50 points.
Find the area of the shaded regions:

18 pi cm^2

18 (3.14) =56.52 cm^2

or use the pi button 56.54866776 cm^2

Step-by-step explanation:

First find the area of the entire circle

A = pi r^2

A = pi 9^2

A = 81 pi

The area of a circle is 360 degrees.  The shaded area is 80 degrees

Take the fraction of the circle that is shaded and multiply by the total area

80/360 * 81 pi

2/9 * 81 pi

18 pi

We can approximate pi

18 (3.14) =56.52

or use the pi button

56.54866776

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