Black diamond ski resort charges $50 for ski rental and $15 an hour to ski, bunny hill ski resort charges $75 for ski rental and $10 an hour to ski create an
equation to determine at what point the cost of both ski slopes is the same
15x - 75 = 10x - 50
15x - 50 = 10x - 75
15x + 50 = 10x + 75
15x + 75 = 10x + 50

  15x + 50 = 10x + 75

Step-by-step explanation:

The cost at Black Diamond for ski rental and x hours of skiing is ...

  50 +15x

The cost at Bunny Hill for ski rental and x hours of skiing is ...

  75 +10x

These costs will be equal when ...

  15x + 50 = 10x + 75

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