Acircle has an area of 20. what's the radius?

  2√(5/π) ≈ 2.523

Step-by-step explanation:

The radius can be found using the area formula:

  A = πr²

  20 = πr² . . . . . fill in the given value

  20/π = r² . . . . . divide by π

  √(20/π) = r = 2√(5/π) . . . take the square root and simplify

You can use your calculator to find a numerical value for this:

  r = 2√(5/π) ≈ 2.52313

Comment on the form of the answer

Radicals are often considered to be in simplest form when they do not contain fractions or square factors. Here, the "simpler" form would be ...

  r = (2/π)√(5π)

involving the irrational number π in two calculations. My preference for evaluating the expression for r is to leave it as √(20/π) or 2√(5/π).

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: 48

just remember to use pemdas:

parentheses

expressions

multiplication

division

addition

subtraction