A rectangular prism is made of 81 unit cubes. The prism is 9 unit cubes long. Choose two sets of numbers that could be the width and the height of the rectangular prism.

A width: 3 unit cubes

height 3 unit cubes

Width 6 unit cubes

height 12 unit cubes

Cwidth: unit cubes

height 7 unit cube

width: 18 unit cubes

height 4 unit cubes

OE with 24 unit cubes

height 3 unit cubes

A width: 3 unit cubes

height 3 unit cubes

Step-by-step explanation:

Volume of rectangular prism = 81 unit cubes

= Length of rectangular prism = 9 unit cubes

= Width of rectangular prism

= Height of rectangular prism

Volume of a rectangular prism is given by

The product of width and height must be 9 so from the options this is only possible when width and height both are 3 units.

So, the width is 3 unit cubes and the height is 3 unit cubes.

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

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step-by-step explanation: