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valkas [14]
3 years ago
7

Evaluate the double intergal between the two cirlces

Mathematics
1 answer:
svp [43]3 years ago
5 0

<span>3down votefavoriteFind the area between the circles <span><span><span>x2</span>+<span>y2</span>=4</span><span><span>x2</span>+<span>y2</span>=4</span></span> and <span><span><span>x2</span>+<span>y2</span>=6x</span><span><span>x2</span>+<span>y2</span>=6x</span></span> using polar coordinates.I have found that the equation of the first circle, call it <span><span>C1</span><span>C1</span></span>, is <span><span>r=2</span><span>r=2</span></span> on the other hand, for <span><span>C2</span><span>C2</span></span>, I get that its equation is <span><span>r=6cosθ</span><span>r=6cosθ</span></span>. Then, to find the bounds of integration, I have found that their angle of intersection should be <span><span>θ=arccos(1/3)</span><span>θ=arccos⁡(1/3)</span></span> and <span><span>θ=−arccos(1/3)</span><span>θ=−arccos⁡(1/3)</span></span>. Then, to set up the double integral:<span><span>A=<span><span>∫<span>arccos(1/3)</span><span>−arccos(1/3)</span></span><span><span>∫2<span>6cosθ</span></span>rdrdθ</span></span></span><span>A=<span><span>∫<span>−arccos⁡(1/3)</span><span>arccos⁡(1/3)</span></span><span><span>∫<span>6cos⁡θ</span>2</span>rdrdθ</span></span></span></span>However, when evaluating this integral with the calculator, I get a negative value. What would be the problem in this case? Thanks in advance for your help.</span>
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3 years ago
The sum of two numbers is 48.when the smaller number is subtracted from the larger number,the difference is 12. What are the two
Savatey [412]

Answer:

The two numbers are:

30 and 18

Step-by-step explanation:

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From the first eq.

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2 years ago
Rephrase in contrapositive form:
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Step-by-step explanation:

Consider the provided information.

For the condition statement p \rightarrow q or equivalent "If p then q"

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Remember negative means opposite.

Contrapositive: If xy < 0 then x<0 and y<0.

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3 years ago
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