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Joot*ootNa ofidexoud: Naelxwa'Yarr bighCaculddd baight (cd) using cotvation fcta =...

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Joot*ootNa ofidexoud: Naelxwa'Yarr bighCaculddd baight (cd) using cotvation fcta =

Joot *oot Na ofidexoud: Naelxw a' Yarr bigh Caculddd baight (cd) using cotvation fcta =



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$$\begin{aligned} &\text { Given: } \frac{\odot \mathrm{O}}{\mathrm{CD}} \cong \overline{\mathrm{DE}}\\ &\text { Prove: } \angle \mathrm{COD} \cong \angle \mathrm{DOE} \end{aligned}$$ (FIGURES CANNOT COPY)

We have this diagram of some triangles over on the left and were given some information about it. And our ultimate goal is to be able to tell us what see the equals. We are told that ACT is perpendicular to B. C. That means this right here. This whole thing is a 90° angle. We're also told that C. D. Is perpendicular to a B. So this is a 90° angle and we are told that the measure of angle B is 30 degrees, So this is a 30 degree angle and that B C is eight, Tends to Square 2 3. So if this right here is a 30 degree angle and we've got this 90 degree angle here, That means this piece here is 60°,, which means this is 30 that eight square roots of three is across from the right angle. So it is the hypothesis of that triangle. And because it is a 3060 90 triangle, we can use that. So triangle C D B Is a 30 60 90 Triangle. This allows us to use those rules about 3060 90 triangle Where the short leg at Times two is the hypothesis and the short leg Time to Square 2, 3 is the long leg. And we can use this information to help us figure out what CD is. I'm going to call C. D. X. So B. C. Is the high partners C. D. Which is X. That's what we want to find is our short leg. So we know the hypothesis and want to find the short light. So what we can do to do that, it's A X. Equals eight times square to three divided by two. If the short leg times two is the hypothesis, then we're going to work it backwards and the high partners divided by two would give us the short light. So X equals eight divided by two is four and we get four square words of three. Therefore, CD is for Square roots of three.

So, based on this diagram of one larger triangle in one smaller triangle, we want to ultimately determine the length of wine segment. Yeah, see? And to do that is going to take to parts. But using the same theory theory um, we're gonna use is the triangle proportionality the room which states that if a line if a line that is parallel toe one side of a triangle intersex the two other sides of that triangle, then it divides those two sides into segments that are proportional to one another film. Let's first look at Triangle A D and in triangle A. D. We have that, um, line segment A D is parallel toe line segment. Um, well, we'll call that point why one segment x y and because of that, we can set up the proportion. Um, a X over X e equals so a the length of a X and actually are proportional to the lengths of d y. And why I e. And to find our unknown, which in this case is ax E. We can just substitute the known values for the sidelines. So a X is 17 over x e. That's what we want to solve for the wine is 18 over. Y e is 16. From there we can cross multiply, though, so we get 17 times 16 is to 72 equals 18 times x e. If you divide by 18 on both sides, these eighteens will cancel out. So you get that X e equals, um, 15.1 repeating which we can just approximate to 15.11 about, um, so we found the length of X e so we can write that in their nets 15 going 11 approximately and then to find the, um, length of E. C. We're just gonna do the same thing, but with Triangle ABC. So in this triangle, we have the, um, line segment D E parallel to lions thing and BC, which means that, um segment A d and G b their lengths are proportional to a e and e see. And again, we could just repeat our process from the last step and plug in the values so a G is 15 over DB is seven point five equals e months. A A is gonna be 17 plus 15.11 which is going to turn out to be 32 0.11 over are unknown. E see again we cross multiply so we get 15 times you see is equal to 32.11 times 7.5 which is equal to approximately 200 240.83 We then divide both sides by 15. Those fifteens cancel out divide the other side by 15 and you get that e c equals approximately 16 0.0 six.

We're going to do problem number 36. So in this question, what we're going to do, we're going to judge solve the given question. These are the values which are given to us. That is Jesus G s given. That is explosive. 3.5 today is given. It is given in HK is given. Okay, So what we are going to do is as it is, a zit. IHS said in the question that gj is parallel toe ikea. Okay, so we can just apply here. Or we can just use the concept off strangle proportionality to Europe. Okay, Rangel, throw personality to your, um okay. This year, um, we can apply. So according to that, your, um what do we can write? Weaken Right A Z Let me right between the standard of one that is G bye energy is he calls toe G by h G is equals toe Jake by HIV. Okay. No, this value is not given to us. That is G is not given to us. And j k is also not given to us. So we can write this G in the terms off h E and H G as this value can be written as Let me right here. That is E h manners energy. Similarly, we will write for Jackie, so just let us substitute these terms. G and Jacob in the terms off e Etch are sk. Okay, so let us do that. So what? We can write? You can write gs. You can write g s. You decided e Etch Manners E h Manus What is given given this GH Um okay, let us right. Edgy. Okay, let us right. This is SG or it would be better if I writer h g Okay, so that you should not have any confusion as if we see mm edge G Yeah. It would be better to write a GH only G h Okay, now? No, it's better. That's far better. What we can write us. What we can write to G is we can write. G is e h. Many strategy are e h Manus at g r g h. Both are same. So let us right idea. So have we had written the h no j k can be written similarly in the same way we can write this J k s hk HK menace at a menace at DJ. Okay, so let us writer. We cannot This is HK minus h g by energy. So let us solve this further. You can barely says e h by GH Manus GF by GH similarly on the right hand side also HK by at G menace at a nearby at today Okay, so g eight bad years that will become one So it would be better now there just about to get the final equation or you can say or you can use it as the expression whenever you get this type of answer management by HK by HJ Similarly, here we will have management. Now this management and management will cancel each other as both assemble you and same sign Now the final equation which we got is e etch by GH physicals toe HK biology So let us put the value there Let us put the value off E edge which is given to us is 21 and G s G f duties given doses X plus 3.5 is because you know HK HK is given that the seven now h g h d is given X minus 8.5. Okay, Now, as both are in the numerator, so we can cancel our diseases like this. That is seven threes or 21 so we can write this three into X Manas 8.5. Is it calls Toe X Plus 3.5. Okay. No, that is right. We will like three x manners. Let us find it that it's 8.5, 8.5 and 23 So this will be 25.5 physicals. Toe X plus 3.5 now. Three X man assets. This will be two x two X now here 25.5 plus 3.5. So from here, we will live to exit vehicles, too. 25.5 plus 3.5. How much this is. This is 26 plus 26 plus three. That is 29. Okay, so from here we got Finally we got the value effects. That is 29 by two. So this is 14.5. So the value of X, which we have is exit vehicles to 14.5. This is the answer. Thank you very much.

If we have any equilibrium and we disrupt the equilibrium, the reaction shifts in an attempt to partially offset the disruption. So here's the equilibrium that we are considering for this problem. If we increase the CD two plus concentration, we've bulked up the right hand side so it shifts to the left to get rid of the bulk. If we increase the S two minus concentration we've bulked up the right hand side, so it shifts to the left. If we decrease the cd two plus concentration, we created a whole so it shifts to the right to fill the hole. If we decrease the S two minus concentration again we have a hole on the right, so it shifts to the right to fill the hole. If we add more of the solid, the solid is excluded from the equilibrium expression. So no shift occurs. If we add something that contains CD two plus, will increase the CD two plus concentration. To get rid of that increase, it needs to shift to the left. If we had sodium nitrate that it's not part of the reaction. No shift occurs, and if we add H plus, the H plus can actually react with the sulfide, decreasing the sulphide concentration, and as the sulphide concentration decreases, it shifts to the right to offset that decrease.


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