are giving you the equation h= -16t2 +120t -106. This means the initial height is -106 (cavern is 106 feet deep) and the initial velocity is 120 ft/sec. Since the height is measured down from the top of the canyon wall, they are telling you that the top of the canyon wall is 0 feet. So h = 0!
ReplyDeleteThis gives us the following equation:
0 = -16t2 +120t -106; where h = 0.
So we solve like we would any non-factorable equation, either with the method used in 96, or with the quadratic formula. Let’s use the quadratic formula this time:
(-b +/- sqrt (b2 – 4ac))/2a where
a =-16; b= 120; c=-106
Putting those into the equation, we get that
t= 1.02 seconds, I leave the exact form for you!
NS