Page 41 - WCS - Electrical
P. 41

28+
                     +
                 4
                 56
                     −
                 4

               -
                 9
                +
               − 96
                28+ + + - 72 = = = = + −8 7 14
                     +16
                   =
                     7
                4 28
               +  + − 6  20 7
               5y
                56 =
                     +
              +
                  =
          WORKSHOP CALCULATION & SCIENCE  - CITS
                 4 28
                      14
                +  +
                     −
                   =
                5
                    5 7
                    =
                     +
               x 4
                +
              - - + - + 4 56 = = −8 − 14
               72
                 4 56
               + - 4 9 72  = − 14
                  4
                 -
               5x =
              − 96
           Division = = 25 −8
                 9 72
                + -
                    +16
                5
               − 6 96  = 5−8
               −
               10a 9
           1   5y − − + = 6 96 20+= 16
                2a
                    =
               5 5y  5 20 +16
                 8ac = 6
                −
               x − 5 5y  5 20
                 2bc =
               -3ax ÷ -6x
           2   4x 5m −×5 6n − 7p
               −5
              5x  =  25
               4 x
                    28mn
               5 5x  − 20
                    5 25
                4
               5a + =
               15xy ÷ -5
           3  10a    5 25
                5 5x
               7a + =
               2a m 5  28 5
               10a
               a 8ac
                10a
              − 2a  = a m− n
                 8a
           4     n 2bcc
              − − a 2a  6n − 7p
                5m −×
                3
                 8ac
               2 2bc 2 − 6n −−  2 = 7p 1  2
                     3
                −
                           2 =
               −
                  − ×
                  =28mn
                 5m
                22bc
           5  5a + 20 28mn 7p6n −−×
               2
                −
                 5m
                   −
                  2×
               2×
              7a ++ 28 20 2  =  8  = 2
               5a
                   −
                     28mn
                m
                 2×
                   28 20
              a 5a + 2  m− n 4
               7a +
           6    n = a a  n
                m
                    
                  = 28
               a a n a 7a + =  m−
                       n
                    a
                n 3 m
                     b 
               b 2 n = =  3 m− n  2 = 2
                a
                            1
                a
                     a
                   2 −
                        2 2 =
                3 3 n
                           2×
                              2
                                  4
                     2 
                    
               2 2 2 a
                     3
                             1
              2
           Algebra - Theory of indices, Algebraic formula, related
                  = =
                                = 2
                         = 2 ==
                        2
                     2 −
                 3
                    2
                        8
                2 2×
              2×
                 2 2
                                  9
                              3
                           3× 1
                     3
               3 2
                           2
                         =

                     3  =
                                2
                   =
                         2 =
                            2 =
                    2 −
                 n 2×
                      1 48
                   2 2
                2×
                − 2× 2
           problems         2 2
                2
                      n =
                   =
                          =
               a n
                        4 8
                      n  2
                   ×
              a 2× 22×
                    a 2
                     a
                           =
                   
                       =
                 =
                       n
                      1
                n
                n a 2×
                 2 b  a  42
                − 
               2 b
                   =
                  =
           Calculations involving powers
                    
                       n
                 n
                     2 2  
              2 b 3 n a  =     b a 2 2    2× 2  4
                   2 
                   
                         =
           Power : Concept 2  32 =  94
                  =
                        2
                       
                        7 
                    
                 3  b 
                3 n
                2 2 b
                          3× 2×
                1   2 
                    3 
               a.a.a... upto n  times is = a
                3  n 2 3  =    =    2  =  3 2 =  9 4  n
                       
               −2
                        4  2×
                 4  1 2 
              a3  =  3    3×  =
                      49 =
                  7 
                   =
               7
                 × n 2
                     n 1
                                  9
                              3
                            3×
                    = a 3 
               a 3 − a is the base, n is the exponent.
                     
                   =
                      16
               4
                  4 1 n 1
                 2
               −
                  n
                 −
              2
                  = a
                    =
               a
           When a number, say 2 is multiplied by itself 4 times, we write it as 24 (two to the power of 4) and it is equal to
                     2 1 n
                    2
               2 − 2  = a
                          2
                   2
                      2 1
           2 x 2 x 2 x 2 = 16.
               −
                       7 
                3  2
                       2
                2
                    =
                      
                    =
              
               1  2
                          2
                       2
                      
                       4  7 
                4  3  2
              
           The exponent denotes how many times the base number is multiplied by itself.
              7   1  2 =   4   2
                     49
                  7
                 4 3 
                        7 
               
                    = 
                       
                ×
           Powers with a positive base have a positive result.
                      =
                          
                1 
                
                       
                     16 49
                  47
              47
                  4 
                
                       
                         4 
                    =
                 ×
               4 7
                   4 7
           Powers with a negative base and with an exponent that is even will have a positive result.
                      16 49
                 ×
                     =
                4
           The sign  4  16
               (+a)   =       a n
                    n
               (– a)   =      a 2n
                    2n
               (2)     =      2 x 2 = 4 and
                  2
               (– 2)    =     – 2 x – 2 = +4 but
                    2
               (– 2)    =     – 2 x – 2 x – 2 = – 8
                    3
           Addition and subtraction of powers
           Powers with the same base and exponents can be added or subtracted by addition or subtraction of the coefficients.
               x.a  + y.a n   =      a  (x + y)
                                      n
                  n
               x.a  – y.a     =      a  (x – y)
                                      n
                  n
                       n
               Ex .4x  + x  – 3x  = x  (4 + 1 – 3) = 2x .
                              2
                     2
                                  2
                         2
                                                 2
           Multiplication
           Powers with the same bases are multiplied by involving the common base raised to the power of sum of the
           exponents.
                                                           28
                                            CITS : WCS - Electrical - Exercise 4
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