What is the equation of the circle passing through the point (6,5) and centered at (3.-4)?

(x - 3)² + (y + 4)² = 90 or [3√10)²

Step-by-step explanation:

We need to calculate the radius of this circle.  To do this we calculate the distance from the center (3, -4) to the point (6, 5).  

As we move from (3, -4) to (6, 5), x (the run) increases by 3 and y (the run) increases by 9.  Thus, the distance between these points, according to the Pythagorean Theorem, is

r = √[3² + 9²], or r = √90, or r = 3√10.

Using the standard equation of the circle, (x - h)² + (y - k)² = r², we obtain

(x - 3)² + (y + 4)² = 90 or [3√10)²

the solution is h=10 because you add 9 to each side of the equation.

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