Question

Help please!

A tower in Centerville sends radio signal a certain distance (in miles) according to the equation: x^2 + y^2 = 3,600. The Martinez family lives 50 miles north and 70 miles east of Centerville. Can the Martinez family receive the radio signal from Centerville? In complete sentences, explain your reasoning.

Answer 1

Calculate the square of distance from the tower, which is
(50^2+70^2)=7400
Since 7400 > 3600, unfortunately the Martinez will not be able to make use of the tower in centerville, which requires the square of distance x^2+y^2 <=3600.

Answer 2

Are you sure that's how you solve it? why would you square the 50 and 70?

Answer 3

Usually we square the x- and y-coordinates, sum them, and take the square-root to find the distance.
The given condition of x^2+y^2=3600 is equivalent to saying reception is possible within a radius of sqrt(3600)=60, which at first sight, the Martinez family will not get the reception because 70>60.
To make the calculations easier to understand, I made the squares of the distances and compare the squares instead, which is verbatim with the requirements.

To make things more complicated, the given condition says x^2+y^2=3600 (instead of <3600), which is not a reasonable requirement. Signal reception is usually expressed in an area within a given radius. I have assumed the more general interpretation.

Hope my explanations are understandable.