Calculus challenge

- anonymous

Calculus challenge

- jamiebookeater

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- 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

ok

- anonymous

then

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## More answers

- anonymous

once you find two x values , they are your answer for a)

- anonymous

is x two negative values

- anonymous

is x squred?

- anonymous

ya here is the equation again \[\frac{ x^2 }{ 4 } + y^2 = 1\]

- anonymous

ahh, that's different, this is ellipse
x^2/4 + (y-3)^2 = 1

- anonymous

now plug in y=3,
x^2/4=1
x^2=4
x=2,-2
that's your part a

- anonymous

sweet ur r doing grt go ahead

- anonymous

part b is graphing,

- anonymous

Here's the graph, done without benefit of the above

##### 1 Attachment

- anonymous

i wud just graph that right

- anonymous

oh thx @dlipson1 can u go further

- 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

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

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

so from negative 2 to 2...right

- anonymous

Yeah, use the top half, y = sqrt(...), then (I just looked it up): Length = integral (sqrt(1+(y')^2))dy

- anonymous

ya and what kinda graphing calculator r u using dude

- anonymous

http://www.padowan.dk/
and Google --> http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx

- anonymous

thx...getting my next question...i wud give u a lot of awards but unfortunately this site doesnt aloow lol

- anonymous

"Graph" (from padowan.dk) gives me the curve length of 4.882, then +3+3 +4 for the entire perimeter.

- anonymous

sweet thanks

- anonymous

hey @dlipson1 one more thing, how wud we find area on top of the toast

- 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

do u need the derivative...i have it

- anonymous

-x/(4y-12)....now wht to do

- 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

Here is almost the same problem:
http://www.youtube.com/watch?v=PSlsj0IP8R8

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