1. Mark is designing a pentagonal shaped play area for a daycar facility. He has 30m of nylon mesh to enclose the play area. The triangle in the diagram is equilateral. Find the dimension of the rectangle plus the triangle, to the nearest tenth of a metre, that was maximize the area he can enclose for the play area.
2. The daigram of a practice field shows a rectangle with a semicircle at each end. The track and field coach wants two laps around the field to be in 1000m. The physical education deparement needs a rectangluar field that is as large as possible.
a) Determine the dimensions of the track that will maximize the entire enclosed area. Do these dimensions meet the needs of the track coach and the phys. ed. department?
b) if only the rectanglular portion of the field is maximized, can the track team run the 100m dash along a straight part of the track? Justify ur answer.
PLEASE HELP SHOW UR WORK! i have my exam tomorrw :(
2007-07-22 16:43:19 · 6 answers · asked by mystery_girl07 2 in Science & Mathematics ➔ Mathematics
wow mean people :( i tried doing it
2007-07-22 16:51:42 · update #1
1. Let S = the side of the triangle, also the width of the rectangle.
L = length of the rectangle
3S + 2L = 30
A = (1/4)S^2√3 + SL
L = (30 - 3S)/2
A = (1/4)S^2√3 + S(30 - 3S)/2
A = (1/4)S^2√3 + 15S - (3/2)S^2
From here you can put the equation in vertex form or differentiate and set the derivative to 0 to find S
2.a. Let L = length of the rectangle,
D = width of the rectangle and diameter of circle.
2L + πD = 500 (2 laps for 1,000)
A = LD + (π/4)D^2
L = (500 - πD)/2
A = D(500 - πD)/2 + (π/4)D^2
A = 250D - (π/2)D^2 + (π/4)D^2
A = 250D - (π/4)D^2
Maximize by vertex form or differentiation.
2.b.
A = D(500 - πD)/2
A = 250D - (π/2)D^2
Maximize by vertex form or differentiation.
With these constants, maximizing by differentiation is by far the easiest.
2007-07-22 17:51:35 · answer #1 · answered by Helmut 7 · 0⤊ 0⤋
such an easy question, but i don't know have the time to do everythings for u
2007-07-22 16:52:19 · answer #2 · answered by kevin 1 · 0⤊ 0⤋
Why don't you post one question at a time?
2007-07-22 16:46:55 · answer #3 · answered by Anonymous · 1⤊ 0⤋
You figure it out yourself im not doing your damn homework for you!
2007-07-22 16:47:14 · answer #4 · answered by wondering goose 2 · 0⤊ 2⤋
lol cheater do ur own homework
2007-07-22 16:45:29 · answer #5 · answered by Crystal 3 · 1⤊ 3⤋
help help i'm lazy help....blah!!!
2007-07-22 16:50:39 · answer #6 · answered by Bucket 2 · 1⤊ 0⤋