Question

2. The beam of a lighthouse can be seen for up to 20 miles. You are on a ship that is 10 miles east and 16 miles north of the lighthouse. Write an inequality to describe the region lit by the lighthouse beam. Can you see the lighthouse beam on your ship?​

Answer 1

Answer:

The person on the ship can see the lighthouse

Step-by-step explanation:

The Circle Function

A circle centered in the point (h,k) with a radius r can be written as the equation

$(x-h)^2+(y-k)^2=r^2$

Any point (x,y) can be known if it's inside of the circle if

$(x-h)^2+(y-k)^2\leq r^2$

The question is about a beam of a lighthouse than can be seen for up to 20 miles. If we assume the lighthouse is emitting the beam as the shape of a circle centered in (0,0), then its radius is 20 miles. Thus any person riding a ship inside the circle can see the lighthouse. This means that

$x^2+y^2\leq 20^2$

$x^2+y^2\leq 400$

The ship's coordinates respect to the lighthouse are (10,16). We should test the point to verify if the above inequality stands

$10^2+16^2\leq 400$

$356 \leq 400$

The inequality is true, so the person on the ship can see the lighthouse