SOLUTION: 1) A rectangular enclosure,subdivided into 3 congruent pens,is to be made using a barn as one side and 120 meters of fencing for the rest of the enclosure.FInd the value of x that

Question 830403: 1) A rectangular enclosure,subdivided into 3 congruent pens,is to be made using a barn as one side and 120 meters of fencing for the rest of the enclosure.FInd the value of x that gives the maximum area for the enclosure.
-Answer is 15,but I don't know how to get the answer.
2)The water in a cylindrical tank 4 ft in diameter empties through a hole in the bottom.Assuming that the water has a depth of 16ft at time t=0 and empties at the rate of 5 ft^3/s,express the depth of the water as a function of time.
-Answer is d(t)=16-(5/4pi)t
Don't know how to solve.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1) A rectangular enclosure,subdivided into 3 congruent pens,is to be made using a barn as one side and 120 meters of fencing for the rest of the enclosure.FInd the value of x that gives the maximum area for the enclosure.
-Answer is 15,but I don't know how to get the answer.
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Draw the picture.
You have 4 fences (perpendicular to the barn) that are x meters long.
You have 1 fence (parallel to the barn) that is 120-4x meters long.
Area = x(120-4x) = 120x-4x^2 sq meters
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Maximum Area occurs when x = -b/(2a) = -120/(-8) = 15 meters
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2)The water in a cylindrical tank 4 ft in diameter empties through a hole in the bottom.Assuming that the water has a depth of 16ft at time t=0 and empties at the rate of 5 ft^3/s,express the depth of the water as a function of time.
---
Volume of water = pi*r^2*h = pi*4*16 = 64pi ft^3 ; depth = 16 ft
Volume = 0 after 64pi/5 = 12.8pi seconds ; depth = 0 ft
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You have 2 points (0,16) and (12 4/5,0) relating time to depth.
slope = (16-0)/(0-12.8) = -1.25
d(t) = 16 - (5/4)t
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Cheers,
Stan H.
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