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8. If Ixl + x+y = 75 and x + |bl -b = 150 then what is the value of Ixl + lyl1056090cannot be determined...

Question

8. If Ixl + x+y = 75 and x + |bl -b = 150 then what is the value of Ixl + lyl1056090cannot be determined

8. If Ixl + x+y = 75 and x + |bl -b = 150 then what is the value of Ixl + lyl 105 60 90 cannot be determined



Answers

(II) If $$\vec { \mathbf { A } } = 9.0 \hat { \mathbf { i } } - 8.5 \hat { \mathbf { j } } , \quad \vec { \mathbf { B } } = - 8.0 \hat { \mathbf { i } } + 7.1 \hat { \mathbf { j } } + 4.2 \hat { \mathbf { k } } , \quad$$ and $$\vec { \mathbf { C } } = 6.8 \hat { \mathbf { i } } - 9.2 \hat { \mathbf { j } } ,$$ determine $$( a ) \vec { \mathbf { A } } \cdot ( \vec { \mathbf { B } } + \vec { \mathbf { C } } ) ; ( b ) ( \vec { \mathbf { A } } + \vec { \mathbf { C } } ) \cdot \vec { \mathbf { B } }$$ $$( c ) ( \vec { \mathbf { B } } + \vec { \mathbf { A } } ) \cdot \vec { \mathbf { C } }$$

So here we're talking about a two pair. So that's when two numbers A and the when their reciprocal attitude So one over a plus one over b equals to do here were given, um, one value we use off the other. So a equal to 7/3. Okay, that's we need to find what beacon? Be the question. So the reciprocal of a would be 3/7 plus B is equal to two. Okay, So in order to do that, I'm gonna think about we're gonna make them both seventh, because being control what b is. So how can I make what goes here in acts to make this somebody to? Will it work to make this some B two? Really? What the saying? Three plus act replace X over seven is equal to two. Um, and so if I want some amount of seventh, that's too. I could change. That's to be 14. So or another weird thing about this is multiplying both sides by seven. And I end up with three plus x on this side and 14 on the other side. Um and so here I consult for what? X another way I could think about how I was doing that, um is so seven. Seventh is one. So 14 7th is to just multiplying that by two. Okay, so we have three plus Xs 40. So let me subtract three from both sides. This question saw for X and they ended with 14 miles three, which is 11 11 is not our kind of answer. We're looking for a B, Remember, On B is this whole thing. The reciprocal so be is the reciprocal of 11/7, which is 7 11 x.

Okay, So if we know that these two are both I saw sleep strangles and one eighty minus e is equal to two. Why and why Isaac to seventy five. So first, let's fill this in. So this is seventy five. We're looking for the value of X. If we know that that seventy five then we can also plug this into find. See, we have one. Eighty on the C is equal to two times seventy five. So one eighty minus C is equal to one fifty. So I'm going to subtract one eighty funded both sides. If you mean negative C is equal to negative thirty What by both sides By negative one giving us that C is equal to three. So here is thirty. But then because we know that these are I saw sleaze triangles. That means that this angle and this angle are also the same. So let's just call those eh? And eh? So that means we know that one eighty is a total angle measure of a triangle. So one eighty must be the sum of thirty plus a plus A, which is one eighty is equal to thirty plus two a and so we just have to isolate for R A. So I'm going to subtract thirty from both sides. Giving us one fifty is equal to two, eh? And then I'm going to divide both sides by two. Giving us that seventy five is people too, eh? Then let's look at this line in isolation. So if we look at that line, looks like this. Here's X. You're seventy five. We know that the total angle measure of a Linus one eighty. So we take one eighty minus seventy five, which people solve for X, then that's going to become one of five, so X is equal to one of five degrees.

Okay, so if we have a sum of three numbers and what cause is that X Y and see? And we know that that sum is eight fifty five and then it says one of the numbers X is fifty percent more than the other two numbers. Uh, the some of the other two numbers. The some of the other two numbers is five foot see, but we know it's fifty percent more, which we can call one point five because we always want to express it as a one plus our or a one Linus are. But because it's one fifty percent more we're going do one plus fifty percent presented out of decimal, which is one plus your point five, which is one point five. So then, from here, we want to figure out a way to isolate the variables. So to do that, I'm going to go ahead and son used the Y policy as one collaborative variable and try Teo substitute that in. So in order to do so, I'm going to subtract X from both sides of the top equation, which gives us why plus C is equal to eight fifty five minus X so then we have a wife will see here in a pipe. Lissy here. So I'm gonna take this and substitute this right up there. So when I get X is equal to one point five, I'm a fifty five minus X in parentheses. So then we have an equation with just one variable, which is very solvable. So I'm gonna distribute this one point five to both the eight. Fifty five and the X. And if we do a fifty five times one point five, I get one two eight two point five minus one point five x is equal to X from here. I'm gonna add extra both sides. I'm going to bring that over here. So one point five x plus x is two point five x is equal to one two eight, two point five. Finally, I'm going to divide both sides by two point five. And if I do that I get to that X is equal to five. Thirteen She'll be should be our crack answer

In the question it is being said that you have to suppose that the value of y is 10 X plus two. Okay. Leaving any value of why we're here now we want y to be ridden 0.2 units of six over here. So we just have to find out the values of excess that this statement is True. Right? So since why has to be within 0.002 units of six um we can just write the expression as why -6 is there's an 0.002. Right? I've just written an absolute value inequality over health. Now the subject of the value of buying as 10 X plus two on the left hand side. Sorry I just forgot to run that minus six as well. Right so this is less than 0.2 Now just combine of the light items together so we'll get 10 X -4 is less than 0.00 two. Now, since this was an absolute value inequality, I can just write this as 10 X minus four should be greater than minus 0.2 and it should be less than 0.2 right Now, what you have to do is you just have to add a four on both the sides of the equation. So I'm doing that. I'll get 10. X is greater than 3.998 and it is less than 4.002. Next justify both the sides of the inequality by 10. So we'll get access Greater than 0.3998 and it is less than 0.4, That means that it should be within the interval 0.3998-0.4002. If access within this interval then that means the difference between Y and sex is within 0.002. Yeah, so this is the required interval over ship.


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