You are sky diving and are trying to land on a target with a radius of 15 m. You land 10 m west and 10 m north of the center of the target.

a. Write an inequality to describe the region inside the target area.
b. Do you land within the target area?
c. If another skydiver lands 4 m east and 14 m north of the center of the target, who is closer to the center.

I believe that the vertices would be (-15, 0) and (15,0), but I don't really know where to go from there.

Let the center of the target be (0,0)

You have a circle of radius 15.

x^2 + y^2 < 225

a square of side 10 has diagonal 14.14, just inside the target area

4^2 + 14^2 = 16 + 196 = 212
10^2 + 10^2 = 200

so you are closer

swagger.

To answer these questions, we need to consider the coordinates of your landing point relative to the center of the target.

a. To describe the region inside the target area, we need to find the distance between your landing point and the center of the target. Since you landed 10 m west and 10 m north of the center, your landing coordinates are (-10, 10). The distance formula can be used to find the distance between two points on a coordinate plane. In this case, let's call the center of the target point C and your landing point L. The distance between C and L is given by:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values, we have:

distance = √((10 - (-10))^2 + (0 - 10)^2)
= √(20^2 + (-10)^2)
= √(400 + 100)
= √500

Therefore, the inequality that describes the region inside the target area is:
√((x - 0)^2 + (y - 0)^2) ≤ √500

b. To determine if you landed within the target area, we need to compare the distance you traveled (from the center) to the radius of the target. In this case, the radius is given as 15 m. Therefore, if the distance calculated in part a is less than or equal to 15, you landed within the target area.

√500 ≤ 15

We can compare the square of each side to simplify the inequality:

500 ≤ 15^2
500 ≤ 225

Since 500 is not less than or equal to 225, you did not land within the target area.

c. If another skydiver lands 4 m east and 14 m north of the center of the target, we can calculate the distance to the center for this person as well. Their landing coordinates would be (4, 14). Using the distance formula as we did before:

distance = √((4 - 0)^2 + (14 - 0)^2)
= √(4^2 + 14^2)
= √(16 + 196)
= √212

Therefore, the distance from this person to the center is √212.

Comparing the distances, we see that √212 is smaller than √500, so the skydiver who landed 4 m east and 14 m north is closer to the center of the target.