Which of the fallowing best completes the sequence 12,8,5, a) 1 b) 2 c)4 d)0

  B) 2

Step-by-step explanation:

The first differences are increasing by 1 from term to term:

8-12 = -4

5-8 = -3

3-5 = -2

2-3 = -1 . . . . . if the next term is 2, as we believe it should be.

Comment on number sequences

Any finite length sequence of n numbers can be modeled exactly by an n-1 degree polynomial. That is, a 4th-degree polynomial can be made to describe the sequence regardless of the next term you may choose.

If you choose the next term to be 2 as we suggest, then the sequence can be modeled by a 2nd-degree polynomial ...

  (n² -11n +34)/2 . . . . for n = 1, 2, 3, ...

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12