Question 490482: I have been working on solving is quadratic equation. I can get it set up but it is part of a word problem which has a two decimal answers.The prob. is a modeling problem. An astronaut on the moon throws a baseball upward. The astronaut is 6ft 6inches tall and the initial velocity of the ball is 30ft per sec. The height s of the ball in feet is given by the equation s=-2.7t^2 +30t+6.5 where t is the number of seconds after the ball is thrown. Part A: After how many seconds is the ball 12ft above the moon's surface? Round to the nearest 10th. Part B. is how many second will it take for the ball to return to the surface? Round to the nearest hundredth. What I have so far is:
multiplied by 10 to get rid of the decimals
120=-27t^2 + 300t + 65,
120-120=-27t^2 + 300t + 65-120,
0=-27t^2 + 300t + -55
x=-(300)+or -the sq.root(300)^2-4(27)(-55)
divided by 2(27)
I am getting x=-300 +or- sq.rt95940
divided by 5.4.
I am having trouble simplifying this further, I have the answers from my book, but I don't know how to bring this problem to a conclusion. Ans. are a).19sec, 10.92sec b)11.32sec
Thank you kindly for your help
Carolyn
Answer by John10(297)   (Show Source):
You can put this solution on YOUR website! I don't understand why you have to multiply both sides by 10. Just leave it in decimals.
Part A:
s = -2.7t^2 + 30t + 6.5 = 12
-2.7t^2 + 30t - 5.5 = 0
Find the discriminant:
D = (30)^2 - 4(-2.7)(-5.5) = 900 - 59.4 = 840.6
t = (-30 +/- √840.6)/2(-2.7) = 0.19 seconds or 10.92 seconds
Part B: after the ball return to the surface s = 0
-2.7t^2 + 30t + 6.5 = 0
D = (30)^2 - 4(-2.7)(6.5) = 900 + 70.2 = 970.2
t = (-30 +/- √970.2)/2(-2.7) = -0.21 second (VOID) or 11.32 second
I think that you messed up at finding the DISCRIMINANT.
John10:)
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