Shared Flashcard Set

Details

Product over Sum or Difference
Rate of Work, Parallel Circuit Resistance, and Focal Problems
15
Mathematics
10/05/2013

Term
 24/7 hours or 3 3/7 hours(Take Product over Sum: 8*6/(8+6) and simplify)
Definition
 Working alone, Jim works a job in 8 hours. Working alone, Jane works a job in 6 hours. If they work together, then how long does it take to do the job?
Term
 5 hours (Take Product over Difference: 4*20/(20-4) and simplify)
Definition
 Working together, Jim and Jane work a job in 4 hours. Working alone, Jane takes 20 hours to do the job. How long does it take Jim to work the job working alone?
Term
 12 ohms (Take Product over Sum: 20*30/(20+30) and simplify)
Definition
 A parallel circuit has two branches with resistances of 20 and 30 ohms, respectively, in the branches. What is the effective resistance of the parallel circuit?
Term
 90 ohms (Take Product over Difference: 36*60/(60-36) and simplify)
Definition
 A parallel circuit has an effective resistance of 36 ohms. One branch has a resistance of 60 ohms. What is the resistance in the other branch?
Term
 25/13 feet or 1 12/13 feet (Take Product over Sum: 50*2/(50+2) and simplify)
Definition
 What should the focal length of a lens be if an object 50 feet away from the lens is to be projected on a surface 2 feet away from the lens?
Term
 10 feet (Take Product over Difference: 40*8/(40-8) and simplify)
Definition
 A lens has a focal length of 8 feet. An object is 40 feet away from the lens. How far from the lens should the film be from the lens so that the object is in focus?
Term
 1/f = 1/do + 1/di
Definition
 What is the formula that relates the focal length f of a lens to the distance do from the object to the lens to the distance di from the image of the object to the lens?
Term
 f = (do*di)/(do + di), which is a product over sum
Definition
 What formula is obtained when one solves 1/f = 1/do + 1/di for f?
Term
 do = (f*di)/(di - f), or di = (f*do)/(do - f), both of which are a product over difference
Definition
 What formula is obtained when one solves 1/f = 1/do + 1/di for do (or di)?
Term
 1/t = 1/t1 + 1/t2
Definition
 What is the formula that relates the time t1 it takes a person to do a job by themselves, the time t2 it takes another person to do a job by themselves, and the time t it takes to do the job when the two people work together?
Term
 t = (t1*t2)/(t1 + t2), which is a product over sum
Definition
 What formula is obtained when one solves the equation 1/t = 1/t1 + 1/t2 for t?
Term
 t1 = (t*t2)/(t2 - t), or t2 = (t*t1)/(t1 - t), both of which are a product over difference
Definition
 What formula is obtained when one solves 1/t = 1/t1 + 1/t2 for t1 (or t2)?
Term
 1/r = 1/r1 + 1/r2
Definition
 What is the formula that relates the effective resistance r of a parallel circuit with 2 branches, the resistance r1 in the first branch, and the resistance r2 in the second branch?
Term
 r = (r1*r2)/(r1 + r2), which is a product over sum
Definition
 What formula is obtained when one solves the equation 1/r = 1/r1 + 1/r2 for r?
Term
 r1 = (r*r2)/(r2 - r), or r2 = (r*r1)/(r1 - r), both of which are a product over difference
Definition
 What formula is obtained when one solves 1/r = 1/r1 + 1/r2 for r1 (or r2)?
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