anonymous
  • anonymous
Calculus challenge
Calculus1
schrodinger
  • schrodinger
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anonymous
  • anonymous
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
anonymous
  • anonymous
ok
anonymous
  • anonymous
then

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anonymous
  • anonymous
once you find two x values , they are your answer for a)
anonymous
  • anonymous
is x two negative values
anonymous
  • anonymous
is x squred?
anonymous
  • anonymous
ya here is the equation again \[\frac{ x^2 }{ 4 } + y^2 = 1\]
anonymous
  • anonymous
ahh, that's different, this is ellipse x^2/4 + (y-3)^2 = 1
anonymous
  • anonymous
now plug in y=3, x^2/4=1 x^2=4 x=2,-2 that's your part a
anonymous
  • anonymous
sweet ur r doing grt go ahead
anonymous
  • anonymous
part b is graphing,
anonymous
  • anonymous
Here's the graph, done without benefit of the above
1 Attachment
anonymous
  • anonymous
i wud just graph that right
anonymous
  • anonymous
oh thx @dlipson1 can u go further
anonymous
  • anonymous
Uh oh, I think that's a line integral, I'd have to look that up. Do you know anything about Stochastic Optimization?
anonymous
  • anonymous
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
anonymous
  • anonymous
Well, the rectangle is trivial (is the side along the x-axis included?), the top is just half the ellipse, that's the only real calculus (integration) you have to do.
anonymous
  • anonymous
so from negative 2 to 2...right
anonymous
  • anonymous
Yeah, use the top half, y = sqrt(...), then (I just looked it up): Length = integral (sqrt(1+(y')^2))dy
anonymous
  • anonymous
ya and what kinda graphing calculator r u using dude
anonymous
  • anonymous
http://www.padowan.dk/ and Google --> http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx
anonymous
  • anonymous
thx...getting my next question...i wud give u a lot of awards but unfortunately this site doesnt aloow lol
anonymous
  • anonymous
"Graph" (from padowan.dk) gives me the curve length of 4.882, then +3+3 +4 for the entire perimeter.
anonymous
  • anonymous
sweet thanks
anonymous
  • anonymous
hey @dlipson1 one more thing, how wud we find area on top of the toast
anonymous
  • anonymous
The rectangle + 2*integral (by symmetry) from 0 to 2 of y = sqrt(1-x^2/4)... hmm, do we need substitution here?
anonymous
  • anonymous
do u need the derivative...i have it
anonymous
  • anonymous
-x/(4y-12)....now wht to do
anonymous
  • anonymous
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(4-x^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
anonymous
  • anonymous
Here is almost the same problem: http://www.youtube.com/watch?v=PSlsj0IP8R8

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