MAT2500-03/04 10S Test 1 Print Name (Last, First) _________________________________|__
Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use arrows and equal signs when appropriate. Always simplify expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC, MathCad). You are encouraged to use technology to check all of your hand results.
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The parametrized curve 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
is shown in the figure together with the vector 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 and line segments connecting the 3 points 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, showing that this is not a plane curve.
a) Evaluate and simplify 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,LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2LVEifGdyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHRkQtSSZtb3ZlckdGJDYlLUkjbWlHRiQ2J1EickYnLyUlYm9sZEdGOS8lJ2l0YWxpY0dGOS9GMFEsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictRiw2LlEtJlJpZ2h0QXJyb3c7RicvJSxwbGFjZWhvbGRlckdGOUYvL0YzUSZ1bnNldEYnL0Y2RmduRjcvRjtGZ24vRj1GZ24vRj9GZ24vRkFGZ24vRkNRJjAuMGVtRicvRkZGXm8vRkFGOS1GLDYtUSInRidGL0YyRjUvRjhGNEY6RjxGPkZARkJGX29GYW8tSShtZmVuY2VkR0YkNiQtRiM2JC1GSzYlUSJ0RidGUC9GMFEnaXRhbGljRidGL0YvRi8=| and their values (including 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) at 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.b) Evaluate the unit vector 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 in the direction of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkmbW92ZXJHRiQ2JS1JI21pR0YkNidRInJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHRjQvJSxtYXRodmFyaWFudEdRLGJvbGQtaXRhbGljRicvJStmb250d2VpZ2h0R1ElYm9sZEYnLUkjbW9HRiQ2LlEtJlJpZ2h0QXJyb3c7RicvJSxwbGFjZWhvbGRlckdGNC9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRkcvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGRy8lKGxhcmdlb3BHRkcvJS5tb3ZhYmxlbGltaXRzR0ZHLyUnYWNjZW50R0ZHLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVi9GU0Y0LUY+Ni5RIidGJ0Y1L0Y4USdpdGFsaWNGJy9GRlEmZmFsc2VGJy9GSUZqbi9GS0Zqbi9GTUZqbi9GT0Zqbi9GUUZqbi9GU0Zqbi9GVVEsMC4xMTExMTExZW1GJ0ZXLUkobWZlbmNlZEdGJDYkLUYjNiQtRi82JVEidEYnRjVGZ25GQ0ZDLUY+Ni1RKCZ0aW1lcztGJ0ZDRmluRltvRlxvRl1vRl5vRl9vRmBvL0ZVUSwwLjIyMjIyMjJlbUYnL0ZYRl9wLUY+Ni1RIn5GJ0ZDRmluRltvRlxvRl1vRl5vRl9vRmBvRlRGV0YrLUY+Ni1GZm5GQ0ZpbkZbb0Zcb0Zdb0Zeb0Zfb0Zgb0Zhb0ZXRmRwRmNvLUY+Ni1RIUYnRkNGaW5GW29GXG9GXW9GXm9GX29GYG9GVEZXRkM=.c) Write the equation of the plane through 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 containing the tangent vector and the second derivative there.d) Write the parametrized equations of the tangent line through 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.
e) Find the coordinates of the point on the top of the box in the figure where that tangent line passes through this plane (namely the plane LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk=).
f) Write down an integral formula for the length of the curve 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 from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GV0Y5to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk=. Numerically evaluate this using technology. and compare your result to the length of the straight line segment between its endpoints (which is the shortest distance between those points!). How close are the latter numbers, i.e., what is the ratio of the length of the curve to the length of the straight line? What percent longer is the curve? Does this seem reasonable?g) Evaluate the scalar tangential projection 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 along 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 of the acceleration 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 and its scalar normal projection 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 exactly. Does the sum of their squares equal the square of the magnitude of the acceleration as it should? Is that sum a lucky number?solutiona) b)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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMvJStleGVjdXRhYmxlR0Y0Ri8=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 vector LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the simplest normal to the plane of the plane curve which retains the direction of 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. c) 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d)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e) set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk= for the parametrized curve and solve forLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0YrRi8=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then evaluate the other two coordinates: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 thing I did not ask this to be evaluated, eh?
