Find the radius and center of the circle given by the equation below. (x – 6)2 + (y + 4)2 = 7 r = √7 and center at (-4, 6) r = 7 and center at (6, -4) r = 7 and center at (-6, 4) r = √7 and (6, -4)

r = , centre = (6, - 4 )

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

with (h, k) the coordinates of the centre and r the radius

(x - 6)² + (y + 4)² = 7 ← is in standard form

with centre = (6, - 4) and r² = 7 , hence r =

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