MAT2500-01/04 17S Quiz 2 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).Given three points 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 and the parallelopiped formed from their three position vectors 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. [Note 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 all point towards us in the first octant, withLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LlEifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRS1GLDYuUSFGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZDRkYtSSZtb3ZlckdGJDYlLUYjNiYtSSVtc3ViR0YkNiUtSSNtaUdGJDYoUSJyRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0ZZRi8vRjNRLGJvbGQtaXRhbGljRicvJStmb250d2VpZ2h0R1ElYm9sZEYnLUYjNiUtSSNtbkdGJDYlUSIxRidGL0YyRi9GMi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkhGL0YyLUYsNi9RLSZSaWdodEFycm93O0YnRi8vJSxwbGFjZWhvbGRlckdGWUYyL0Y2USZ1bnNldEYnL0Y4RmpvL0Y6RlkvRjxGam8vRj5Gam8vRkBGam8vRkJGam9GQ0ZGL0ZCRllGL0Yy most forward.]
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U^EeAcT\\iboedQmxJEdAGtW=BaiyrcS:?e\\KCb?b\\K;v[HNprY]YfrYOu=Cx=grUr;[DvwYc;YqisO[iiufcUTWYEGoTesghUFiQYY_cJWxhQTTgyf;HcMvBiS=GiK_FDQbuec^CUTASUSXmqIvsgaGhVCgYsTYkSeOE:UDhYXicspQW>]vwoEAcIsyBtMCw[D;_CpCGsWEq[Uj]gtGDLiIraYweRGcBN=RKcBNIrym6@\"\{\}LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlXTpGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiU/R0YqLSUpQ0hJTERSRU5HNiI=a) Write the parametrized equations of the line LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1RkE= through the point with position vector 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 as shown in this view. Where does this line intersect the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjBGJ0YyRjxGMkY8 plane?
b) Find a normal vector 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 for the plane LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEpJiM1ODUzOTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUYvNiZRKHRvcGZhY2VGJ0YyRjVGOEYyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjUvRjlRJ25vcm1hbEYn which contains the top back left face (shaded) of the parallelepiped shown in the figure.
c) Write the simplified equation for this plane. Does the point at the tip of the parallelopiped (where the line LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGQS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZaRjVGQQ==touches the top left back face LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEpJiM1ODUzOTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Ji1GLzYlUSh0b3BmYWNlRidGMkY1RjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Y1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGPS9GNlEnbm9ybWFsRic= ) satisfy this equation as it should?
d) Find the scalar projection LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn of 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 along 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. [LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRS1JKG1mZW5jZWRHRiQ2Jy1GIzYmLUkjbWlHRiQ2JlEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnRi8vRjNRJ2l0YWxpY0YnRitGL0YyRi9GMi8lJW9wZW5HUSJ8Z3JGJy8lJmNsb3NlR0ZYRi9GMg== is just the distance of the top face plane from the origin, or its height if we instead think of that face as the top of the parallelopiped.]
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFRi9GMg==e) Evaluate the area LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn of the top left back face of the parallelopiped, a parallelogram formed by the edges parallel to 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.f) Does the volume V=|LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifGdyRidGMi9GNlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjExMTExMTFlbUYnLyUncnNwYWNlR0ZOLUY5Ni5RIn5GJ0YyRjxGPkZAL0ZDRjRGREZGRkhGSi9GTVEmMC4wZW1GJy9GUEZWLUYsNiZRIkFGJ0YvRjJGNUYyRjw= of the parallelopiped equal the triple scalar product |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 as it should?solutiona) We introduce the position vectors and the two relevant difference 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 add the top back left face shaded to clarify the 3d diagram.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a) The line in question has the position vector LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEjcjFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIitGJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRk4tRiw2JlEjcjJGJ0YvRjJGNUYyRjw=, while the orientation is along LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEjcjNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyL0Y2USdub3JtYWxGJw==:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkobWZlbmNlZEdGJDYmLUYjNiktSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJ5RidGNEY3RjotRjE2JVEiekYnRjRGNy8lK2V4ZWN1dGFibGVHRkJGPkY+LyUlb3BlbkdRJyZsYW5nO0YnLyUmY2xvc2VHUScmcmFuZztGJy1GOzYtUSJ+RidGPkZAL0ZERkJGRUZHRklGS0ZNRk8vRlNGUS1GOzYtUSI9RidGPkZARmBvRkVGR0ZJRktGTS9GUFEsMC4yNzc3Nzc4ZW1GJy9GU0Zmby1GMTYlUSNyMUYnRjRGNy1GOzYtUSIrRidGPkZARmBvRkVGR0ZJRktGTS9GUFEsMC4yMjIyMjIyZW1GJy9GU0ZfcC1GMTYlUSNyMkYnRjRGN0ZbcC1GMTYlUSJ0RidGNEY3Rl1vRl1vLUYxNiVRI3IzRidGNEY3RmVuRj4=Where does this line hit the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjBGJ0YyRjxGMkY8 plane?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At the point 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.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFRi9GMg==b) e) the magnitude of this cross product is the area of the parallelogram face formed by these two 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFRi9GMg==c) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEjcjNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyL0Y2USdub3JtYWxGJw== is a position vector on this plane, 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Does the main diagonal satisfy this equation?LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVElRGlhZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRI3IxRidGL0YyLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GVi1GLDYlUSNyMkYnRi9GMkZSLUYsNiVRI3IzRidGL0YyLyUrZXhlY3V0YWJsZUdGPUY5LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElc3Vic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYxLUYsNiVRInhGJ0YvRjItSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQtSSNtbkdGJDYkUSIyRidGQS1GPjYtUSIsRidGQUZDL0ZHRjFGSEZKRkxGTkZQL0ZTUSYwLjBlbUYnL0ZWUSwwLjMzMzMzMzNlbUYnLUYsNiVRInlGJ0YvRjJGPS1GWDYkUSI0RidGQUZlbi1GLDYlUSJ6RidGL0YyRj0tRlg2JFEiOUYnRkFGZW4tRiw2JVEpRXFuUGxhbmVGJ0YvRjIvJStleGVjdXRhYmxlR0ZFRkFGQUZccEZBYup.d)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJURpYWdGJ0YvRjItRjY2LVEpJm1pZGRvdDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMTY2NjY2N2VtRicvRk5GVi1GLDYlUSVuaGF0RidGL0YyLUY2Ni1RIjtGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRidGTS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRmluL0ZORmpuLUYsNiVRJmV2YWxmRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEiJUYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5RmpvRjk=f)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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFRi9GMg==They 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