You are designing an RPG (role-playing game) for a gaming console and have decided to use an open world design, where players can explore the terrain freely, encountering enemies by chance. Your design team has coded this in-game world to exist on the circle x^2 + y^2 ≤ 900 on the xy-plane. At any point (x,y) in this world you've also associated a danger function d(x,y) that measures how likely it is to encounter an enemy at that point. Thus high values of d(x,y) correspond to dangerous points, while low values of d(x,y) correspond to safe points. If d(x,y) = e^(-x^2)(y), find the safest point(s) and most dangerous point(s) in-game.
You are designing an RPG (role-playing game) for a gaming console and have decided to use an open world design, where players can explore the terrain freely, encountering enemies by chance. Your design team has coded this in-game world to exist on the circle x^2 + y^2 ≤ 900 on the xy-plane. At any point (x,y) in this world you've also associated a danger function d(x,y) that measures how likely it is to encounter an enemy at that point. Thus high values of d(x,y) correspond to dangerous points, while low values of d(x,y) correspond to safe points. If d(x,y) = e^(-x^2)(y), find the safest point(s) and most dangerous point(s) in-game.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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You are designing an RPG (role-playing game) for a gaming console and have decided to use an open world design, where players can explore the terrain freely, encountering enemies by chance. Your design team has coded this in-game world to exist on the circle
x^2 + y^2 ≤ 900
on the xy-plane. At any point (x,y) in this world you've also associated a danger function d(x,y) that measures how likely it is to encounter an enemy at that point. Thus high values of d(x,y) correspond to dangerous points, while low values of d(x,y) correspond to safe points. If d(x,y) = e^(-x^2)(y), find the safest point(s) and most dangerous point(s) in-game.
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