Question

A pair of fire towers uses technology to search for forest fires. Let the center of the forest be the origin on a coordinate grid. The first fire tower is located 5 km east and 8 km south of the center, and the second fire tower is located 7 km west and 4 km north of the center. The technology at the first tower can locate fires within a radius of 10 km, and the second tower within a radius of 9 km. The system of inequalities represents this scenario.

At which location, from the origin, would a fire be detected by both towers?

O 2 km east and 3 km south
O 3 km east and 2 km north
O 2 km west and 1 km north
O 1 km west and 2 km south

Answer 1

Answer: D

Step-by-step explanation: I did it, it was 100%

Answer 2

The fire detected by both towers would be at the location 2 km west and 1 km north of the origin, which corresponds to the coordinates (-2, 1) on a coordinate grid.

Step-by-step explanation:

The question relates to the detection range of the two fire towers and where they would intersect. To solve this, we need to consider the coordinates and ranges of both towers.

The first fire tower is at coordinates (5, -8) with a detection radius of 10 km, while the second fire tower is at coordinates (-7, 4) with a detection radius of 9 km. We can plot these as circles on a coordinate grid and find their intersection points.

However, the question simplifies this process by providing us with options. We must determine which of these points would fall within both radii. After checking the distances from each fire tower to each given option, the fire detected by both towers would be 2 km west and 1 km north of the origin (-2, 1).

This can be calculated using the Pythagorean theorem to ensure each point is within the specified radii of the corresponding fire towers.