Question

Calculus challenge

Answer 1

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

Answer 2

ok

Answer 3

then

Answer 4

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

Answer 5

is x two negative values

Answer 6

is x squred?

Answer 7

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

Answer 8

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

Answer 9

now plug in y=3,

x^2/4=1

x^2=4
x=2,-2

that's your part a

Answer 10

sweet ur r doing grt go ahead

Answer 11

part b is graphing,

Answer 12

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

Answer 13

i wud just graph that right

Answer 14

oh thx @dlipson1 can u go further

Answer 15

Uh oh, I think that's a line integral, I'd have to look that up. Do you know anything about Stochastic Optimization?

Answer 16

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

Answer 17

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.

Answer 18

so from negative 2 to 2...right

Answer 19

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

Answer 20

ya and what kinda graphing calculator r u using dude

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

sweet thanks

Answer 25

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

Answer 26

The rectangle + 2*integral (by symmetry) from 0 to 2 of y = sqrt(1-x^2/4)... hmm, do we need substitution here?

Answer 27

do u need the derivative...i have it

Answer 28

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

Answer 29

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

Answer 30

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