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nataly862011 [7]
3 years ago
13

Find the centroid of a semi circle using polar coordinates and a double integral. Given a radius of r, and theta being between 0

and pi.
Mathematics
1 answer:
Fittoniya [83]3 years ago
4 0
The area for a semi circle in Cartesian coordinate system with the flat edge against the x-axis is:A=∫0r2−x2√∫−rrdxdy
Bounding limits for x are from -r to r. And for y, this comes from the equation for a circle:x2+y2=r2
Solve for y:y=±r2−x2−−−−−−√
But since we are only dealing with a semi circle, we can always look at the positive answer. 
To convert to a polar coordinate system, we used some equations you have probably seen:x=rcosθy=rsinθdxdy=rdrdθ
The substitute to convert to polar coordinate system:A=∫0π∫0rrdrdθSolve this for the area.A=πr2/2

To find the x coordinate of the centroid:x=1/A∫∫xdxdyorx=1/A∫0π∫0rrcosθ(rdrdθ)Solve and you will find x = 0 which intuitively makes sense.
Similar for the y coordinate of the centroid:y=1/A∫∫ydxdyory=1/A∫0π∫0rrsinθ(rdrdθ)Solve and you will find y=4r/3π
This means the centroid of a semicircle is at: (0,4r/3π)
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Ja'Kiree has a bunch of quarters and nickels in her piggy bank totaling $8.75. If Ja'Kiree has 26 quarters, how many nickels doe
evablogger [386]
Start off by stating your facts. You have a maximum of $8.75. We know that each quarter is 25 cents so we multiply 25x26 equaling 650. Yet we need a decimal so it would be $6.50. Each nickel is worth 5 cents so then you would minus $8.75 and $6.50 getting us to $2.25. Now divide it by 5 cents and you should get 45 nickels. You can also do this by stating that 10 nickels is 50 cents and go until you get 45
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3. You have 3 consecutive numbers, with the smallest number n.
lbvjy [14]

Heyo !!

☕️   \bold{Jace~ is~ here~ to~ help~ !}    

\frac{A~n~s~w~e~r~ :}{}

<h2>A. What are the 7 numbers in the term of n?</h2>

——————————

———————————

 EXPLANATION :

Because when you have 3 consecutive numbers, you have to put 7 numbers in the term of the n.

Hope It Helped!

<u>And Tell me if The answer is wrong. . .</u>

<h3><u>Good Luck With Your Assignment!</u></h3><h3 />

#LearnWithBrainly

 \underline{A ~n~s~w~e~r~:}

﹋﹋﹋﹋﹋﹋﹋

Jace ^-^

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Answer:

i. x^2 – 1

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iii. x^4 - 1

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Products are obtained by multipliyng each left term by each rigth term as follows:

i. (x- 1)(x+ 1) = (x^2  – x + x - 1) = x^2 – 1 (equal terms with opposite sign substracts and the result is 0)

ii. (x- 1)(x^2 + x + 1) = (x^3 – x^2 + x^2 – x + x – 1) = x^3 – 1

iii. (x- 1)(x³ + x² + x + 1) = (x^4 – x^3 + x^3 – x^2 + x^2 – x + x – 1) = x^4 - 1

7 0
3 years ago
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