數學問題 Differentiate the trig. (application problem) part 2

2008-05-09 6:47 pm

1. A steel grider 9m long is to be moved horizontally around a corner from one corridor 2.5m wide into a second corridor at right angles to the first. How narrow can the second corridor be and still permit the girder to go around the corner? Neglect the horizontal width of the grider.

2. Show that the maximum value of y= a sinx +b cosx is (a^2 +b^2)^(1/2) and the minimum value is - (a^2 +b^2)^(1/2).

3. A wall is 1.8m high and 1.2m from a building. Find the length of the shortest ladder that will touch the building, the top of the wall, and the ground beyond the wall.

*Diagrams are preferred for all questions.

回答 (1)

2008-05-18 5:01 pm

✔ 最佳答案

1.
Let W=minimum width of corridor
t=angle between girder and far wall of corridor of width W
then
W(t)=9sin(t)-2.5tan(t)
W'(t)=9cos(t)-2.5sec(t)^2=0 at critical width
Solving, cos(t)^3=2.5/9, cos(t)=0.6524, t=.85994, W=3.91669, or 3.92

Please try differentiation for 2,3 and 4.
If you need further help, it may be easier to post a separate question for each problem. The point (marks) is unimportant for most people. Not everyone has time to solve all four problems. Someone ready to answer problem 3 may not have time to do all four. This is probably why you have not got any answers yet for these interesting and challenging problems.

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