Sam and you are going to paint your room together. Sam takes 10 minutes to paint 25 square feet. It takes you 5 minutes to paint 25 square feet. Sam says, "If we paint together, then it will take 15 minutes for us to cover 50 square feet." Give an explanation to convince Sam that she is incorrect.

well sam it took you 10 minutes to paint 25 square feet while i did it in 10. so if we both spent 15 minutes painting then i would cover 75 square feet while you would cover about 38 square feet.

Step-by-step explanation:

paula, cory, and krista

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