Question #00a87
1 Answer
The length of the fence the dog can travel is
Explanation:
Since the dog has 8 feet of chain to travel, and the line will never reach a distance longer than 8, we can assume the dog can reach all the fence distance in the positive quadrant 1. However, here is the calculation that proves it:
Find the equation of the circle the dog can travel:
#x^2 + y^2 = 64#
Substitute in our equation for y.
#x^2 + (8-x)^2 = 64#
#x^2 + 64 - 16x + x^2 = 64#
#2x^2 - 16x = 0#
Factor and solve for x
#2x( x-8) = 0#
#2x = 0#
#x = 0#
#x-8 = 0#
#x = 8#
So we know that the dog can travel the fence from the interval 0 to 8. Now we plug these x values into our equation to determine the y values, and plug the y values into our distance formula.
#y = 8 - 0 = 8#
#y = 8 - 8 = 0#
The points are (0,8) and (8,0)
#"distance" = sqrt((y_1 - y_2)^2 + (x_1 - x_2)^2)#
#"distance" = sqrt(8^2 + (-8)^2)#
#"distance" = sqrt(128)#
This is our answer, we can reduce it to
Hope this helped!