A person who is 6 feet tall walks away from a flagpole toward the tip of the shadow of the flagpole. When the person is 12 feet from the flagpole, the tips of the person's shadow and the shadow cast by the flagpole coincide at a point 3 feet in front of the person.

h = 29.4 f

Step-by-step explanation: (see annex)

I conclude the question of the problem is the height " h " of the flagpole

From the draft in annex, is clear the angle ABC is common to the triangles

ABC and BDE

In triangle BDE  

BE = √ (3)² + (6)²         ⇒ BE = √9 + 36       ⇒BE = √45

BE = 6,71 f

then      sin ∠ ABC  =  6/6.71     ⇒   sin ∠ ABC  = 0,89

then arcsin 0,89      ∠ABC  =  63°

Now in triangle ABC

tan  ∠ ABC  = h/( 12 + 3 )        ⇒   tan  ∠ ABC  = h/15

tan ∠ 63°   =  1.96

Then       1.96  =  h/15

h  =  1.96 * 15

h = 29.4 f

x divided by 8=y

step-by-step explanation:

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.