Answered: . A vertical line segment of length 8…

. A vertical line segment of length 8 ft is moving horizontally at a rate of 3 ft/sec. At what rate is area being swept out by the moving vertical segment?

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter47: Applications Of Formulas To Cutting Speed, Revolutions Per Minute, And Cutting Time

Section: Chapter Questions

Problem 41A: Compute the following problems. Express the answers to 1 decimal place. Use: T=LFN A slot 812.00...

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Question

1. A vertical line segment of length 8 ft is moving horizontally at a rate of 3 ft/sec. At what rate is area
being swept out by the moving vertical segment?

Consider the area formed by the line f(x) = mx, the x axis, and the vertical segment at location x.
The vertical segment is moving to the right at 3 ft/sec. At a certain time, say t = T, the height of the
vertical segment is 8 ft.

At t = T is the area of the triangle increasing at a rate equal to, or greater than, the rate area is
swept by the segment in Problem 1? (Ok to guess here). Let A(x) be the area of the triangle. Find the rate at which the area is increasing when t = T.

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