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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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ch4aika [34]

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Step-by-step explanation:

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Scilla [17]

Answer:

According to tangents secant segments theorem,

11) x(16+x) = (x + 6)^2

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Dividing the whole eq. by 8,

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x^2 - 7x - 18 = 0

x^2 - 7x - 18 = 0

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x = -2 or x = 9

length cannot be negative,so,

x = 9

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Please help with math question! This question is stressing me out (View Image)
TEA [102]
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but first lets find the volume of the rectangle...
In order to find the Volume of a rectangle we need to use this formula...
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length = 10in
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lets solve:)
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or we write it like this 
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now time to find the volume of the half cylinder:)
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</span>now since we found an entire cylinder and we only want half of a cylinder lets divide our answer in half
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so we write it like this 235.5units³
But we have to add both of our multiples together so lets do that
Volume of rectangle = <span>480in³
</span>volume of half sphere = 235.5units³
480 + 235.5 = 715.5
answer = 715.5units³
I hope this helped and everyone learned something new
anyways don't forget to
MARK ME BRAINLIEST! :D
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3 years ago
Find the value of X in the simplest radical form
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Step-by-step explanation:


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