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February 7th, 2017, 06:48 AM   #1
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Unhappy Application in real life of Derivatives

A train starting @noon, travels north at 40m/hr. Another train, starting from the same point @2pm travels east at 50m/hr. Find to the nearest mile/hr how fast the train are separating @3pm.



How should I do this? please explain to me of how or what should I do to answer this? ㅠㅠ
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February 7th, 2017, 07:04 AM   #2
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Set up equations, let $t=0$ be noon and the starting position at the origin.

Train #1 ...

$y = 40t$

Train #2 ...

$x = 50(t-2)$

Distance between the two is $s=\sqrt{x^2+y^2}$

Determine the value of $\dfrac{ds}{dt}$ at time $t=3$
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February 7th, 2017, 07:59 AM   #3
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Should I use Pythagorean for finding ds/dt?
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February 7th, 2017, 08:10 AM   #4
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Quote:
Originally Posted by SlayedByMath View Post
Should I use Pythagorean for finding ds/dt?
Pythagoras was used to find $s = \sqrt{x^2+y^2}$. The difficult part is done ... it's all set up for you.

you have two ways to go with this ...

1. take the implicit derivative w/r to time, i.e.

$\displaystyle \frac{d}{dt}\left(s = \sqrt{x^2+y^2}\right)$

2. take the explicit derivative w/r to time ...

$\displaystyle \frac{d}{dt}\left(s = \sqrt{[50(t-2)]^2+(40t)^2}\right)$

Remember that you're finding the value of $\displaystyle \frac{ds}{dt}$ at $t=3$, which also means you'll need the values of $x$ and $y$ at that time also if you go the implicit route.

Do not substitute values in until after you find the derivative.
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Last edited by skipjack; April 24th, 2019 at 12:23 AM.
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February 7th, 2017, 08:13 AM   #5
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Oh~ Thanks a lot! ^^
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April 17th, 2019, 08:41 PM   #6
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Hello, can you help me show the solution of this problem, please?

Last edited by skipjack; April 24th, 2019 at 12:22 AM.
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April 18th, 2019, 04:56 AM   #7
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Quote:
Originally Posted by Awniyan View Post
Hello, can you help me show the solution of this problem, please?
What have you tried to determine $\displaystyle \frac{ds}{dt}$ at the specified time?

Last edited by skipjack; April 24th, 2019 at 12:22 AM.
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April 23rd, 2019, 05:54 PM   #8
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I always find the explicit form bad practice. It’s a related rate. Set up the total differential then take the derivative with respect to time. However, the OP struggled with the explicit case and absconded when no solution was given.
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April 24th, 2019, 08:19 AM   #9
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Quote:
Originally Posted by NineDivines View Post
I always find the explicit form bad practice. It’s a related rate. Set up the total differential then take the derivative with respect to time. However, the OP struggled with the explicit case and absconded when no solution was given.
How do you know the OP struggled with the explicit case? No attempts at working the problem or follow-on queries were made by either the OP or the second poster.

To say one method is "always" bad practice is rather presumptuous, don't you think? Sometimes, using both explicit & implicit methods helps to confirm a solution.
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April 25th, 2019, 04:46 PM   #10
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I wouldn't say bad practice; I'd consider it a habit for the less able. A lot of knowledge can be expressed implicitly in a statement two inches in length.
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