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HomeToolsmaths resit pdfSign In1109 R 5 | Q / 6 LUICSUI iubci LUuC ec [UBEICfuuClCfy 4C . LUUM CIZU This courscwork will be asscsscd by the student presenting their...

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HomeToolsmaths resit pdfSign In1109 R 5 | Q / 6 LUICSUI iubci LUuC ec [UBEICfuuClCfy 4C . LUUM CIZU This courscwork will be asscsscd by the student presenting their clear hand-written solutions (on A4 shccts with their full name, student registration number, date and the title EXIOI0 Mathematics [: Re-sit Coursework: 2019) to the following three questions_ during 30 minute one-to-one meeting with Professor Crouch. The meeting will be arranged (by Professor Crouch_ by email) to occur in C128 betw

Home Tools maths resit pdf Sign In 1109 R 5 | Q / 6 LUICSUI iubci LUuC ec [UBEICfuuClCfy 4C . LUUM CIZU This courscwork will be asscsscd by the student presenting their clear hand-written solutions (on A4 shccts with their full name, student registration number, date and the title EXIOI0 Mathematics [: Re-sit Coursework: 2019) to the following three questions_ during 30 minute one-to-one meeting with Professor Crouch. The meeting will be arranged (by Professor Crouch_ by email) to occur in C128 between 15-19th July 2019. A square with side lengths 5 centimetres is positioned with one apex at the centre of second square (which has side lengths of centimetres)_ The longest side of the overlapping shaded) quadrilaterab region has length of 3 centimetres scc below)_ Calculate the arca of the shaded region Show your full working' out together with an appropriately labelled sketch Share Soarch tools Export PDF Adobe Export PDF Convcrt PDF Filcs Wcrd Excel Online Select PDF File maths rosit paf Convert t0 Microsoft Wora docx} Document Language: English (U.S ) Change Convert Given the stiffness matrix [K] and force vector {f} Create PDF CAn DNC ~3 [K] = 106 N.m-I {J} = {11 17 -8}' x 103 N 32 find_ using Gaussian elimination, {d} (where {d} = {d d3}') if [KKd} = {f} Make sure that you first write down the Augmented Matrir and then each step of the row operations (plus the back-substitution steps as part of your solution. Convert edit PDFs wth Acrobat Pro DC Slart Free Trial



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Please do the following. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums $\Sigma x, \Sigma y, \Sigma x^{2}, \Sigma y^{2},$ and $\Sigma x y$ and the value of the sample correlation coefficient $r$. (c) Find $\bar{x}, \bar{y}, a,$ and $b .$ Then find the equation of the least-squares line $\hat{y}=a+b x$. (d) Graph the least-squares line on your scatter diagram. Be sure to use the point $(\bar{x}, \bar{y})$ as one of the points on the line. (e) Interpretation Find the value of the coefficient of determination $r^{2} .$ What percentage of the variation in $y$ can be explained by the corresponding variation in $x$ and the least-squares line? What percentage is unexplained? Answers may vary slightly due to rounding. Data for this problem are based on information taken from Prehistoric New Mexico: Background for Survey (by D. E. Stuart and R. P. Gauthier, University of New Mexico Press). It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let $x$ be the elevation (in thousands of feet) of an archaeological site in the southwestern United States. Let $y$ be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The following data were obtained for a collection of archaeological sites in New Mexico: $$\begin{array}{c|ccccc}\hline x & 5.25 & 5.75 & 6.25 & 6.75 & 7.25 \\\hline y & 19 & 13 & 33 & 37 & 62 \\\hline\end{array}$$ Complete parts (a) through (e), given $\Sigma x=31.25, \Sigma y=164, \Sigma x^{2}=197.813, \Sigma y^{2}=6832, \Sigma x y=1080$ and $r \approx 0.913$. (f) At an archaeological site with elevation 6.5 (thousand feet), what does the least-squares equation forecast for $y=$ percentage of culturally unidentified artifacts?

Were given the set of data points listed at the top of this whiteboard X fly. And we want to use these data points to answer the following questions. A through F. Starting off with part A on the left, we want to produce a scatter plot of these data points. I've already included the scatter plot. As you can see where the data points X. Y are demarcated by the black crosses or exits next to the right and part B. We want to compute the sum is relevant to the state to as well as the Pearson correlation coefficient. R The sums are given by following the forms exactly. So some access to some of the X values. Some why is some of the individual Y values and so on. To compute are we use the following formula which takes us input, our sample size and and the Sun is just computed. This gives our equals .9126. Next below. In parts you want to find the equation of the line of best fit which requires finding these parameters first are simple mean X bar and a sample mean Y bar are given by the sum of our X values about it by n 6.25 And some of our Y values over M 32.8. Yeah, we can find the parameters for our best fit. Line being a. As follows. The slope B is given by the equation here, which takes us input and the sample size and the sums we found above Plugging In. We get the equal 22 and then plugging in. Ry bar be an X bar to our A equation on the right gives us intercept negative 104.7. This means we have equation for the line of best fit why hat equals negative 104.7 plus 22 X. Next part Do we want to return to the scatter plot on the left and graph ry hat. Doing so we want to make sure we include our X. Men and women, which looks like this next in the bottom right part. You want to calculate? The coefficient of determination are square and interpret its meaning. This is simply the square of the correlation coefficient 0.83 to eight. We interpret this to mean that roughly 83 of the variation of the data can be explained by the corresponding variation and excellently squares line 17 of the data accordingly cannot be explained by this. Finally, in part, after the bottom, we predict y where x equals 6.5 Plugging into our white hat, we obtain 38.3.

So for this problem we're going to need um a few determinants. In fact we're gonna need four determinants, so we'll create 1/4 determinant here for those who are curious on how to make determinants. Um We can do this where this block right here is going to be equal to m the term, that's the function and then it's going to be of this whole thing and then shift enter. So now that we have these determinants, we want to determine the different values. So we have um 12.79 era 67.21, 12.30. And we have um 53 zero. Actually these are going to be 67.21 12.3. And this is gonna be um 53.05 47.12. 53.05 47.12. This will be um What? X. three and Y. three. So um 10.09 53.11. And then lastly we have 10 you're nine 53.11. And um we have Our ex not why not again? So it's gonna be 12.79. Mhm. Your point is your hero. These are determined determinants. We end up getting as a result. So we want to um add all these up and then take the One half times them. So we're gonna have 0.5 times this plus this, plus this plus this, Calculate that we get to 167.25. So that's going to be our approximate answer 21 67.25 is the area and that's going to be um in units squared.

A triangle that's been, uh, kind of rotated and translated around. Let me make sure I do this right. One similar to this. So to explain how the outer shape is a square is if each one of these triangles is concurrent and they're right triangles, that means the the larger angle in the small angle are complementary and some we add them together, we're gonna get right angles. And because of how apartness is gonna be the same for each of them, we know that we're gonna have four right angles and four sides the same so four right angles and for equal sides. Okay, so that means it's a square. Okay, so part being just wants to know what the length of each side of that square is. And so if we look at that, the long side is be eso part being, and we're gonna along the long leg is be. And so the length of the side of square on the inside let's not call it the let's call it D. Cancer de is gonna eat will be minus a on that we can see that because B is the long length and in a is that shorter length. Okay. Okay. So the last problem says that the outer square has sidelined C square. And then we can also add up all the areas on the on the inside. Um, okay, So we're gonna have C squared. That's the area of the outer square is equal. Teoh B minus a squared. And then plus four. Because it for the strangles times one have be a times a someone half base, times height. Okay, so if we expand it out, we're gonna be square minus two A B plus a square. Four times. 1/2 is two plus two a b. And then the two babies canceled, leaving us with a squared plus B squared. Okay, since about these things described the same area, we can conclude that a squared plus B squared is equal to C squared. Thank you very much.


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