My mom built a new sandbox that is 3 \text { m}3 m3, start text, space, m, end text long, 2 \text { m}2 m2, start text, space, m, end text wide, and 1 \text { m}1 m1, start text, space, m, end text high for my sister and me. Sand for the sandbox costs \$4.50$4.50dollar sign, 4, point, 50 per cubic meter. How much will it cost to completely fill the sandbox with sand? \$$dollar sign

$27

Step-by-step explanation:

The dimensions of the sandbox (that is a rectangular prism) are 3m x 2m x 1m.

We need to first find the volume of the sandbox.

The volume of a rectangular prism is:

V = L * W * H

where L = length

W = Width

H = height

The volume of the sandbox is:

V = 3 * 2 * 1 =

Sand for the sandbox costs $4.50 per cubic meter.

The cost to completely fill the sandbox is:

4.50 * 6 = $27

8y^50

step-by-step explanation:

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