A flagpole casts a shadow that is 12 ft long. A 6-ft tall man casts a shadow
that is 8 ft long. The two triangles created are similar. How tall is the
flagpole?

9ft

Step-by-step explanation:

Since the triangles are similar, the corresponding sides are proportional.

Let the height of the flag pole be x feet.

We multiply both sides by 6 to get:

We reduce the fraction to get:

We now simplify

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

answer: when you burn wood, the carbon reacts with the oxygen in the air to create ash and smoke. that is a permanent change you cannot undo that.

step-by-step explanation: