Two phone companies, Unitel and Cellberry, offer different cell phone data plans. Unitel's plan charges $19.95 per month and $14.95 for each gigabyte of data. Cellberry's plan charges $9.95 per month and $17.50 for each gigabyte of data. a. Write a system of equations to represent the two plans and solve it by graphing.

b. Interpret the solution to the system. How many gigabytes do you get when the two plans cost the same amount. What will the cost of the plans be?

c. If you need more than 3.92 gigabytes of data, which company should you choose.

For The First Question a Part Do You Need a Graph ?

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