## Best_Mathematician Group Title Calculus challenge one year ago one year ago

1. Best_Mathematician Group Title

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

2. Best_Mathematician Group Title

ok

3. Best_Mathematician Group Title

then

4. modphysnoob Group Title

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

5. Best_Mathematician Group Title

is x two negative values

6. modphysnoob Group Title

is x squred?

7. Best_Mathematician Group Title

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

8. modphysnoob Group Title

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

9. modphysnoob Group Title

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

10. Best_Mathematician Group Title

sweet ur r doing grt go ahead

11. modphysnoob Group Title

part b is graphing,

12. dlipson1 Group Title

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

13. Best_Mathematician Group Title

i wud just graph that right

14. Best_Mathematician Group Title

oh thx @dlipson1 can u go further

15. dlipson1 Group Title

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

16. Best_Mathematician Group Title

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

17. dlipson1 Group Title

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.

18. Best_Mathematician Group Title

so from negative 2 to 2...right

19. dlipson1 Group Title

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

20. Best_Mathematician Group Title

ya and what kinda graphing calculator r u using dude

21. dlipson1 Group Title
22. Best_Mathematician Group Title

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

23. dlipson1 Group Title

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

24. Best_Mathematician Group Title

sweet thanks

25. Best_Mathematician Group Title

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

26. dlipson1 Group Title

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

27. Best_Mathematician Group Title

do u need the derivative...i have it

28. Best_Mathematician Group Title

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

29. dlipson1 Group Title

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

30. dlipson1 Group Title

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