Question

An earthquake can be felt in a circular pattern from the epicenter. If the equation of this pattern is x2 + y2 = 2500, how many miles away from the epicenter can you feel the effects of the earthquake?

Answer 1

the radius of the circle ( which is the same as the distance from the epicenter) = square root of 2500 which is 50

Answer is 50 miles.

Answer 2

We can feel the effects of the earthquake 50 miles from the epicenter.

Explanation:

The given expression is

`x^(2) +y^(2)=2500`

Which represents a circumference. So, if this circunference represents the pattern of an earthquare, that means the radius of such circumference represents the miles away from the epicenter.

The given expression is the explicit form of a circumference, like this

`x^(2) +y^(2)=r^(2)`

Where
`r` is the radius.

So, in this case,

`r^(2)=2500\\ r=√(2500)\\ r=50`

Therefore, we can feel the effects of the earthquake 50 miles from the epicenter.