Bosco

   The variables x and y are inversely proportional.  If x = 1, then y = 2.  And if x = 2, then y = ___.     

   When two variables are inversely proportional, their product is always equal to a constant.     

   Given that when x = 1, then y = 2     

   In this problem, xy = 2 . . . and xy in this proportion must always equal 2.     

   When x changes to 2, then xy must still equal 2 ( y = 2 / x ) and so  y = 1     

   _.     

   The population of a town increased from 3550 in 2005 to 4400 in 2009.     

   Find the absolute and relative (percent) increase.     

   Absolute increase              4400 – 3550  =  850     

   Relative increase               850 / 3550  =  0.239  =  23.9%     

   _.     

   The store is selling lemons at $0.53 each.     

   Each lemon yields about 2 tablespoons of juice.     

   How much will it cost to buy enough lemons to make two 9-inch lemon pies, each requiring half a cup of lemon juice?     

   Two pies, requiring half a cup each, equals 1 cup of juice is needed.     

   My Betty Crocker cookbook says there are 16 tablespoons in 1 cup.     

   At 2 tbsp per lemon, you will have to buy 16 / 2 lemons = 8 lemons.     

                                               8 lemons • 0.53 $ / lemon  =  $ 4.24     

                                               plus sales tax, if applicable     

   _.     

   If we increase a by 10%, then we obtain b.     

   If we increase b by 10%, then we obtain c.     

   Overall, we can obtain c by increaseing a by ___ %.     

   a • 1.10  =  b     

   b • 1.10  =  c     —>     (a • 1.10) • 1.10  =  c     

                                        1.10 • 1.10  =  1.21  =  121%     

   _.

I think 4 is not.  I think that would be directly proportional.     

The problem:  The variables x and y are inversely proportional.  If x = 1, then y = 2.  And if x = 2, then y = ___.     

Definition:  When two variables are inversely proportional, their product is always equal to a constant.     

                  For a colloquial visualization of the concept, consider:  When x gets larger, y gets smaller.     

                   Given that when x = 1, y = 2     This xy = 2 . . . and this xy will always equal 2.     

                   When x changes to 2, the product xy must still equal 2, i.e., y = 2/2, so  y = 1     

   _.     

   How long does it take to get hot water to a 1.5 gpm faucet if there is 13 ft of 3/4" copper pipe

   and 8 ft of 1/2" copper pipe to the faucet?     

   The time for it to reach full temperature due to pipe temperature is not an issue at this point.     

   For these calculations, we assume the measurement of the pipe to be inside diameter.     

   13' of 3/4" copper pipe       V  =  (π)  •  (3/8 in)²  •  (13 ft • 12 in/ft)     

                                             V  =  (3.1416)  •  (9/64)  •  (156) in³     

                                             V  =  68.92 in³     

   8' of 1/2" copper pipe         V  =  (π)  •  (1/4 in)²  •  (8 ft • 12 in/ft)     

                                             V  =  (3.1416)  •  (1/16)  •  (96) in³     

                                             V  =  18.85 in³     

   total volume                       V  =  68.92 in³ + 18.85 in³     

                                              V  =  87.77 in³     

   Per the conversions in my Chemical Rubber Book, 1 cubic inch holds 0.004329 gallon.     

   convert to gallons              V  =  87.77 in³  •  0.004329 gal/in³       

                                             V  =  0.38 gal     

   time to flush line                T  =  0.38 gal / 1.5 gal/min     

                                             T  =  0.25 min     

   _.     

   what is the Least Common Multiple of six and twenty?     

   60 is the smallest integer that is evenly divisible by both 6 and 20.     

   _.     

   how do i do inverse of sine on the calc     

   Click the 2^nd function key.  The "sin" key changes to "asin"     

   which stands for arcsin, alternative nomenclatures for sin^–1     

   _.