f) Length of curve is integral of speed.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Compared to the shortest distance between the endpoints, it is pretty close but larger as expected.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 ratio shows the curve is 10 percent longer, pretty reasonable.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiVRIkxGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JS1GLzYlUSNMU0YnRjJGNUYyRjUvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkIvJSliZXZlbGxlZEdRJmZhbHNlRicvJStleGVjdXRhYmxlR0ZHL0Y2USdub3JtYWxGJw==g)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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMvJStleGVjdXRhYmxlR0Y0Ri8=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMvJStleGVjdXRhYmxlR0Y0Ri8=a check:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEjYVRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JS1JI21uR0YkNiRRIjJGJy9GNlEnbm9ybWFsRidGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiUtRi82JVEjYU5GJ0YyRjVGOEZALUZENi1RIjtGJ0Y+RkdGSkZMRk5GUEZSRlRGVi9GWlEsMC4yNzc3Nzc4ZW1GJ0YrLUZENi1RIitGJ0Y+RkcvRktGSUZMRk5GUEZSRlQvRldRLDAuMjIyMjIyMmVtRicvRlpGZW9GZm5GW28tRkQ2LVEifkYnRj5GR0Zjb0ZMRk5GUEZSRlRGVi9GWkZYLUYsNiUtRi82JVElYW1hZ0YnRjJGNUY4RkAvJStleGVjdXRhYmxlR0ZJRj4=To get an idea of the shape of the projection rectangle, here is the rectangle whose sides are the two scalar projections and whose diagonal is the acceleration vector length.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hmm.making the diagram and 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we include the part of the tangent line which hits the ceiling of our display box.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It does not take much more effort (easy for you to say, bob) to put in all the vectors of the projection process as well as the TNB triad.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The 3 black vectors are LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiTkYnRi9GMkY1LUYsNiVRIkJGJ0YvRjJGOQ==. The green vector is the velocity, cyan the acceleration and the blue triangle is the dcomposition of the acceleration. The thick blue line is the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= axis from the origin, and the other blue arrow with the same initial point is the position vector coming out of the origin.pledgeWhen you have completed the exam, please read and sign the dr bob integrity pledge and hand this test sheet stapled on top of your answer sheets as a cover page, with the first test page facing up:"During this examination, all work has been my own. I have not accessed any of the class web pages or any other sites during the exam. I give my word that I have not resorted to any ethically questionable means of improving my grade or anyone else's on this examination and that I have not discussed this exam with anyone other than my instructor, nor will I until after the exam period is terminated for all participants."
Signature: Date: TTdSMApJNlJUQUJMRV9TQVZFLzE1MDg0MzE2MFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkJSJ0RyokRikiIiMsJiIiIkYtKiRGKSIiJSEiIjYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjI0MzkyOFgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIiIsJCUidEciIiMsJCokRiwiIiQhIiU2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MjI0NDAwMFgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIiEiIiMsJCokJSJ0R0YrISM3NiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjI0NDIwOFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkKiQsKCIiIkYrKiQlInRHIiIjIiIlKiRGLSIiJyIjOyMhIiJGLiwkKiZGKkYzRi1GK0YuLCQqJkYqRjNGLSIiJCEiJTYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjI0NDEwNFgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQsJCokJSJ0RyIiJCEjOywkKiRGLCIiIyIjN0YxNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjI2MDY0NFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkLCQqJiwoIiIiRiwqJCUidEciIiciI2sqJEYuIiIlIiNPIyEiIiIiI0YuIiIkISIpLCQqJkYrRjRGLkY2Ri8qJEYrRjQ2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MjI3NzA0MFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIyEiIiIiIyMiIiIiIiUjIiM6IiM7NiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjI3NzExMlgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIiIhIiIjRioiIiM2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MjI3NzIxNlgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIiEiIiMhIiQ2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MjI3NzI4OFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIyIiIyIiJCMhIiNGKyMiIiJGKzYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjI3NzM5MlgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIiMiIiRGKjYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjI5MzkxMlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIyEiIiIiIyMiIiIiIiUjIiM6IiM7NiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjI5NDA4OFgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQsJiUieEciIiIjRiwiIiNGLCwmJSJ5R0YsIyEiIiIiJUYsLCYlInpHRiwjISM6IiM7Riw2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MjMxMDU2NFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkJSJ4RyUieUclInpHNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjMyNjY5NlgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQsJiMhIiIiIiMiIiIlInRHRi4sJiNGLiIiJUYuRi9GLCwmIyIjOiIjO0YuRi8jRi5GLTYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjMyNjg3MlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIyEiJCIiKSMiIiJGK0YtNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjMyNjk0NFgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQsJiooLCgiIiJGLSokJSJ0RyIiJyIjayokRi8iIiUiI08jISIiIiIjRi8iIiYsKEYtRi0qJEYvRjdGM0YuIiM7RjUhI0MqKEYsRjVGOUY1Ri9GLSEiIywmKiZGLEY1RjlGNUYtKihGLEY1Ri9GMEY5RjUhI0ssJiooRixGNUYvRjNGOUY1ISM7KihGLEY1Ri9GN0Y5RjUhIic2Ig==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TTdSMApJNlJUQUJMRV9TQVZFLzE1MjM3NzA2OFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIyIiIyIiJCMhIiNGKyMiIiJGKzYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjM3NzE0MFgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQjIiIlIiIkIiIjRio2Ig==