find-the-area-of-the-shaded-region-graph-cant-copy-4

Question

Find the area of the shaded region.
(Graph cant copy)

Noraney Ocampo · Accepted Answer

you&#x27;re being asked to find the area off this shaded part in green, and you&#x27;re given a few pieces of information to help you out. So first of all, you know that the sights of this triangle inside this circle, the sites are too. And you know that this angle right here is 120. So one thing that you could don&#x27;t is remember that the area the whore circle this pie are square. So if you were if you were being asked to find the area of the circle, let me just write this area of the circle. It would be this, but remember, you don&#x27;t have the whole circle if you divide the holster cost 360 degrees. But you only want 100 20 part of that. So you only want 1/3 off your circle so I can assure you. So that&#x27;s wondered. And this that would be 2/3. And then there will be treaters. So you only one want dirt off it. So then your area for this whole park and ah, from here all the way there, including the triangle, it would be 1/3 pi r Square. So let me write area off the dirt off the circle. Images make this clearer here so that you understand where I&#x27;m trying to go. So the area Oh, 1/3 of circle would be wander Hi, our square again because the 120 degrees that means that you&#x27;re gonna fit that three times into the circle. But you only want 1/3 off it. So the radius, we know it&#x27;s too. So this is going to be 1/3 hi for two squared. So this becomes four. Third&#x27;s by now. You would be done if they were asking you for the area off that part of the circle. But they don&#x27;t want you include this little piece, this little trying. So then, toe, find the area of the shaded region. You would do the area off here in blue. Just put this one. So the area, well, your little point of the 1/3 off the circle minus the area off the triangle. This triangle that we have here, How do I find the area of this triangle right here? Because I don&#x27;t want I don&#x27;t want to include that part in my area again. You have the formula for the area, which is 1/2 part aside a which is to times Side B, which is also to time sign off 120 degrees because that&#x27;s the tango in between. So and remember the area off the whole water. Third off the circle IHS for over three pie. So you&#x27;re gonna take away that piece of the triangle. So if you put this into the calculator, you get a 4/3 pi my nest. This is 1/2 times two times two. That&#x27;s just it&#x27;ll and sign of 120 this radical 3/2. Now notice that you can cancel out this tools so you&#x27;re left with 4/3 pi minus radical three, and then you are going to put that into the calculator way. This war over three times pi minus radical three and you&#x27;re going to get the area off this. Let me show it off. This part in green Toby close to to a point five square units again to repeat, repeat the process. We&#x27;re looking for this area and green. The first thing that I could think office find the area of the whole circle, which would be pi r square. But I don&#x27;t want the holster Co. I want only 1/3 off it. That&#x27;s how I got the Wonder Pyre Square, which is for pie or for over three pie. Once I plugged it into the formula. The next port iss. I don&#x27;t want the whole section. I don&#x27;t want the third off the circle. I wonder of the circle minuses triangle because I don&#x27;t want to count the triangle. So the area of this triangle, it&#x27;s one huh? Times your side, which is two times your other side, which is also two times sign off the ankle in between, and the and going between us 120 you&#x27;re gonna simplify, and then you&#x27;re gonna put it into your calculator, and you should get 2.5 square units.

