(Absolute value inequalities) 50 points!

-6|4p+2|+8 > -34

Step-by-step explanation:

1) Subtract 8 from both sides.

2) Simplify -34 - 8 to -42.

3) Divide both sides by -6.

4) Two negative numbers makes a positive.

5) Simplify 42/6 to 7.

6) Rewrite the inequality without the absolute value.

7) Subtract 2 from the whole equation.

8) Simplify.

9) Divide the whole equation by 4.

Therefor, the answer is - 9/4 < p < 5/4.

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