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September 19th, 2016, 11:19 AM   #1
MBI
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Hey guys. How would I go about solving this?

A falling object travels a distance given by the formula
d = 2t + 16t^2,
where t is measured in seconds and d is measured in feet. How long will it take for the object to travel 68 ft?

I don't even know where to start lol.
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September 19th, 2016, 11:24 AM   #2
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Can you solve

$68 = 2t + 16t^2$
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September 19th, 2016, 11:31 AM   #3
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Quote:
Originally Posted by JeffM1 View Post
Can you solve

$68 = 2t + 16t^2$
No. I am honestly not too sure. How would I even go about doing that? I Know that I can't combine terms that aren't alike. I'm so lost right now.
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September 19th, 2016, 12:04 PM   #4
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You should not have been given this problem if you have not studied the quadratic formula.

Do you understand why $68 = 2t + 16t^2$ is correct?

You can rearrange that to get $16t^2 + 2t - 68 = 0.$

That is STANDARD FORM for a quadratic equation.

You can solve any quadratic equation in standard form using the quadratic formula. So here goes.

$ t = \dfrac{-\ 2 \pm \sqrt{2^2 - 4(16)(-\ 68 )}}{2 * 16} = \dfrac{-\ 2 \pm \sqrt{4 + 4352}}{32} = \dfrac{-\ 2 \pm 66}{32} \implies$

$t = \dfrac{64}{32} = 2.$
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September 19th, 2016, 12:47 PM   #5
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to solve $16t^2+2t=68$

we simplify by 2 to get

$8t^2+t-34=0$

$8t^2-32+t-2=0$

$8(t+2)(t-2)+(t-2)=0$

$(t-2)(8(t+2)+1)=0$

$(t-2)(8t+17)=0)$

thus $t=2 s$
$-17/8$ can't be a solution.
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September 19th, 2016, 08:40 PM   #6
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Quote:
Originally Posted by abdallahhammam View Post
to solve $16t^2+2t=68$

we simplify by 2 to get

$8t^2+t-34=0$

$8t^2-32+t-2=0$

$8(t+2)(t-2)+(t-2)=0$

$(t-2)(8(t+2)+1)=0$

$(t-2)(8t+17)=0)$

thus $t=2 s$
$-17/8$ can't be a solution.
The student just learning how to solve a quadratic equation wouldn't be adequately helped with those series of steps,
because there is no motivation as to why you knew to split up -34 into those particular numbers.
It may be natural for you, though, if you've been doing it this way off and on for years.

Also, this step inserted between the second and the third steps makes it flow better:

$\displaystyle 8(t^2 - 4) + t - 2 = 0$
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