What is the solution to Problem 88?

In summary: I'm glad to know you got it resolved.It did. But knowing the question wasn't helping to know what you were doing wrong. Which was your actual question. I'm glad to know you got it resolved.In summary, the conversation discusses solving problem 88 involving two circles with radius 3 and centers at (-2,0) and (2,0) intersecting to find the area of the shaded region. The conversation includes attempts at solving the problem using both calculus and geometry methods, as well as using online resources for guidance. Eventually, it is determined that the angle must also be adjusted in the equation to get the correct answer.
  • #1
xdrgnh
417
0

Homework Statement



http://books.google.com/books?id=gR.... .Find the area of the shaded region&f=false Problem 88

Homework Equations



equation of each circle (x-2)^2+y^2=9
(x+2)^2+y^2=9

The Attempt at a Solution



I solve for y for the circle (x-2)^2+y^2=9 then I took the integral of that from -1 to 0. I noticed that the shape looked symmetrical so I multiplied it by 4. But when I do it algebraically and using geometry I get a different answer then when I use the calculus.
 
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  • #2
Nobody can say why you are getting different answers until you show how you did it and what you got.
 
  • #3
Dick said:
Nobody can say why you are getting different answers until you show how you did it and what you got.

Well I really didn't do it algebraically the internet told me how to do it algebraically and it wasn't the same answer I got with my calculus. So the integral of one of the circles is .5(9arcsin(x-2)/3)+(x-2)(9-(x-2)^2)^.5) the limits are from -1 to 0. So I evaluated it and I got 1.584, something around there. And you see the shape is symmetrical on the link I put in. So I mult it by 4 but that did not give the right answer according to the internet. Did I do it the right way.
 
  • #4
I get something about like that for one fourth of the region. 1.548. I think you are probably right. What's the 'internets' answer?
 
  • #7
Dick said:
Ok, so what did you put in for the angle? It's likely not the same as in that problem.

I just did the same thing they did except using a my radius of 3 instead of 10. Do you think that my answer is right and maybe what they are doing just doesn't apply in my case. The problem is supposed to be solved using calculus not geometry.
 
  • #8
Yes, I think your answer is right. And this problem does apply, but you have to change the angle as well, not just radius. If you actually work that example fully through you should get the same answer. In the future, could you state the question more fully before you post, instead of having us guess what your references are?
 
  • #9
Dick said:
Yes, I think your answer is right. And this problem does apply, but you have to change the angle as well, not just radius. If you actually work that example fully through you should get the same answer. In the future, could you state the question more fully before you post, instead of having us guess what your references are?
I posted a link which should of taken you to the question
 
  • #10
xdrgnh said:
I posted a link which should of taken you to the question

It did. But knowing the question wasn't helping to know what you were doing wrong. Which was your actual question.
 

1. What is the formula for finding the area between two circles?

The formula for finding the area between two circles is A = π(r1^2 - r2^2), where r1 and r2 are the radii of the two circles.

2. How do you calculate the area between two circles if they overlap?

If the two circles overlap, you can split the area into smaller sections and calculate the area for each section using the formula A = πr^2, where r is the radius of the overlapping section. Then, add the areas of all the sections together to get the total area between the circles.

3. Can the area between two circles be negative?

No, the area between two circles cannot be negative. The area is always a positive value, even if the circles do not overlap.

4. How does the size of the circles affect the area between them?

The size of the circles directly affects the area between them. The larger the circles, the larger the area between them will be. Similarly, smaller circles will result in a smaller area between them.

5. Is it possible for the area between two circles to be infinite?

No, the area between two circles cannot be infinite. As the circles get larger, the area between them will increase, but it will never reach infinity.

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