What are the center and radius of the circle defined by the equation x^2+y^2-6x+4y+4=0

Option B

center (3,2)

radius 3

Step-by-step explanation:

Given:

x^2+y^2-6x+4y+4=0

x^2+y^2-6x+4y=-4

Now completing square of x^2-6x by introducing +9 on both sides:

x^2-6x+9+y^2+4y=-4+9

(x-3)^2+y^2+4y=5

Now completing square of y^2+4y by introducing +4 on both sides:

(x-3)^2+y^2+4y+4=5+4

(x-3)^2 + (y-2)^2= 9

Now comparing with the circle equation:

(x-h)^2 + (y-k)^2= r^2

where

r= radius of circle

h= x-offset from origin

k= y-offset from origin

In given case

r=3

h=3

k=2

Hence, option B is correct with radius =3 and center =(3,2)!

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

the answer is 31.27mph