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09062009, 01:15 PM  #1  
 
Class 3R Laser Join Date: Feb 2008 Location: Norfolk, Uk
Posts: 2,364
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Hey guys, I know many of you are geniuses. Can you help with my maths please? I have like 4 questions that I can't do. 1. Make f the subject of 1/f = 1/u + 1/v Basically I have no idea with this one. If I multiply by fuv, then it goes completely wrong. I remember something about just inverting it somehow so it is f/1 = u/1 + v/1, but don't know if this is possible 2. Simultaneous equations. I need to solve these. 2x  y+3=0 and y²  5x²=20 Thanks
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09062009, 01:38 PM  #2  
 
Class 2M Laser Join Date: Jun 2009
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i think this may be right 1/f=1/u+1/v 1/f=1/uv 1=f 1/uv (times both sides by f/1) UV=F (Times both sides by uv/1)
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09062009, 04:01 PM  #3  
 
Super Moderator Join Date: Mar 2008 Location: Sunny Southern California
Posts: 16,646
Rep Power: 823  EVERY "C" on my transcripts is from a math class. Peace, dave  
09062009, 10:30 PM  #4  
 
Class 3R Laser Join Date: Aug 2007
Posts: 2,046
Rep Power: 211 
2x  y + 3=0 and y²  5x² = 20 Separate variables of one equation: y = 2x + 3 Substitute to eliminate variable: y²  5x² = 20 = (2x + 3)²  5x² Simplify: (2x + 3)²  5x² = 4x² + 12x + 9  5x² = x² +12x + 9 = 20 Solve: x² +12x = 11 By inspection: x = 1. Plug back in: y = 2x + 3 = 2(1) + 3 = 5 x = 1, y = 5 The other problem: 1/f = 1/u + 1/v Multiply each part of the right side by 1: 1/f = (1/u)*(v/v) + (1/v)*(u/u) Simplify: 1/f = v/(uv) + u/(uv) = (u + v)/(uv) Invert both sides: f = (uv)/(u + v). That seems simple enough to me, do they want it any more simplified than that?  
09062009, 10:38 PM  #5  
 
Class 3R Laser Join Date: Aug 2007
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09072009, 02:19 AM  #6  
 
Class 4 Laser Join Date: Sep 2007 Location: Wisconsin
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My results mirror yours for the first problem. But for the second, you didn't use the quadratic equation. You're right up untill x² +12x = 11. From there we have x² +12x  11 = 0 b ± √(b² 4ac)  2a 12 ± √(12² 4(1)(11)) 2(1) 12 ± √(144  4x11) 2 12 ± √(100) 2 12 ± 10 2 Which solves as the points (1,5) AND (11,25). This becomes more evident when we graph both of the equations. The left graph is as it appears with xmin/max of 40 and ymin/max of 40. The right is zoomed in to better show where the lines intersect.  
09072009, 04:07 AM  #7  
 
Cereal Eater 
1. 1/f = 1/u + 1/v You can just invert it (everything ^1): f = u+v But you can always just: 1 = (1/u + 1/v)*f > 1/(1/u + 1/v) = f > u + v = f I don't know if that's what you were looking for here, I can do math in Spanish...now... in English... 2. PBD's approach is correct.  
09072009, 05:12 AM  #8  
 
Class 4 Laser Join Date: Sep 2007 Location: Wisconsin
Posts: 8,852
Rep Power: 1363  Quote:
You don't invert "everything," per se, you invert both sides, but that's just a shortcut for: w/x=y/z (*z): wz/x=y (*x): wz=xy (÷w): z=xy/w (÷y) z/y=x/w Now let's plug my number set (2,4,4) which works in the original equation into PBG's answer: f = (uv)/(u + v) 2 = (4*4)/(4 + 4) 2 = 16/8 Bingo Last edited by Cyparagon; 09072009 at 05:29 AM. Reason: grammar  
09072009, 06:02 AM  #9  
 
Class 3R Laser Join Date: Aug 2007
Posts: 2,046
Rep Power: 211  Quote:
Of course in our wonderful technological world, a calculator will solve all that for you, and save you time for more important things. But you should definitely learn to do it all by hand.  
09072009, 08:03 AM  #10  
 
Class 3B Laser Join Date: Apr 2009 Location: No. California
Posts: 2,577
Rep Power: 253 
Yeah, my math courses were a while back. Glad to see you were put on the right track!
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09072009, 11:41 AM  #11  
 
Class 4 Laser Join Date: Sep 2008 Location: Quebec, Canada
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Rep Power: 477  Hey Dave... does that mean all "other" subjects were better or worse.... Jerry
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09072009, 03:15 PM  #12  
 
Class 3B Laser Join Date: Nov 2008 Location: Germany
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1/f=1/u+1/v i dont think u can invert the part 1/u + 1/v without first doing v+u/v*u. So u do first v+u/v*u and then invert so it would be v*u/v+u. Like 1/f = 1/u + 1/v => 1/f = v+u/v*u => f = v*u/v+u It's the same process as trying to find a resistance to replace 2 others which are in parallel connection. 1/R = 1/R1 + 1/R2 => 1/R = R1+R2/R1*R2 => R = R1*R2/R1+R2 Last edited by Elektrotechniker; 09072009 at 03:18 PM.  
09092009, 05:09 PM  #13  
 
Cereal Eater 
Oh Chuck I just realized I made a BIG mitake, LOL I can't believe I passed Math Analysis II and couldn't invert that simple equation 1/f = 1/u + 1/v f = 1/(1/u + 1/v) Sorry for the previous mistake, man  
09092009, 06:54 PM  #14  
 
Class 2M Laser Join Date: Mar 2009
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BIG doesn't begin to describe it...
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