Buddy and Michael get into a snow fight with some boys on the
way home from school. It seems
as though Buddy can throw 4
times as many snowballs as the
boys can. If Buddy throws 1200
snowballs, how many did the boys
throw? Write an equation and
solve.

This means the boys throw 300 snowballs while Buddy throws 1200 snowballs

Step-by-step explanation:

Equations

Let's call

x = number of snowballs the other boys throw.

4x = number of snowballs Buddy throws.

We know Buddy throws 1200 snowballs, thus

4x = 1200

Divide by 4:

x = 1200/4

x = 300

This means the boys throw 300 snowballs while Buddy throws 1200 snowballs

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

details

step-by-step explanation: