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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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natulia [17]

Answer:

1648

Step-by-step explanation:

5/9 are girls. The 9 represents the total.

Set up a proportion and you have

5/9 = ?/3708

3708/9=412

412x5= 2060 girls

3708-2060= 1648

8 0
3 years ago
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A weather balloon is descending from the atmosphere. Its altitude changes by
OlgaM077 [116]

The change in altitude after 135 seconds was a decrease of 810 meters, that is, -810 meters.

Given that a weather balloon is descending from the atmosphere, and its altitude changes by -6 meters every second, to determine what is the change in altitude after 135 seconds the following calculation must be performed:

  • Amount of time x change per second = total change
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  • -810 = X

Thus, the change in altitude after 135 seconds was a decrease of 810 meters, that is, -810 meters.

Learn more in brainly.com/question/24654925

3 0
3 years ago
Each package of paper contains 100 sheets. At the beginning of the school year, each of Mr.Castillo 's 34 students brought in on
oksian1 [2.3K]

Answer:

3400

Step-by-step explanation:

Just multiply 100 by 34.

7 0
3 years ago
a painter bought 8 gallons of paint just enough to cover 2 rooms. One room is twice the size of the other and requires only 2 co
e-lub [12.9K]
So, he's got 8 gallons of paint, to paint the two rooms, of the two rooms, one is twice as big as the other

now, "x" is how many gallons to paint the larger room with only one coat, however, the larger room uses 2 coats, so, the larger room uses 2x of paint
now, the client declined to paint the smaller one

so hmmm as I read... well, we dunno how many coats will go to the smaller room for one, we know the larger will use 2 coats, or 2x.. if we assume the smaller room was going to use say 1 coat or 1/2x

then one can say the painter bought enough for both rooms, 1coat for the small one and 2coats for the larger one

so, the paint the larger room, you'll 2x of paint, for 2coatsand to paint the smaller room, you'll need 1/2 x, because x gallons is how much is needed for the larger room, but the larger room is twice as big, thus the smaller room uses 1/2 of that in gallons

thus, with those assumptions, that the small room will use only 1 coat
\bf \cfrac{1}{2}x+2x=8\implies \cfrac{5x}{2}=8\implies x=\cfrac{16}{5}
that's who many gallons are needed for 1 coat in the larger roomrecall "x" is 1coat for the larger room

now, the client decides to skip the smaller roomso, the painter will only need 2x gallons then

\bf 2x\implies 2\cdot \cfrac{16}{5}\implies \cfrac{32}{5}\implies 6.4\ gallons

he bought 8 gallons, 8 - 6.4, he's got left 1.6 gallons
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3 years ago
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X =1 I had this question
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