Aubrey has a new art box in the shape of a rectangular prism. The box is 12 cm by 20 cm by 5 cm. The only thing in the art box is a new pink eraser with the dimensions shown below.
0.5 cm
2 cm
4 cm
What is the volume of the art box not taken up by the eraser?

1196cm³

Step-by-step explanation:

Step 1

Find the volume of the Rectangular Prism = Length × Width × Height

Length = 12 cm

Width = 20 cm

Height = 5 cm

Volume of a Rectangular prism = 12 × 20 × 5

= 1200cm³

Step 2

Volume of the Eraser

The Eraser has the shape of a box.

Volume = Length × Width × Height

Length = 0.5 cm

Width = 2 cm

Height = 4 cm

Volume = 4cm³

Step 3

Find the volume of the art box not taken up by the eraser

Volume of the art box not taken up by the eraser = Volume of the Art box - Volume of the Eraser

= 1200cm³ - 4cm³

= 1196cm³

Therefore, volume of the art box not taken up by the eraser is 1196cm³

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

heyyy

step-by-step explanation: