A gutter having trapezoidal cross-section is to be made by bending a strip of tin 1 meter wide. If the width of base is 50cm, what width across the top gives the greatest carrying capacity?

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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Solve the following problems applying derivatives of trigonometric/inverse trigonometric functions. Provide illustrations for each problem.
Round the answer up to the 4th decimal place.

1. A gutter having trapezoidal cross-section is to be made by bending a strip of tin 1 meter wide. If the width of base is 50cm, what width across the top gives the greatest carrying capacity?
2. A boat is pushed off from a beach at 2m/sec. A man on shore holds a rope, tied to the boat, at a height of 2m. Find how fast the angle of elevation of the rope is decreasing, after 5 sec.

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