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anonymous
 5 years ago
I need help with this calculus question.
Some ancient Egyptians decided to build a pyramid with a square base that measured 750 feet on a side. The height of the pyramid was 500 feet. The density of the rock used in construction was 120 pounds per cubic foot.
It was assumed that the work force would remain constant. Each laborer could do 160 foot pounds of work per hour, working 12 hour days for 330 days per year for 20 years.
Determine, under these conditions, the number of laborers needed to construct the pyramid.
anonymous
 5 years ago
I need help with this calculus question. Some ancient Egyptians decided to build a pyramid with a square base that measured 750 feet on a side. The height of the pyramid was 500 feet. The density of the rock used in construction was 120 pounds per cubic foot. It was assumed that the work force would remain constant. Each laborer could do 160 foot pounds of work per hour, working 12 hour days for 330 days per year for 20 years. Determine, under these conditions, the number of laborers needed to construct the pyramid.

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Is it a solid pyramid? you know, for ceremonial purposes :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(1/3)*(750)^2*500 ft^3 * 120lbs/ft^3 * 1hr/(160lbs)/12hrs

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i know its a definite integral equation that is the density * volume * distance(or ht.) I just can't figure out how to represent the volume.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(S) A(y) dy {0,h} or something like that.... but the formula for any conelike volume is (1/3)(Base Area)(height)...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0intuition would say, find the amount of rock you need, figure out how much one laborer does in the alloted time span, then multiply that by how many laborers it take to do the job..... but other than that, I dont know...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{50}(120)(volume)(y)\] the equation to find the work needed is something like this, i just can't figure out the section for volume.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0volume is integrated thru taking sections of the base area as it moves thru the height....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0also the volume is representing the volume of a slice

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0each slice is x^2 dy in volume right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0and x changes with repect to height...or y

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0what is the slope of the face?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah basically, but the size of the slice changes since it is getting smaller going up

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i don't know that isn't given

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0500/(750/2) would be a cross section of the "triangle"

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the slope of a face is 500/375....might need to reduce. the equation relating that to x and y is y = 500/375(x) + 500

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0slope is 4/3 when reduced

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x increase by 2 for every 3/4 increase in y .... if that helps

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(3/2) (S) y dy {0,500} = (3/4) y^2 {0,500} 500^2 = 250000(3/4) = 750000/4 = 187500 that matches 500(750)/2 = 187500 for a flat area..... not sure how it helps tho :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x^2 is the area of a normal base and it changes with respect to "y" at a rate of (3/2)(y) dy ?? It looks right, but this is still shakey ground fer me :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah i think ive gotten it now, thanks.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0if I messed up anything, youlet me know :)
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