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Best_MathematicianBest ResponseYou've already chosen the best response.0
The 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
 one year ago

modphysnoobBest ResponseYou've already chosen the best response.1
once you find two x values , they are your answer for a)
 one year ago

Best_MathematicianBest ResponseYou've already chosen the best response.0
is x two negative values
 one year ago

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

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

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

Best_MathematicianBest ResponseYou've already chosen the best response.0
sweet ur r doing grt go ahead
 one year ago

modphysnoobBest ResponseYou've already chosen the best response.1
part b is graphing,
 one year ago

dlipson1Best ResponseYou've already chosen the best response.1
Here's the graph, done without benefit of the above
 one year ago

Best_MathematicianBest ResponseYou've already chosen the best response.0
i wud just graph that right
 one year ago

Best_MathematicianBest ResponseYou've already chosen the best response.0
oh thx @dlipson1 can u go further
 one year ago

dlipson1Best ResponseYou've already chosen the best response.1
Uh oh, I think that's a line integral, I'd have to look that up. Do you know anything about Stochastic Optimization?
 one year ago

Best_MathematicianBest ResponseYou've already chosen the best response.0
hey 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
 one year ago

dlipson1Best ResponseYou've already chosen the best response.1
Well, 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.
 one year ago

Best_MathematicianBest ResponseYou've already chosen the best response.0
so from negative 2 to 2...right
 one year ago

dlipson1Best ResponseYou've already chosen the best response.1
Yeah, use the top half, y = sqrt(...), then (I just looked it up): Length = integral (sqrt(1+(y')^2))dy
 one year ago

Best_MathematicianBest ResponseYou've already chosen the best response.0
ya and what kinda graphing calculator r u using dude
 one year ago

dlipson1Best ResponseYou've already chosen the best response.1
http://www.padowan.dk/ and Google > http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx
 one year ago

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

dlipson1Best 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.
 one year ago

Best_MathematicianBest ResponseYou've already chosen the best response.0
sweet thanks
 one year ago

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

dlipson1Best ResponseYou've already chosen the best response.1
The rectangle + 2*integral (by symmetry) from 0 to 2 of y = sqrt(1x^2/4)... hmm, do we need substitution here?
 one year ago

Best_MathematicianBest ResponseYou've already chosen the best response.0
do u need the derivative...i have it
 one year ago

Best_MathematicianBest ResponseYou've already chosen the best response.0
x/(4y12)....now wht to do
 one year ago

dlipson1Best ResponseYou've already chosen the best response.1
I'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
 one year ago

dlipson1Best ResponseYou've already chosen the best response.1
Here is almost the same problem: http://www.youtube.com/watch?v=PSlsj0IP8R8
 one year ago
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