The area that an Olympic swimming pool takes up is 1,250 m². Nick is installing a new pool in his yard to practice for his swim meets. The pool he is installing is similar to the Olympic pool, but one-third the dimensions. What is the area of Nick's pool?

Area of Nick's swimming pool = 417 m²

Step-by-step explanation:

Let a x b represent the dimension of an Olympic swimming pool

let 1/3(a x b) represent the dimension of Nick's swimming pool

Using direct proportion;

a x b 1250 m²

¹/₃(a x b) x m²

X = 1250 x ¹/₃(a x b) / a x b = 416.66667 m² ≅ 417 m²

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.