S1. Viewing angles An auditorium with a flat floor has a large screen on one wall. The lower edge of the screen is 3 ft above eye and the upper edge of the screen is 10 ft above eye level (see figure). How far from the screen should you stand to maximize your viewing angle? level 10 ft 3 ft

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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#51
**Chapter 4: Applications of the Derivative**

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**51. Viewing Angles**

In an auditorium with a flat floor, there is a large screen on one wall. The lower edge of the screen is 3 feet above eye level, and the upper edge of the screen is 10 feet above eye level. How far from the screen should you stand to maximize your viewing angle?

*Diagram Explanation:*

There is an illustration showing a person standing at a distance \( x \) from the screen. The screen height ranges from 3 feet to 10 feet above the viewer’s eye level. The angle \(\theta\) represents the angle of vision from the person’s eye to the top and bottom edges of the screen.

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**52. Suspension System**

A load must be suspended 6 meters below a high ceiling using cables attached to two supports that are 2 meters apart. How far below the ceiling (\( x \) in the figure) should the cables be joined to minimize the total length of cable used?

*Diagram Explanation:*

The diagram shows a horizontal bar, representing the ceiling, with two points marked 2 meters apart. Cables are depicted as lines descending from these points and converging at a point \( x \) meters below the ceiling, with a vertical distance labeled as 6 meters.

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Transcribed Image Text:**Chapter 4: Applications of the Derivative** --- **51. Viewing Angles** In an auditorium with a flat floor, there is a large screen on one wall. The lower edge of the screen is 3 feet above eye level, and the upper edge of the screen is 10 feet above eye level. How far from the screen should you stand to maximize your viewing angle? *Diagram Explanation:* There is an illustration showing a person standing at a distance \( x \) from the screen. The screen height ranges from 3 feet to 10 feet above the viewer’s eye level. The angle \(\theta\) represents the angle of vision from the person’s eye to the top and bottom edges of the screen. --- **52. Suspension System** A load must be suspended 6 meters below a high ceiling using cables attached to two supports that are 2 meters apart. How far below the ceiling (\( x \) in the figure) should the cables be joined to minimize the total length of cable used? *Diagram Explanation:* The diagram shows a horizontal bar, representing the ceiling, with two points marked 2 meters apart. Cables are depicted as lines descending from these points and converging at a point \( x \) meters below the ceiling, with a vertical distance labeled as 6 meters. ---
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