The equation x^2+(y-5)^2=64 models the boundary on a local map for which Darren can hear his friend Tom on his two-way radio when Darren is at home. How far (in miles) can Tom walk from Darren's home and still be heard?
Indicate your specific subject in the "School Subject" box, so those with expertise in the area will respond to the question.
To determine how far Tom can walk from Darren's home and still be heard, we need to find the radius of the circle formed by the equation x^2 + (y - 5)^2 = 64. The equation represents a circle centered at (0, 5) with a radius of 8.
To find the radius, we can compare the given equation to the standard equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2. In this case, the center is (h, k) = (0, 5), and the radius squared is r^2 = 64. Thus, the radius is √(64) = 8.
Therefore, Tom can walk up to a distance of 8 miles from Darren's home and still be heard on the two-way radio.