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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?​

Respuesta :

elcharly64

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

[tex](x-h)^2+(y-k)^2=r^2[/tex]

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

[tex](x-h)^2+(y-k)^2\leq r^2[/tex]

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

[tex]x^2+y^2\leq 20^2[/tex]

[tex]x^2+y^2\leq 400[/tex]

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

[tex]10^2+16^2\leq 400[/tex]

[tex]356 \leq 400[/tex]

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

facundo3141592

The inequality is:

√(x^2 + y^2) ≤ 20 mi.

And you can see the lighthouse beam from your ship.

How to write the inequality?

First, let's define our coordinate system, North will be the positive y-axis and east will be the positive x-axis. Such that the origin is the lighthouse.

The distance between a point (x, y) and the lighthouse is given by:

d = √(x^2 + y^2).

And we know that the lighthouse beam can be seen for up to 20 miles, so you can only see the lighthouse if your position (x, y) is such that the inequality is true.

√(x^2 + y^2) ≤ 20 mi.

Now, can you see the lighthouse beam from your ship?

Your ship's position is: (10 mi, 16 mi)

Replacing that in the inequality we get:

√((10mi)^2 + (16mi)^2) ≤ 20 mi

18.87 mi ≤ 20 mi

The inequality is true, then you can see the beam from the ship.

If you want to learn more about inequality, you can read:

https://brainly.com/question/25275758

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