Rational Function word problem

dboybbfs

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Feb 19, 2006
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I had this problem on a test. Teacher marked the 304(t) wrong. I got the answer marked right though. I asked the teacher why I he marked 304(t) wrong, he said I shouldn't have plugged 304 in for h. I have to redo this problem and show my work. I can't figure out what I did wrong though. Could someone please explain?

thank you


After t seconds, the height of a ball thrown upward is given h(t)=-16t^2 + 80t + 240 feet. When will the ball be 304 feet high?

This is how I solved it:

304(t)=-16t^2 + 80t + 240

304t=-16t^2 + 80t + 240
-304t -304t

0=-16t^2 -224t + 240

0=-16(t^2 + 14t -15)

(t + 15)(t - 1)

t=-15 t=1

can't be -15 feet so answer is:

At 1 second, the ball will be 304 feet high.
 
dboybbfs said:
I had this problem on a test. Teacher marked the 304(t) wrong. I got the answer marked right though. I asked the teacher why I he marked 304(t) wrong, he said I shouldn't have plugged 304 in for h. I have to redo this problem and show my work. I can't figure out what I did wrong though. Could someone please explain?

thank you


After t seconds, the height of a ball thrown upward is given h(t)=-16t^2 + 80t + 240 feet. When will the ball be 304 feet high?

This is how I solved it:

304(t)=-16t^2 + 80t + 240

304t=-16t^2 + 80t + 240
-304t -304t

0=-16t^2 -224t + 240

0=-16(t^2 + 14t -15)

(t + 15)(t - 1)

t=-15 t=1

can't be -15 feet so answer is:

At 1 second, the ball will be 304 feet high.

h(t) represents the height at "t" seconds.

You want to know when the height is 304 feet. So, substitute 304 for h(t):

h(t) = -16t<SUP>2</SUP> + 80t + 240
304 = -16t<SUP>2</SUP> + 80t + 240

NOW solve for t....start by subtracting 304 from both sides of the equation.....
 
Hello, dboybbfs!

I think you know that \(\displaystyle h(t)\) means "\(\displaystyle h\) of \(\displaystyle t\)", a function . . . and not "\(\displaystyle h\) times \(\displaystyle t\)".
If not, you'd better go back and review the meaning of \(\displaystyle f(x)\).



After \(\displaystyle t\) seconds, the height of a ball thrown upward is: \(\displaystyle \,h(t)\:=\:-16t^2\,+\,80t\,+\,240\) feet.
When will the ball be 304 feet high?
\(\displaystyle \text{Let }h(t)\,=\,304\)

\(\displaystyle \;\;304\:=\;-16t^2\,+\,80t\,+\,240\)

Your quadratic is: \(\displaystyle \,16t^2\,-\,90t\,+\,64\:=\:0\;\;\Rightarrow\;\;t^2\,-\,5t\,+\,4\:=\:0\)

\(\displaystyle \;\;\)which factors: \(\displaystyle \,(t\,-\,1)(t\,-\,4)\:=\:0\)

\(\displaystyle \;\;\)and has two roots: \(\displaystyle \,t\,=\,1\,\) and \(\displaystyle \,t\,=\,4\).
 
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