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Thread: Who's good at Calc?
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11-13-2008, 01:56 PM #1
Who's good at Calc?
Problem 1. A box has a square base and a volume of 1000 cubic
feet. Find the dimensions that minimize the surface area.
Problem 2. A box with a square base is to be constructed using
wood for the sides (at $2 per square foot) and metal for the top
and bottom (at $5 per spare foot). If you have a budget of $100 for
supplies, what's the largest volume the box can hold?
Problem 3. A car accelerates from a stop and then slows to a halt
three minutes later. It's position p relative to the starting line at
time t is given by p = ¡t4 + 18t2, where p is measured in feet and t
in minutes.
(a) How far has the car traveled at the end of the three minutes?
(b) How fast is the car traveling after 1 minute?
(c) When is the car traveling fastest?
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11-13-2008, 02:00 PM #2
I think the first one is 15.9 by 15.9 by 3.97....
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11-13-2008, 02:27 PM #3
nope scratch that its 10x10x10
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11-13-2008, 02:33 PM #4
been a while but I believe you need to establish equations using variables to come up with the answers......or you can rely on the guys on LS1.com for answers.
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11-13-2008, 02:34 PM #5
I'm doing it its just making sure im doing it right if soone definately knows what they are doing...
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11-13-2008, 05:51 PM #6
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triple-black- 2000 CamaroSS convertible
problem 1:
square base (x by x) with height h
Volume = hx^2 = 1000, so h = 1000/[x^2]
A = 4 sides + top + bottom
A = 4xh + 2x^2
A = 4x[1000/x^2] + 2x^2
A = 4000/x + 2x^2
minimize de A is when dA/dx = 0
dA/dx = -4000/x^2 + 4x = 0
so 4x = 4000/x^2
so 4x^3 = 4000
so x^3 = 1000
so x = 10... therefore, h = 10 too.Eugenio_SS
almost stock triple-black 2000 SS convertible with 17x11s on all 4 w/ 315s at the track or on the street with 18x10.5s on all 4 w/ 315s: (1), (2)
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11-13-2008, 06:09 PM #7
see i got that one, same method too...
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11-13-2008, 06:10 PM #8
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triple-black- 2000 CamaroSS convertible
number 2.
similar to problem 1 [square base (x by x) with height h]
V = hx^2
Area(sides) = 4xh @ 2$
Area(bases) = 2x^2 @ 5$
So 100$ = 2$*4xh + 5$*2x^2
100 = 8xh + 10x^2
8xh = -10x^2 + 100
h = 1/4{-5x + 50/x}
since V = hx^2
V = 1/4{-5x + 50/x}x^2
V = 1/4{-5x^3 + 50x}
V is @ max when dV/dx = 0
dV/dx = 1/4{-15x^2 + 50} = 0
15x^2 = 50
x^2 = 10/3
x = SQRT(10/3) so h = (5/6)SQRT(30)
V = hx^2
V = (25/9)SQRT(30)
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11-13-2008, 06:12 PM #9
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triple-black- 2000 CamaroSS convertible
problem 3.
is it a typo: p = ¡t4 + 18t2
Assuming you mean p = it^4 + 18t^2... but what is "i" ??? (typo??)
you sure it's an "i" and not a 1, maybe 8 or 9 (since they are close to "i") ?
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11-13-2008, 06:23 PM #10
p=-t^4 + 18t^2
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11-13-2008, 06:24 PM #11
btw Eugenio i owe you my life about now... i might make it home tonight yet....
Last edited by Eugenio_SS; 11-13-2008 at 07:52 PM. Reason: spell my name right !!!
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11-13-2008, 06:31 PM #12
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TA-White, Camaro-Black- Track-TA98A4 DD-98z28M6
wow.... i will never talk to Eugenio... he will make me look tarded.... hahahahahaha
i would be by just saying hey
hahahahahhaahLast edited by Eugenio_SS; 11-13-2008 at 07:52 PM. Reason: spell my name right !
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11-13-2008, 06:31 PM #13
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TA-White, Camaro-Black- Track-TA98A4 DD-98z28M6
o btw....
wade your still a bitch for "TSP link
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11-13-2008, 06:49 PM #14
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11-13-2008, 06:54 PM #15
Eugenio, i keep geting something closer to 180 for the volume instead of 15ish for number 2
Last edited by Eugenio_SS; 11-13-2008 at 07:53 PM. Reason: strike 2 @ spelling... getting Eugeni:Owned:
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11-13-2008, 07:01 PM #16
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Mystic Teal- 1999 Camaro Z28 - A4
God I hate calc.. It kicks my ass so much.. I'm studying to be an engineer and damn.. So much math.. So little brain..
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11-13-2008, 07:45 PM #17
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BLACK- 2000 Camaro SS
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11-13-2008, 07:49 PM #18
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triple-black- 2000 CamaroSS convertible
problem 3:
p=-t^4 + 18t^2, where p is measured in feet and t in minutes.
(a) How far has the car traveled at the end of the three minutes?
t = 3
p(t=3) = -(3)^4 + 18(3)^2
p(t=3) = -81 + 162 = 81ft
(b) How fast is the car traveling after 1 minute?
v = dp/dt
v = -4t^3 + 36t
v(t=1) = -4(1)^3 + 36(1)
v(t=1) = -4 + 36 = 32 ft/min
(c) When is the car traveling fastest?
fastest is when v(t) reaches maximum
ie dv/dt =0
dv/dt = -12t^2 + 36 =0
12t^2 = 36
t^2 = 3
t = SQRT(3) minutesLast edited by Eugenio_SS; 11-13-2008 at 07:55 PM.
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11-13-2008, 07:50 PM #19
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11-13-2008, 07:54 PM #20
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