Toni's has a net cash inflow, excluding long-term financing expenses, for the quarter of $418.02. The beginning cash balance is $187.40. The firm has $546 in short-term debt with a quarterly interest rate of 1.2 percent. New company policy is to maintain a minimum cash balance of $140. How much does the firm need to borrow or how much can it repay on its loan to have a zero cumulative surplus for the quarter

The answer & explanation for this question is given in the attachment below.

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

add 8+12 to get a simplified answer of 12r-20