31º - Matemática

14/08/14

Exercícios

1- Calcule o valor de:

a) C7,5=   7!   =7.6.5=21

               7!-5!   2! 5! 

b) C6,3+C9,2=   6!  =6.5.4.3=20+  9!  =9.8.7=36 ->20+36=56
                         6!-3!    3! 3!           9!-2!  7! 2!

c) 2!C8,3+3!C7,4=   8!  =8.7.6.5=56+  7!  =7.6.5.4=35 ->112+210=322

                                8!-3!    5! 3!          7!-4!    3! 4! 

d)   C10,3  =

   C8,3-C5,3 

C10,3=   10!   =10.9.8.7=120

              10!-3!     7! 3!  

C8,3=   8!   =8.7.6.5=56

          8!-3!     5! 3! 

C5,3=   5!   =5.4.3=10

           5!-3!   2! 3!

  120  =120=2,6

56-10   46 

2- Resolver as equações:

a) An,2=56

   n!    -> n.(n-1).(n-2)!   -> n.(n-1)=56

 (n-p)             (n-2)!             8.(8-1)

                                              8.7=56

b) An,3=8.An,2

   n!   =8.   n!   ->  n!(n-2)! =8 -> (n-2).(n-3)!

(n-3)!     (n-2)!     (n-3)! n!               (n-3)!

                                                        n-2=8

                                                        n=8+2=10

  A10,3=8.A10,2

 10.9.8=8.10.9

     720=720