Bosco

   What is the square root of 2,000,000,000,000,000,000,000,000,000,000,000,000,000,000?     

   There are 42 zeros.  Therefore, the square root is sqrt(2) x 10²¹     

   _.     

   A shell fits into a golden rectangle 8 inches long. What is the shell's width? Simplify to the most simplified radical.     

   The Length to Width ratio of a Golden Rectangle is 1.618 to 1.     

   The Width of the rectangle in this problem is 8 / 1.618 = 4.944.     

   You might wish to round 4.944 to 5 to observe significant digits.     

   _.     

   The diameter of a wheel is 8 inches.     

   The wheel makes 87 complete revolutions along the length of a path.     

   To the nearest foot, how long is the path?     

   8 in • 3.1416  =  25.1328 in     

   25.1328 in • 87  =  2186.5536 in     

   2186.5536 in / 12 in/ft  =  182.21278 ft     

          to the nearest foot is 182 ft     

   _.     

   Janine is 7 years younger than Lucy and 4 years older thanSamantha.     

   The average of their ages is 16.   What are their ages?     

   J = L – 7                   ==>   L = J + 7     

   J = S + 4                   ==>   S = J – 4     

   (J + L + S) / 3 = 16    ==>   J + L + S = 48     

                                              (J) + (J + 7) + (J – 4)  =  48     

                                                                     3J + 3  =  48     

                                                                     3J        =  45     

                                                                             J  =  15     

                                                                             L  =  J + 7  =  15 + 7     

                                                                             L  =  22     

                                                                             S  =  J – 4  =  15 – 4     

                                                                             S  =  11     

   _.     

     JDI  =  39^o     

     JID  =  180^o – 105^o  =  75^o     

     DJI  =  180^o – (39^o + 75^o)  =  66^o     

     AJF  =  DJI    

     AJF  =  66^o     

     AJF is the same as the x requested     

     angle x  =  66^o     

   _.     

   how do we factor quadratic equations? for example how do we factor x2-9?     

   x² – 9 isn't a typica; example, but is a special case: "the difference of squares".     

   You recognize that x² is a square (duh LoL), also that 9 is a square, namely 3².     

   When you have the difference of squares, x² – y², you factor it as (x + y)(x – y).     

   The specific example you cited, x² – 9, this would be factored as (x + 3)(x – 3).     

   _.     

    olivia bought a music system worth $18,000 in the year 2001.     

    in 2003, a fire in her house destroyed the system. according to insurance,     

    the system depreciated by 6% each year. How much was her system worth in 2003?     

    $18,000 • (100% – 6%)²  =     

    $18,000 • (1.00 – 0.06)²  =     

    $18,000 • (0.96)²             =     

    $18,000 • 0.9216             =  $16,588.80     

   _.