Bosco

   order of opperation     

   The standard is PEMDAS     

_.     

   A guy wire fastened 50 m from the base of a tower makes an angle of 55 degrees with the ground.     

   How high up is the tower does the guys wire reach?     

   tangent  =  opposite over adjacent     

   tan(55^o)  =  height / 50     

   1.4281    =  height / 50     

   height     =  (50) (1.4281)     

   height     =   71.405 rounds to 71.4 m     

 _.     

   simplify this expression (2x)^3     

   That's already about as simple as it gets.     

   Maybe 8x³ might be easier to understand.     

_.     

   find the sale price to the nearest cent     

   60% discount total discont is $32.50     

   ( retail price ) x ( discount pctg )  =  ( discount amount )     

                  Retail x 0.60  =  32.50     

                  Retail             =  32.50 / 0.60     

                  Retail             =  54.17     

     ( sale price )  =  ( retail price ) – ( discount amount )     

                  Sale price  =  54.17 – 32.50     

                  Sale price  =  21.67     

_.     

   It took a hockey puck 1.8seconds to slide from the center line to the goal line of a 61-meter-long hockey rink.     

   The puck slid from one line to the other at 15meterspersecond. What is the distance between the two lines?     

   Distance = Rate x Time     

   D  =  ( 15 m/sec ) • ( 1.8 sec )     

   D  =  27.0 m     

_.     

a driver covers 100 miles in 4 hours. during the first hour he rode 16 3/4 miles;during the second hour , 25 1/2 miles; and during the third hour 21 1/8 miles. how many miles did he ride during the fourth hour?     

This is just arithmetic.  4th leg = (total distance) minus (distance already travelled)     

4th  =  100 – ( 16³/₄ + 25¹/₂ + 21¹/₈ )     need equivalent fractions with a common denominator     

       =  100 – ( 16⁶/₈ + 25⁴/₈ + 21¹/₈ )     

       =  100 – ( 62¹¹/₈ )     

       =  100 – ( 63³/₈ )     

       =  36⁵/₈ mi     

_.     

The first term of a geometric sequence is 48, and the 5th term of the sequence is 24316 . What are the geometric means between these terms?      

I don't know what a geometric mean is,     

but, if it's asking for the common ratio, then     

   1st term       48    

   2nd term      48 • r     

   3rd term      (48 • r) • r     

   4th term      (48 • r • r) • r     

   5tth term     (48 • r • r • r) • r     

   48 r⁴  =  24,316     

        r⁴  =  506.5833     

        r    =      4.7442     

_.     

   A right circular cylinder has a height of 2214 ft and a diameter 225 times its height. What is the volume of the cylinder?     

   V  = π r² h     

   r  =  (1/2) • (diameter)  =  (1/2) (225 • 2214)  =  249,075     

   V  =  (3.1416) (249,075²) (2214)     

   V  =  (3.1416) (62,038,355,625) (2214)     

   V  =  431,507,931,441,741 ft³