3. the side of a square is 20 cm long. what is the circumference of the circle when …
a. the circle is inscribed within the square?
b. the square is inscribed within the circle?

a. 20π cm.

b. 20(√2)π cm,

Step-by-step explanation:

a. The diameter (d) of the circle = side of the square = 20 cm.

So the circumference =  π d = 20π cm.

b. In this case the diameter = the length of the diagonal of the square.

The diagonal = diameter of the circle =sqrt ( 20^2 + 20^2) = √800 = 20√2.

So the circumference = πd = 20(√2)π.

answer: 91

step-by-step explanation:

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