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A boat is on the top of a flat lake (the top of the lake can be pictured as being on the xy-plane, with distances in meters) at the point (3, 1). The lake is modeled by the part of the graph in R³ of L(x, y) = ²+-5y-20 where z ≤ 0. A. What is the shape of the top of the lake? B. If the boat is at (3, 1) and moving in the direction of (2, -1), is the depth from the boat to the bottom of the lake getting larger or smaller? At approximately what rate? C. What direction should the boat move if it wants to increase the depth the fastest? (Give your answer as a unit vector.) D. How deep is the lowest part of the lake?

A boat is on the top of a flat lake (the top of the lake can be pictured as being on the xy-plane, with distances in meters) at the point (3, 1). The lake is modeled by the part of the graph in R³ of L(x, y) = ²+-5y-20 where z ≤ 0. A. What is the shape of the top of the lake? B. If the boat is at (3, 1) and moving in the direction of (2, -1), is the depth from the boat to the bottom of the lake getting larger or smaller? At approximately what rate? C. What direction should the boat move if it wants to increase the depth the fastest? (Give your answer as a unit vector.) D. How deep is the lowest part of the lake?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 7DE
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A boat is on the top of a flat lake (the top of the lake can be pictured as being on the xy-plane, with distances in meters) at the point (3, 1). The lake is modeled by the part of the graph in R³ of L(x, y): +-5y-20 where z ≤ 0. = A. What is the shape of the top of the lake? B. If the boat is at (3, 1) and moving in the direction of (2, -1), is the depth from the boat to the bottom of the lake getting larger or smaller? At approximately what rate? C. What direction should the boat move if it wants to increase the depth the fastest? (Give your answer as a unit vector.) D. How deep is the lowest part of the lake?
Transcribed Image Text:A boat is on the top of a flat lake (the top of the lake can be pictured as being on the xy-plane, with distances in meters) at the point (3, 1). The lake is modeled by the part of the graph in R³ of L(x, y): +-5y-20 where z ≤ 0. = A. What is the shape of the top of the lake? B. If the boat is at (3, 1) and moving in the direction of (2, -1), is the depth from the boat to the bottom of the lake getting larger or smaller? At approximately what rate? C. What direction should the boat move if it wants to increase the depth the fastest? (Give your answer as a unit vector.) D. How deep is the lowest part of the lake?
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