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 November 11th, 2012, 04:55 PM #1 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 A particle moving around a circle and a point Problem says: A particle is traveling around the cirlce x^2 + y^2 =25 where x and y are measured in inches. At the instant the particle is at the point (3,4), dx/dt = 7/sec. Find dy/dt at this time ???
November 11th, 2012, 05:11 PM   #2
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Re: A particle moving around a circle and a point

Quote:
 Originally Posted by mathkid Problem says: A particle is traveling around the cirlce x^2 + y^2 =25 where x and y are measured in inches. At the instant the particle is at the point (3,4), dx/dt = 7/sec. Find dy/dt at this time ???
You can solve this using implicit differentiation with respect to t ...

$\frac{d}{dt} \ (x^2+y^2) \= \ \frac{d}{dt} \ (25)$

$2x \frac{dx}{dt} \ + \ 2y \frac{dy}{dt} \= \ 0$

Divide out the constant 2, then plug in, there is only one unknown so you can solve for it.

 November 11th, 2012, 05:19 PM #3 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: A particle moving around a circle and a point wait do I take the dx or the dy over to the otherside of equation and then divide by 2? please show me so I can use as a key for future problems
 November 11th, 2012, 05:23 PM #4 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: A particle moving around a circle and a point wait I think I c so 2y dy/dy = -2x dx/dt dy/dt = -x dx/dt = dy/dt = -3 dx/dt dy/dt = -3(7/sec) dy/dt = -21 inches/ second holy ***** sh** its a miracle
 November 11th, 2012, 05:35 PM #5 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 Re: A particle moving around a circle and a point Did you confirm the answer in the back of the book? You made a small error, let's see if you can find it.
 November 11th, 2012, 05:37 PM #6 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: A particle moving around a circle and a point no even problems not in back of book I don't see the error tell me please
 November 11th, 2012, 05:43 PM #7 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 Re: A particle moving around a circle and a point mathkid, your work is only 5 lines, please check your work. You made an error in line 1 which you corrected in line 2, but you made another error in line 2.
 November 11th, 2012, 06:04 PM #8 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: A particle moving around a circle and a point ok Agent and TY for staying on me I c it 2x dx/dt + 2y dy/dt = 0 2y dy/dt = -2x dx/dt y dy/dt = -x dx/dt dy/dt = -x/y dx/dt dy/dt = (-3/4)(7/1) dy/dt = -21/4 = -5.25 in/sec
 November 11th, 2012, 06:23 PM #9 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 Re: A particle moving around a circle and a point Very good [color=#0000BF]mathkid[/color], i wouldn't be helping you learn if i simply handed all answers to you, I thought in this particular case you were capable of spotting your error if you took the time to go over your work. Spotting our own errors is a very important procedure when learning mathematics of any level.
 November 11th, 2012, 06:26 PM #10 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: A particle moving around a circle and a point TY I PROMISE I AM TRYING GOING ON 6HRS NOW WITHOUT MUCH OF A BREAK

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