a sprinkler is designed to water a circular area that has a radius of 7 feet. the sprinkler is located at…

a sprinkler is designed to water a circular area that has a radius of 7 feet. the sprinkler is located at (0,0) on a lawn. a flowerbed is planted 3 feet east and 6 feet south of the sprinkler. determine if the distance from the flowerbed to the sprinkler places the flowerbed on or within the circular area that this sprinkler can water. no. the flowerbed is 18 feet away from the sprinkler, which is more than the 7 - foot radius. yes. the flowerbed is exactly 7 feet away from the sprinkler. no. the flowerbed is 9 feet away from the sprinkler, which is more than the 7 - foot radius. yes. the flowerbed is √45 feet away from the sprinkler, which is less than the 7 - foot radius.

a sprinkler is designed to water a circular area that has a radius of 7 feet. the sprinkler is located at (0,0) on a lawn. a flowerbed is planted 3 feet east and 6 feet south of the sprinkler. determine if the distance from the flowerbed to the sprinkler places the flowerbed on or within the circular area that this sprinkler can water. no. the flowerbed is 18 feet away from the sprinkler, which is more than the 7 - foot radius. yes. the flowerbed is exactly 7 feet away from the sprinkler. no. the flowerbed is 9 feet away from the sprinkler, which is more than the 7 - foot radius. yes. the flowerbed is √45 feet away from the sprinkler, which is less than the 7 - foot radius.

Answer

Explanation:

Step1: Use distance - formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. The sprinkler is at $(0,0)$ and the flower - bed is at $(3,-6)$. So $x_1 = 0,y_1 = 0,x_2 = 3,y_2=-6$. Then $d=\sqrt{(3 - 0)^2+(-6 - 0)^2}$.

Step2: Calculate the distance

$d=\sqrt{3^2+( - 6)^2}=\sqrt{9 + 36}=\sqrt{45}\approx6.71$ feet.

Step3: Compare with the radius

The radius of the circular area the sprinkler can water is $r = 7$ feet. Since $\sqrt{45}\approx6.71<7$, the flower - bed is within the circular area.

Answer:

Yes. The flowerbed is $\sqrt{45}$ feet away from the sprinkler, which is less than the 7 - foot radius.