Noraney Ocampo · Answer

you want to find the area off everything and green images kind off like color in. So you want to find the area All this part. So basically, the whole circle not in chlorine. This little piece where the green doesn&#x27;t touch and how different options total this. But one way that I am going to do this ISS notice were no that the area of the circle IHS pie are square. You&#x27;re here are your radius is 12 in this case, and this angle right here is in degree in radiance emits pi over three. So notice again. First of all, that your own one, the area off the whole circle. You want almost everything except this little piece. So I&#x27;m gonna call the area of the circle in black. I&#x27;m gonna call everything. It&#x27;s gonna be in black, and it&#x27;s gonna be hi 12 square, which is 144 pie. You could be done already, but I don&#x27;t want that. I want this area to get the area in green. So the area of the can you write it on this site? The area off the part in green. So the shaded area in green is going to be the area of the circle which would be the whole circle minus the area that stayed in red. So the area of the red part the part it doesn&#x27;t have greens on it. So I need to find out what is. How do I How do I find the area of this? So one thing that I could do IHS use the fact that the area of the whole triangle is 144 pi and that since it is split up into pi over three, that means I would be able to fit six triangles so want so three for why? Three? 123456 So I would have six little pieces so I can split up this the area into six parts. So then I would have 1/6 off the circle off times 1 44 Hi. And I would give me the area of this triangle with this little part included, So that would be 24 pi. There will be the area off, uh, six Professor corn. Let me just enable this here. Sixth, both Ah, circle were kind of like this lice of pizza. You would say And now I want to take out this part. How can I take this part away? Will remember. You can always add and subtract with areas, so I&#x27;m gonna use rhetoric percent This part. I am basically going to take the sixth of the circle and take away this triangle. So that&#x27;s going to give me this red park. So I&#x27;m gonna have 24 Hi, minus the triangle inside in black. So I&#x27;m gonna call it the Area of the triangle and again because I already know the degree Did the radiance in this case or the angle in between? I and I know this site is 12 and the site is also 12. I can just private into my equation, that is so One have times a times B times the sign pi over three. So if I&#x27;m using this, find the area in this little port red, It&#x27;s going to be 24 pi my ness 1/2 times, 12 times, 12 times. Sign of pay over three. This radical to be over to. So this is going to give me 24 pi my nest. This whole thing is going to give me 72 and this is going to be a radical 3/2 and I can reduce this one further by doing half off. 72. So this is going to be 24. Pai, minus half off 72 is just 36. So 36 radical three. So this part right here in red, the part that doesn&#x27;t have any green, that&#x27;s the area off it. So now I can go back to my bigger formula, the where I want it. So find the area of everything else in green and I can use the area of the circle. I&#x27;m gonna do it in green now. So the area off that this, uh, portion would be 144 pie, my ness. The whole area that I have here, which is 24. Hi, my nest. 70. Too radical to be over to. And I am going to just pluck all this sent into the calculator. So this is going to keep me Well, first, I&#x27;m gonna simplify. So this is going to be 144 pi minus 24 Pi plus 72 Radical three over you. Actually not. I had already simplified this. This is just 36 pie. I mean, 36 radical three. So let me just this already noise 36 Medical three. And now I can do that. This area is 120 I plus 36 radical three. And now this simplest forms When I&#x27;m going to put into the calculator 120 times I plus 36 tens Radical three. That&#x27;s going to give me that. The area of the shaded region is approximately 439 point 34 square units.

Xiaomeng Zhang · Answer

so we can see this one. He goes to the integral zero to true for minus acts to our off too. And also you have the absolute value. Cool three. And we can see those one for acts miners X to the power of 3/3. And those one the full times to minors Hate over three. Those one. We have four miners. Look, one piece. I was minus eight. Well worth three. So eight miners, eight minutes over three. And that&#x27;s when we have four miners read as 19/3 ricchiuto to 23/3.

Xiaomeng Zhang · Answer

So for those one, we&#x27;re have the integral from minus 1 to 0 Ax choir manner to acts also have the absolute value. So we can see those one axle pop grocery over three minutes. Axe choir minus 10 for those one also acts apart from 3/3 minutes. Axe choir zero and truth. So we&#x27;re how they&#x27;re o minus minus one b Chico&#x27;s toe one raina zero minus one. That&#x27;s why we are how eight minus zero miners full that a co so five minor 7/3. Rudy, call to 8/3.

Xiaomeng Zhang · Answer

So for those while you have the absolute value from 0 to 1, he the power off axe miners E and from one to true eat of horror facts minus e that a seat of power of ax minus E ax zero and one absolute value one and two. We&#x27;ll see e to the power off one minus. See you too. Need to the power off the road that I have called to one My notes e But those while we&#x27;re how e to the power of to minus e minors e we guarantee that ico to one and those when you killed two e Squire my nose to e reach approximately, you call to a true 0.952

Problem

Find the area of the shaded region by (a) integra…

Problem 4 Easy Difficulty

Find the area of the shaded region.
(Graph cant copy)

Answer

$$
\frac{10}{3}
$$

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Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals

Anna Marie V.

Kristen K.

Samuel H.

Michael J.

Integration Review - Intro

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$$\frac{10}{3}$$

Calculus Early Transcendentals

Anna Marie V.

Kristen K.

Samuel H.

Michael J.

Integration Review - Intro

Definite vs Indefinite

Howard Anton, Irl Bivens, Stephen DavisCalculus Early Transcendentals

Anna Marie V.

Kristen K.

Samuel H.

Michael J.

$$
\frac{10}{3}
$$

Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals