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Best_Mathematician
 2 years ago
Calculus challenge
Best_Mathematician
 2 years ago
Calculus challenge

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Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0The type of bread chosen for this special calculus toast isn't the square sandwich shape, but the kind that is curved across the top. Imagine that the toast is composed of the curved part sitting atop the rectangular portion. The equation of the curved part of the toast is x2/4 + y2 = 1, and it sits directly and perfectly on top of a rectangle of height 3 inches. a) What are the equations of the rectangular boundaries? b) Graph the toast boundaries, making certain to include screen shots of the boundary equations, Window settings, and the graph. c) How would you find the length of the curve

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.1once you find two x values , they are your answer for a)

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0is x two negative values

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0ya here is the equation again \[\frac{ x^2 }{ 4 } + y^2 = 1\]

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.1ahh, that's different, this is ellipse x^2/4 + (y3)^2 = 1

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.1now plug in y=3, x^2/4=1 x^2=4 x=2,2 that's your part a

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0sweet ur r doing grt go ahead

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.1part b is graphing,

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.1Here's the graph, done without benefit of the above

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0i wud just graph that right

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0oh thx @dlipson1 can u go further

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.1Uh oh, I think that's a line integral, I'd have to look that up. Do you know anything about Stochastic Optimization?

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0hey hey hey never mind...i know how to find the length of the curve thanks..but i dont knw do i need to find length of whole curve or just the bread as in ur graph

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.1Well, the rectangle is trivial (is the side along the xaxis included?), the top is just half the ellipse, that's the only real calculus (integration) you have to do.

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0so from negative 2 to 2...right

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah, use the top half, y = sqrt(...), then (I just looked it up): Length = integral (sqrt(1+(y')^2))dy

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0ya and what kinda graphing calculator r u using dude

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.1http://www.padowan.dk/ and Google > http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0thx...getting my next question...i wud give u a lot of awards but unfortunately this site doesnt aloow lol

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.1"Graph" (from padowan.dk) gives me the curve length of 4.882, then +3+3 +4 for the entire perimeter.

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0sweet thanks

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0hey @dlipson1 one more thing, how wud we find area on top of the toast

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.1The rectangle + 2*integral (by symmetry) from 0 to 2 of y = sqrt(1x^2/4)... hmm, do we need substitution here?

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0do u need the derivative...i have it

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0x/(4y12)....now wht to do

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.1I'm not sure dy/dx helps. I set up the integral, thought about a trig. substitution, multiplied through by the 2 (as sqrt(4)) to get int(sqrt(4x^2))dx, which I found here, but I think there must be an easier way (like polar coordinates): http://answers.yahoo.com/question/index?qid=20071231235113AAAAfuP

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.1Here is almost the same problem: http://www.youtube.com/watch?v=PSlsj0IP8R8
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