Help Josh and Zach are painting a dog house. If Josh painted the house on his own,
it would take him 6 hours. If Zach painted the house on his own, it would take
him 4 hours. How long will it take them to paint it together?

5 I'm assuming

Step-by-step explanation:

6 + 4 = 10. Since there's 2 people you divide it by 2 so 5 hours.

5 hrs

Step-by-step explanation:

We need to take the average of time for both of them

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