The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width. Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height.

Write the equation that represents the volume of the storage container in terms of its width.

A.
V = 6w2 + 12w
B.
V = 6w2 - 12
C.
V = 6w2 + 12
D.
V = 6w2 - 12w

A

Step-by-step explanation:

Step 1, setting variables:

We already know the exact height of the prism: 6 feet. We can set the unknown width as variable x, and length as x+2 (length is two feet more than width).

Step 2, writing equations:

Great! We have everything now. Let us write the equation by substituting our variables in:

Ok! Let us expand the equation:

I hope this helps! Let me know if you have any questions :)

2

step-by-step explanation:

1+1=2

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