MAT2705-01/04 07S Test 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). You may use technology for row reductions and root finding.
1. a) Express the vector 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 in terms of the four vectors 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 and then check that the linear combination that you find evaluates to the original vector. Be sure to state clearly all steps in the process.
b) From your work for part a), state the linear relationship which exists among these four vectors. Explain.2. 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, 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 .
a) Find the general solution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYn of this differential equation by hand (no decimals).b) Find the particular solution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYn which satisfies the initial conditions, by hand, using matrix techniques once you state the equivalent linear system of equations.c) Your solution should have a single local (and global) maximum for some LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUlZm9ybUdRJmluZml4RicvJSdsc3BhY2VHUS90aGlja21hdGhzcGFjZUYnLyUncnNwYWNlR0ZPLyUobWluc2l6ZUdRIjFGJy8lKG1heHNpemVHUSlpbmZpbml0eUYnLUkjbW5HRiQ2JFEiMEYnRjk=. Make an appropriately chosen window to plot your solution and estimate the location of this peak. Then find its (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUlZm9ybUdRJmluZml4RicvJSdsc3BhY2VHUSQwZW1GJy8lJ3JzcGFjZUdRM3Zlcnl0aGlja21hdGhzcGFjZUYnLyUobWluc2l6ZUdRIjFGJy8lKG1heHNpemVHUSlpbmZpbml0eUYnLUYsNiVRInlGJ0YvRjI=) values exactly using calculus and give accurate approximate numerical values; if you cannot find it exactly, at least find accurate numerical values. Do your numbers look right compared to your plot? Make a completely labeled sketch that conveys this information.3. It is known that the three functions LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkobWZlbmNlZEdGJDYmLUYjNiwtSSNtaUdGJDYlUSRzaW5GJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYsNiQtRiM2Iy1GMTYlUSJ4RicvRjVRJXRydWVGJy9GOFEnaXRhbGljRidGNy1JI21vR0YkNjBRIixGJ0Y3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUlZm9ybUdRJmluZml4RicvJSdsc3BhY2VHUSQwZW1GJy8lJ3JzcGFjZUdRM3Zlcnl0aGlja21hdGhzcGFjZUYnLyUobWluc2l6ZUdRIjFGJy8lKG1heHNpemVHUSlpbmZpbml0eUYnLUZGNjBRIn5GJ0Y3RkkvRkxGNkZNRk9GUUZTRlUvRlhRIUYnRlovRmhuRmZuRmpuRl1vRjAtSSVtc3VwR0YkNiVGOi1GIzYjLUkjbW5HRiQ2JFEiM0YnRjcvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRkVGMC1GLDYkLUYjNiVGXHBGYG9GPkY3LUYxNiVGZW9GQUZDRjcvJSVvcGVuR1EifGZyRicvJSZjbG9zZUdRInxockYn satisfy a triple angle identity which enables 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 to be expressed in terms of the first two odd powers of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0Yy.
