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2 EVALUATE THE LiNE iNTE GRALthun C 6 th< cuicukantJ-2) d QULC Jadw 4 frem O-77 t &3...

Question

2 EVALUATE THE LiNE iNTE GRALthun C 6 th< cuicukantJ-2) d QULC Jadw 4 frem O-77 t &3

2 EVALUATE THE LiNE iNTE GRAL thun C 6 th< cuicukan tJ-2) d QULC Jadw 4 frem O-77 t &3



Answers

Parameterize the line from (4,1) to (6,-2) so that the line is at (4,1) at $t=0,$ and at (6,-2) at $t=1$

So for this problem, they give us two points. They give us the point X value 4.8. Why? Value 2.5 and they give us the point. X value 3.6. And why about you to do? And they want us to find these slips. We know Slope, which is M is going to be a change of why. Over your change. Okay, So with that being said, we're going to the four million give us is our Y two minus? Why? One to fight it by X two minus X one. Okay, so what we did before we actually start plugging us is, And we're gonna go up to our points, and we're going to assign 0.1 and 0.2 doesn't actually matter. So we're just gonna take this first point and said it's their 0.0.1 and where to go and take the second point. So that's our point. So now what? We know that we can start plugging it now, remember, Just like the alphabet, our points go act and then why? Okay, so, any time looking at the why will be like in the second value in the X. The first value. So where to start plugging in now? So it says the why Value of our second points are second point and are why value we have you point to minus the why value of our first point, which is 2.5. You were wanting to divide that by the X value of our second point. So 3.6, minus the X value of our first point, which is four point a. Now, when you do this and you plug this in 2.2 minus 2.5 is going to give you a negative 0.3. And then whenever you take the bottoms of 3.6 and use of truck 4.8, it's going to give you a negative 1.2. Now, we can simplify this as a frat or as a decimal. We can get 0.25 okay. And that's the same thing as a fraction saying 1/4 1/4. Hey, um, the exact scene answer. There's right in a different way. So here are Slope R M is going to be 1/4 Hey, or again, you have your 0.25 which is this

In this question were given the parliamentary equations thanks is equal to four minus sweetie. And why is equal to -2 plus 60? And we had to find the slope. Do you know that Slope? This line will begin can be found at two IT X. Now to find the GTX first we have to computer txt T and He had differentiating 4 -3 T. We get -3 and do a T. And finding the derivative of minus to plus 60. Find six and I want to 80 x here is given by do I need to over TX key And here we get six over minus three. It is equal to -2. So my honest with credit. Oh the line and we know that a straight line is here follows the equation why it's good mix plus C. So in this case we have Y. Is equal to minus two weeks plus six. Now to find a point on this time We sail it at T. is equal to zero X. Is equal to well and why Is equal to -2? So a point HT 0-0 is cool. I mean that's two. Now substituting this point into the equation of a straight line. We can find seek -2 is equal to -254 plus he and we get And as eight Plus C. In the year we find nancy to be positive six. Therefore the equation of online is equal to why Is equal to -2 x plus six. And this is the equation of our lives. Now to grab this we're going to say At X. 0-0. Oh away. Why did she go to 6? Indeed Why is go to 0? Our eggs is equal to X. is equal to 6/-2 which is -3. Now Points. We have a six year and the X intercept is minus three. And if we throw this line The eccentricity is actually positive three positive three. Because from our gradient we can see that. Yeah negative credit. So here we are three neutral hola. So this will be the straight line. Why go to -2 weeks plus six and that's it.

Fusion. Since one of the two lines, since one of the two lines is three X plus four Y equal to zero. So from here we can right that Y will be equal to minus three X by four. This value of why will satisfy will satisfy will satisfy the given equation six X squared minus X. Y plus four C. Y square is equal to zero. Put the value of why in this expression we get six X squared minus x minus three X by four plus four C -3 X by for Holy Square equal to zero. We can write it as six X squared plus three X square. This debate. four plus four C. multiply. This becomes nine x square by 16. That is equal to zero. This becomes excess square 27 plus nine C. That is going to be zero. So from here we can see that 27-plus 9 C. is equal to zero. So this implies is equal to -3. So this is going to be the final answer. C equal to -3.

So we wanted parallel 20 negative. One four negative three. So myself, it would be negative. Three minus negative. One over four minus zero. They have three plus one is negative. Two over or or negative one has. So for our next at a point, that's the equal. Negative one, huh? We have t comma four and three comma p. So I have t minus four or three minus t equals negative 1/2 action. Gonna put this negative in the new predator so it cross multiply and I'm gonna get negative one times three minus t equals two times t minus four. So negative three plus t when I distribute equals to t minus eight. Subtract t and I m t at eight on eight, he equals five.


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