Question

A farmer is building a circular corral to hold livestock. With distances measured in meters, the shape of the corral is modeled by the equation x²+y²=130. Find the length of fencing required for this corral.

a) 2π √ 130 meters, 65π square meters
b) 4π √ 130 meters, 1130π square meters
c) 2 √ 130 meters, 130π square meters
d) 2π √ 65 meters, 65π square meters

Answer 1

The length of fencing required for the circular corral, modeled by the equation x²+y²=130, is 2π √ 130 meters. The area of the corral is 130π square meters.

The correct answer is option a) 2π √ 130 meters, 65π square meters.

Step-by-step explanation:

The equation given, x²+y²=130, represents a circle in a coordinate plane where 130 is the radius squared (r²).

To find the length of fencing required, which is the circumference of the circle, we use the formula 2πr.

First, we find the radius by taking the square root of 130, which gives us √130, and this value of r is then substituted into the circumference formula.

Therefore, Circumference = 2π√130, which simplifies to 2π √ 130 meters. This is the length of fencing required for the circular corral.

As for the area of the corral, which represents the amount of space inside the circular fence, we use the formula πr². Substituting r with √130 gives us Area = π(√130)² = 130π square meters.

Therefore, the correct answer for the length of fencing and the area of the corral is a) 2π √ 130 meters, 65π square meters.

Answer 2

The length of fencing required for the circular corral is 2π√130 meters.

Step-by-step explanation:

To find the length of fencing required for the circular corral, we need to find the circumference of the circle. The equation for the corral is x²+y²=130, which represents a circle with a radius of √130. The formula for the circumference of a circle is C = 2πr, where r is the radius. Plugging in the value of the radius, we get C = 2π√130. Simplifying this expression gives us an answer of 2π√130 meters for the length of fencing required.