Question

prosze o pomoc z matematyki ;) cześć 2 . wszystko jest w załączniku ;)

Answer 1

1)  a)  (0,8:2½)·(2,2 - 1i7/40 ) = (0,8 : 2,5) · (2,2 - 1,175) = (8:25)· 1,025 = 0,32 · 1,025 = 0,328

    

      b) ∛(-2i10/27) - (-4/3)⁻² : 9⁻³/² = ∛(-64/27) - (-¾)² : (1/9)³/² = -4/3 -9/16 : (√(1/9) )³ =

           = -1⅓ - 9/16 : (⅓)³ = -1⅓ -9/16 : 1/27 = -1⅓ - 9/16 · 27 = -1⅓ - 243/16 = -1⅓ - 15 i 3/16 =

           = -1 i 16/48 - 15 i 9/48 = -16 i 25/48

      c)  ∛(8/125) - ∛(2i10/27) = ⅖ - ∛(64/27) = ⅖ - 4/3 = 6/15 - 20/15 = -14/15

      d)  (⅔)⁻² · (1⅓)⁻¹ - (3⁻¹ - 2⁻¹)⁻² = (3/2)² · (4/3)⁻¹ - (⅓ - ½)⁻² = 9/4 ·¾ - (2/6 - 3/6)⁻² = 27/16 -(⅙)⁻² =

            = 1 i 11/16 -6² = 1 i 11/16 - 36 = -34 i 5/16

      e)  I 10 - 6I - I 8 - 10I = I4I - I -2I = 4 - 2 = 2

 

2)      5-√2               (5-√2)(3+√2)                        15+5√2-3√2-2                   13+2√2

        --------------- =  ------------------------------ = ----------------------------------- = ---------------------

         3-√2                (3-√2)(3+√2)                             9 - 2                                   7

 

3)    (9·27⁻²) : (3·81)⁻²                      [3²·(3³)⁻²] : (3·3⁴)⁻²                     (3²·3⁻⁶) : (3⁵)⁻²        

       ------------------------------------ =  ---------------------------------  = ---------------------------------------- =

               9⁻⁴                                          (3²)⁻⁴                                           3⁻⁸

           

        3⁻⁴ : 3⁻¹⁰                   3⁶

   = ----------------------- = ------------- = 3¹⁴

          3⁻⁸                          3⁻⁸

4)   A=<-1, 3),   B = <1, ∞)                                                        I-------------------------------

                                                                               I----------------I----------------I

                                                               -------------I----------------I----------------I------------------->

                                                                              -1                  1                   3

        A U B = <-1,∞)

        A n B = < 1, 3)

        A \ B = < -1, 1 )

        B \ A = < 3, ∞)

5)     I 2x -3I ≥ 2

              2x -3 ≥ 2        ∨       2x -3  ≤ -2

               2x ≥ 5   /:2                2x ≤ 1     /:2

                 x ≥ 2½                       x ≤ ½

                     ----------------------I                   I--------------------------

                     ----------------------I---------------I-------------------------->

                                                ½                2½

         Odp.   x ∈ ( -∞, ½ > U < 2½, ∞)