Question

A radar transmitter on a ship has a range of 15 nautical miles. If the ship is located at a point (227, 33) on a map, write an equation for the boundary of the area within the range of the ship's radar. Assume that all distances on the map are represented in nautical miles. The equation that represents the boundary of the area within the range of the ship's radar is?

Answer 1

The equation for the boundary of the ship's radar range is (x - 227)^2 + (y - 33)^2 = (15 * 1852)^2.

Step-by-step explanation:

To write an equation for the boundary of the area within the range of the ship's radar, we first need to understand the concept of a circle. The equation of a circle with a center at (h, k) and a radius r is given by (x - h)^2 + (y - k)^2 = r^2. In this case, the ship's location is (227, 33) and the range is 15 nautical miles. Since 1 nautical mile is equal to 1852 meters, the range can be converted to meters by multiplying it by 1852. Therefore, the equation for the boundary of the ship's radar range is (x - 227)^2 + (y - 33)^2 = (15 * 1852)^2.