a) Evaluate the Wronskian matrix of these three functions (which form the first row, their derivatives the second row, and their second derivatives the third row), and then evaluate this result at 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 to obtain a matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIi5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUlZm9ybUdRJmluZml4RicvJSdsc3BhY2VHUSQwZW1GJy8lJ3JzcGFjZUdGTy8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJw==b) Find the general solution of the linear system 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 for the coefficients 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 of a linear relationship among these three functions.c) Use it to express 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 in terms of the other two functions.d) Check that it actually holds for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUlZm9ybUdRJmluZml4RicvJSdsc3BhY2VHUS90aGlja21hdGhzcGFjZUYnLyUncnNwYWNlR0ZPLyUobWluc2l6ZUdRIjFGJy8lKG1heHNpemVHUSlpbmZpbml0eUYnLUYsNiVRJyYjOTYwO0YnL0YwRj1GOQ==/6 where you know the exact values of these functions.solutionrestart:
with(VectorCalculus):BasisFormat(false):
with(Student[LinearAlgebra]):LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn1. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSVmb3JtR1EmaW5maXhGJy8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRicvJSdyc3BhY2VHRk8vJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictSShtZmVuY2VkR0YkNiYtRiM2Jy1JI21uR0YkNiRRIjhGJ0Y5LUY2NjBRIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGSi9GTlEkMGVtRicvRlFRM3Zlcnl0aGlja21hdGhzcGFjZUYnRlJGVS1GaG42JFEiMEYnRjlGW28tRmhuNiRRIjJGJ0Y5RjkvJSVvcGVuR1EnJmxhbmc7RicvJSZjbG9zZUdRJyZyYW5nO0YnLUY2NjBRIjtGJ0Y5RjtGXm9GQEZCRkRGRkZIRkpGX29GUEZSRlUtSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGZ3AvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRiw2JlEiQUYnRi8vJStleGVjdXRhYmxlR0Y9RjItRjY2MUY4RmNxRjlGO0Y+RkBGQkZERkZGSEZKRk1GUEZSRlUtRlk2Jy1GIzYpLUZZNictRiM2KC1GaG42JUZURmNxRjktRjY2MUZdb0ZjcUY5RjtGXm9GQEZCRkRGRkZIRkpGX29GYW9GUkZVLUY2NjFRKiZ1bWludXMwO0YnRmNxRjlGO0Y+RkBGQkZERkZGSEZKL0ZOUTBtZWRpdW1tYXRoc3BhY2VGJy9GUUZnckZSRlVGX3JGYXJGX3JGY3FGOUZpb0ZccC1GNjYxUSJ8Z3JGJ0ZjcUY5RjtGPi9GQUYxRkJGREZGRkhGSi9GTlEydmVyeXRoaW5tYXRoc3BhY2VGJy9GUUZec0ZSRlUtRlk2Jy1GIzYnLUZobjYlRmhvRmNxRjlGYXItRmhuNiVGZW9GY3FGOUZhckZfckZjcUY5RmlvRlxwRmlyLUZZNictRiM2Jy1GaG42JVEiM0YnRmNxRjlGYXJGX3JGYXJGZnNGY3FGOUZpb0ZccEZpci1GWTYnLUYjNictRmhuNiVRIjRGJ0ZjcUY5RmFyRmRzRmFyRl9yRmNxRjlGaW9GXHBGY3FGOUZpb0ZccA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUlZm9ybUdRIUYnLyUnbHNwYWNlR1EkMGVtRicvJSdyc3BhY2VHRk8vJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictRjY2MFEiPEYnRjlGO0Y+RkBGQkZERkZGSC9GS1EmaW5maXhGJy9GTlEvdGhpY2ttYXRoc3BhY2VGJy9GUUZobkZSRlUtSSNtbkdGJDYkUSI0RidGOS1GNjYwUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRmVuRk0vRlFRM3Zlcnl0aGlja21hdGhzcGFjZUYnRlJGVS1GNjYwUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkhGZW4vRk5RMG1lZGl1bW1hdGhzcGFjZUYnL0ZRRmhvRlJGVS1GW282JFEiM0YnRjlGXm8tRltvNiRRIjJGJ0Y5Rl5vLUZbbzYkRlRGOS1GNjYwUSI+RidGOUY7Rj5GQEZCRkRGRkZIRmVuRmduRmluRlJGVQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkobWZlbmNlZEdGJDYmLUYjNiUtSSNtaUdGJDYlUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2MFEifGdyRicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRjYvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJWZvcm1HUSZpbmZpeEYnLyUnbHNwYWNlR1EydmVyeXRoaW5tYXRoc3BhY2VGJy8lJ3JzcGFjZUdGVC8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJy1GMTYlUSJiRidGNEY3Rj4vJSVvcGVuR1EnJmxhbmc7RicvJSZjbG9zZUdRJyZyYW5nO0YnLUY7NjBRIjtGJ0Y+RkAvRkRGNi9GRkZCRkdGSUZLRk1GTy9GU1EkMGVtRicvRlZRL3RoaWNrbWF0aHNwYWNlRidGV0ZaLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjBlbUYnLyUmZGVwdGhHRl5wLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUYxNiZRNlJlZHVjZWRSb3dFY2hlbG9uRm9ybUYnRjQvJStleGVjdXRhYmxlR0ZCRjctRiw2JS1GIzYjLUYxNiZRIiVGJ0Y0RmpwRjdGanBGPi1GOzYxRmJvRmpwRj5GQEZjb0Zkb0ZHRklGS0ZNRk9GZW9GZ29GV0ZaRmlvLUYxNiZRM0JhY2t3YXJkU3Vic3RpdHV0ZUYnRjRGanBGN0ZccQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn2.QycqJi1JIipHJSpwcm90ZWN0ZWRHNiQiJCspLCZJInJHNiIiIiIjRiwiIz9GLEYsLCZGKkYsI0YsIiNTRixGLEYsLUknZXhwYW5kR0YmNiNJIiVHRitGLC1JJnNvbHZlRzYkRiZJKF9zeXNsaWJHRitGNA==PkkkZGVxRzYiLy1JIitHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YkSS9WZWN0b3JDYWxjdWx1c0c2JEYpSShfc3lzbGliR0YkNiQtRic2JC1JIipHRig2JCIkKyktSSVkaWZmR0YpNiUtSSJ5R0YkNiNJInhHRiRGPEY8LUYzNiQiI2ctRjc2JEY5RjxGOSIiIQ==PkkmaW5pdHNHNiI2JC8tSSJ5R0YkNiMiIiEiIiUvLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRikiIiI=Pkknc29sZ2VuRzYiLUknZHNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiRJJGRlcUdGJC1JInlHRiQ2I0kieEdGJA==Pkkoc29saW5pdEc2Ii1JJ2Rzb2x2ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYkPCRJJmluaXRzR0YkSSRkZXFHRiQtSSJ5R0YkNiNJInhHRiQ=LUklcGxvdEc2IjYkNyMtSSRyaHNHJSpwcm90ZWN0ZWRHNiNJKHNvbGluaXRHRiQvSSJ4R0YkOyIiISIkKyM=LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYlLUkkcmhzR0YlNiNJKHNvbGluaXRHRicvSSJ4R0YnOyIiISIjXTtGMCIjOQ==QysvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JJHJoc0dGJjYjSShzb2xpbml0RzYiSSJ4R0YsIiIhIiIiPkkiWEdGLC1JJnNvbHZlRzYkRiZJKF9zeXNsaWJHRiw2JEkiJUdGLEYtRi8tSSVzdWJzR0YmNiQvRi1GN0YoRi8+SSJZR0YsLUknZXhwYW5kR0YmNiNGN0YvLUkmZXZhbGZHRiY2JDckRjFGPSIiJg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEqV3JvbnNraWFuRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRjY2Ji1GIzYlLUklbXN1cEdGJDYlLUkjbW9HRiQ2MFEvJkV4cG9uZW50aWFsRTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkkvJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUlZm9ybUdRJ3ByZWZpeEYnLyUnbHNwYWNlR1EkMGVtRicvJSdyc3BhY2VHUTJ2ZXJ5dGhpbm1hdGhzcGFjZUYnLyUobWluc2l6ZUdRIjFGJy8lKG1heHNpemVHUSlpbmZpbml0eUYnLUYjNiUtRkI2MFEqJnVtaW51czA7RidGRUZHRkpGTEZORlBGUkZUL0ZXUSZpbmZpeEYnL0ZaUTBtZWRpdW1tYXRoc3BhY2VGJy9GZ25GZ29GaW5GXG8tRiM2Ji1JJm1mcmFjR0YkNigtSSNtbkdGJDYkRltvRkUtRl9wNiRRIzIwRidGRS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGaXAvJSliZXZlbGxlZEdGSS1GQjYwUTEmSW52aXNpYmxlVGltZXM7RidGRUZHRkpGTEZORlBGUkZURmRvRlkvRmduRmVuRmluRlxvLUYjNiMtRiw2JVEieEYnRi9GMi1GLDYlUSFGJ0YvRjJGZ3EvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUZCNjBRIixGJ0ZFRkcvRktGMUZMRk5GUEZSRlRGZG9GWS9GZ25RM3Zlcnl0aGlja21hdGhzcGFjZUYnRmluRlxvLUY/NiVGQS1GIzYlRmFvLUYjNiYtRlxwNihGXnAtRl9wNiRRIzQwRidGRUZkcEZncEZqcEZccUZecUZicUZncUZncUZqcUZFLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRl1yRmRxRkUtRkI2MFEiO0YnRkVGR0ZgckZMRk5GUEZSRlRGZG9GWS9GZ25RL3RoaWNrbWF0aHNwYWNlRidGaW5GXG8tRiw2JVEiQUYnRi9GMi1GQjYwUSomY29sb25lcTtGJ0ZFRkdGSkZMRk5GUEZSRlRGZG8vRlpGaHNGZ3NGaW5GXG8tRiw2JVElc3Vic0YnRi9GMi1GNjYkLUYjNidGZHEtRkI2MFEiPUYnRkVGR0ZKRkxGTkZQRlJGVEZkb0ZfdEZnc0ZpbkZcby1GX3A2JFEiMEYnRkVGXXItRiw2JVEiJUYnRi9GMkZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUlZm9ybUdRIUYnLyUnbHNwYWNlR1EkMGVtRicvJSdyc3BhY2VHRk8vJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictRjY2MFEiPEYnRjlGO0Y+RkBGQkZERkZGSC9GS1EmaW5maXhGJy9GTlEvdGhpY2ttYXRoc3BhY2VGJy9GUUZobkZSRlUtRiw2JVEjQzFGJ0YvRjItRjY2MFEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZlbkZNL0ZRUTN2ZXJ5dGhpY2ttYXRoc3BhY2VGJ0ZSRlUtRiw2JVEjQzJGJ0YvRjItRjY2MFEiPkYnRjlGO0Y+RkBGQkZERkZGSEZlbkZnbkZpbkZSRlVGNS1GNjYwUSI9RidGOUY7Rj5GQEZCRkRGRkZIRmVuRmduRmluRlJGVUY1LUkobWZlbmNlZEdGJDYmLUYjNiUtSSNtbkdGJDYkUSI0RidGOUZdby1GYnA2JEZURjlGOS8lJW9wZW5HUScmbGFuZztGJy8lJmNsb3NlR1EnJnJhbmc7Ric=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW9HRiQ2MFEqJnVtaW51czA7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJWZvcm1HUSZpbmZpeEYnLyUnbHNwYWNlR1EwbWVkaXVtbWF0aHNwYWNlRicvJSdyc3BhY2VHRlQvJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictSSNtbkdGJDYkRllGPi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjs2MFEifkYnRj5GQEZDRkVGR0ZJRktGTS9GUFEhRicvRlNRJDBlbUYnL0ZWRmNvRldGWi1GOzYwUSI7RidGPkZAL0ZERjRGRUZHRklGS0ZNRk9GYm8vRlZRL3RoaWNrbWF0aHNwYWNlRidGV0ZaRl1vLUYvNiVRIiVGJ0YyRjVGXW8tRjs2MFEiPEYnRj5GQEZDRkVGR0ZJRktGTUZPL0ZTRmpvRmlvRldGWi1GaG42JFEiNEYnRj4tRjs2MFEiLEYnRj5GQEZob0ZFRkdGSUZLRk1GT0Ziby9GVlEzdmVyeXRoaWNrbWF0aHNwYWNlRidGV0ZaRmduLUY7NjBRIj5GJ0Y+RkBGQ0ZFRkdGSUZLRk1GT0ZhcEZpb0ZXRlo=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn3.Ly1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLUkiKkc2JEYmL0krbW9kdWxlbmFtZUdGKEkvVmVjdG9yQ2FsY3VsdXNHRiU2JCIiJEkieEdGKC1JJ2V4cGFuZEdGJjYjLUklc3Vic0dGJjYkLyokKS1JJGNvc0dGJTYjRjIiIiMiIiItSSIrR0YsNiRGQC1JIi1HRiw2IyokKS1GJEY+Rj9GQC1GNDYjRiM=QyctSSdleHBhbmRHJSpwcm90ZWN0ZWRHNiMtSSRzaW5HNiRGJUkoX3N5c2xpYkc2IjYjLUkiKkc2JEYlL0krbW9kdWxlbmFtZUdGK0kvVmVjdG9yQ2FsY3VsdXNHRik2JCIiJEkieEdGKyIiIi1JJXN1YnNHRiU2JC8qJCktSSRjb3NHRik2I0Y1IiIjRjYtSSIrR0YvNiRGNi1JIi1HRi82IyokKS1GKEY/RkBGNkkiJUdGK0Y2LUYkNiNGSg==a), 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you have completed the exam, please read and sign the dr bob integrity pledge and hand this test sheet in 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 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: