In a circle, an arc length of 6.6 is intercepted by central angle of 2/3 radians. Determine the length of the radius.

9.9

Step-by-step explanation:

To solve this problem, we first need to know that the whole length of the circunference is related to a central angle of 2pi radians. Then, we can solve using a rule of three to find the radius:

arc of 6.6 -> central angle of 2/3

arc of 2*pi*r -> central angle of 2pi

2*pi*r * (2/3) = 6.6 * 2*pi

r * (2/3) = 6.6

r = 6.6 / (2/3) = 9.9

So the length of the radius is 9.9

on friday there were 15 birds

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