The maximum distance between the walkers at any given time is (a) 18 meters
Lucas' equation on the circular path is given as:
[tex](x + 8)^2 + (y - 3)^2 = 64[/tex]
Noah' equation on the circular path is given as:
[tex](x - 10)^2 + (y - 3)^2 = 100[/tex]
The equation of a circle is represented as:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
Where:
So, we rewrite both equations as follows:
[tex](x + 8)^2 + (y - 3)^2 = 64[/tex]
[tex](x + 8)^2 + (y - 3)^2 = 8^2[/tex]
[tex](x - 10)^2 + (y - 3)^2 = 100[/tex]
[tex](x - 10)^2 + (y - 3)^2 = 10^2[/tex]
The radii of both equations are:
[tex]r_1 = 8[/tex]
[tex]r_2 = 10[/tex]
The maximum distance between the walkers at any given time is the sum of the radii
[tex]r = r_1 + r_2[/tex]
So, we have:
[tex]r = 8 + 10[/tex]
This gives
[tex]r = 18[/tex]
Hence, the maximum distance between the walkers at any given time is (a) 18 meters
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