MAT2500-01/02 20S Quiz 8 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 EQUAL SIGNS and arrows when appropriate. Always SIMPLIFY expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation when appropriate). Indicate where technology is used and what type (Maple, GC). Only use technology to CHECK hand calculations, not substitute for them.The region R is bounded by the 3 curves 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. Evaluate 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.
a) in Cartesian coordinates as a single iterated double integral, b) in polar coordinates,in each case accompanying your work by a new iteration diagram shaded by equally spaced linear cross-sections and a typical one with bullet point endpoints labeled by the equation of the starting and stopping values of the integration variable for the inner integral and with an arrowhead midway indicating the variable's increasing direction.c) Use Maple to evaluate each such integral exactly. Do they agree as they should?d) What is the average value of the integrand 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on this region numerically evaluated to 4 significant digits?e) Optional challenge post quiz (worth replacing one quiz grade):
Evaluate the the Cartesian coordinates 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 of the centroid of this region, which must lie on the bisector of this sector by symmetry. Then evaluate the corresponding polar coordinates LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtaUdGJDYmUSJSRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSIsRidGNy9GO1Enbm9ybWFsRicvJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYmUScmIzkyMDtGJy9GNUY5RjdGQUY3RkFGN0ZBRjdGQQ==.
Show that the angle of the bisecting line segment of this sector agrees with the ray from the origin to this point, whose slope is 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 and that the radius LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn satisfies the formula for the radius of the centroid of a sector of radius LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMkY0 and angle LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMkY0 , namely 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=solutionso...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 is actually nicer than the polar coordinate result below.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The two areas are of course equal, but the Cartesian expression is simpler!.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 has fun: centroid 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rotate this to be symmetric about the vertical axis.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEndmFycGhpRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLUkmbWZyYWNHRiQ2KC1GLDYlUSUmcGk7RidGL0YyLUYjNiUtSSNtbkdGJDYkUSIyRidGMi9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGW28vJSliZXZlbGxlZEdGMS1GNjYtUSgmbWludXM7RidGMkY5RjtGPUY/RkFGQ0ZFL0ZIUSwwLjIyMjIyMjJlbUYnL0ZLRmRvLUYsNiVRJ2FyY3RhbkYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlRlQvJStleGVjdXRhYmxlR0YxRjJGMkZecEYyLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShkaXNwbGF5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNjMtRiw2JVElcGxvdEYnRjRGNy1GOzYkLUYjNigtRjs2Ji1GIzYoLUY7NiYtRiM2Ky1JI21vR0YkNi1RKiZ1bWludXMwO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGVi8lKXN0cmV0Y2h5R0ZWLyUqc3ltbWV0cmljR0ZWLyUobGFyZ2VvcEdGVi8lLm1vdmFibGVsaW1pdHNHRlYvJSdhY2NlbnRHRlYvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Zfby1JJm1zcXJ0R0YkNiMtRiM2JC1JI21uR0YkNiRRIjVGJ0ZSRlItRiw2JVEkY29zRicvRjVGVkZSLUY7NiQtRiM2Ji1JJm1mcmFjR0YkNigtRiw2JVElJnBpO0YnRl5wRlItRiM2JC1GaG82JFEiMkYnRlJGUi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGY3EvJSliZXZlbGxlZEdGVi1GTzYtUSgmbWludXM7RidGUkZURldGWUZlbkZnbkZpbkZbb0Zdb0Zgby1GZHA2KC1GLDYlUSd2YXJwaGlGJ0ZecEZSRmlwRl5xRmFxRmRxRmZxRlJGUi1GTzYtUSIsRidGUkZUL0ZYRjZGWUZlbkZnbkZpbkZbby9GXm9RJjAuMGVtRicvRmFvUSwwLjMzMzMzMzNlbUYnRmJvLUYsNiVRJHNpbkYnRl5wRlJGX3BGUkZSLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmByLUY7NiYtRiM2Ji1GaG82JFEiMEYnRlJGYHJGZXNGUkZSRltzRl5zRmByLUY7NiYtRiM2KkZib0ZbcC1GOzYkLUYjNiYtRmRwNihGZnAtRiM2JUZbcUY0RjdGXnFGYXFGZHFGZnFGaHEtRmRwNihGXXJGYnRGXnFGYXFGZHFGZnFGUkZSRmByRmJvRmhyRl9wRlJGUkZbc0Zec0ZSRlJGW3NGXnNGYHItRiw2JVEmY29sb3JGJ0Y0RjctRk82LVEiPUYnRlJGVEZXRllGZW5GZ25GaW5GW28vRl5vUSwwLjI3Nzc3NzhlbUYnL0Zhb0ZddS1GLDYlUSZibGFja0YnRjRGN0ZSRlJGYHJGPy1GOzYkLUYjNiQtRjs2Ji1GIzY3RmJvLUZPNi1RIn5GJ0ZSRlRGV0ZZRmVuRmduRmluRltvRmRyL0Zhb0ZlckZbcC1GOzYkLUYjNiQtRiw2JVEidEYnRjRGN0ZSRlJGYHJGanVGYm9GanVGaHJGXnZGYHJGYnZGaXRGY3BGaHFGZHQtRk82LVEjLi5GJ0ZSRlRGV0ZZRmVuRmduRmluRltvRl1vRl12RmB0LUZPNi1RIitGJ0ZSRlRGV0ZZRmVuRmduRmluRltvRl1vRmBvRmR0RlJGUkZbc0Zec0ZSRlJGYHItRiw2JVEqcG9pbnRwbG90RidGNEY3LUY7NiQtRiM2MC1GOzYmLUYjNiQtRjs2Ji1GIzYmRmVzRmByLUZobzYkUSwxLjQ3NzM5NTQ0NEYnRlJGUkZSRltzRl5zRlJGUkZbc0Zec0Zgci1GLDYlUSdzeW1ib2xGJ0Y0RjdGaXQtRiw2JVEsc29saWRjaXJjbGVGJ0Y0RjdGYHItRiw2JVErc3ltYm9sc2l6ZUYnRjRGN0ZpdC1GaG82JFEjMTVGJ0ZSRmByRmZ0Rml0LUYsNiVRJWJsdWVGJ0Y0RjdGUkZSRmByLUYsNiVRKmdyaWRsaW5lc0YnRjRGN0ZpdC1GLDYlRjZGNEY3RmByLUYsNiVRKHNjYWxpbmdGJ0Y0RjdGaXQtRiw2JVEsY29uc3RyYWluZWRGJ0Y0RjdGUkZSRlJGKy8lK2V4ZWN1dGFibGVHRlZGUg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2JVEqcmNlbnRyb2lkRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSZtZnJhY0dGJDYoLUYjNjItSShtc3Vic3VwR0YkNictRjY2LVErJkludGVncmFsO0YnRjkvRjxRJnVuc2V0RicvRj9GZW4vRkFGMS9GQ0Zlbi9GRUYxL0ZHRmVuL0ZJRmVuL0ZLUSYwLjBlbUYnL0ZORl1vLUYjNiYtRlA2KC1GLDYlUSUmcGk7RicvRjBGPUY5LUYjNiUtSSNtbkdGJDYkUSIyRidGOUYvRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmJwLyUpYmV2ZWxsZWRHRj0tRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZbcS1GUDYoLUYsNiVRJyYjOTY2O0YnRmZvRjlGZ29GXXBGYHBGY3BGZXBGOS1GIzYmLUZQNiktRiw2JkZlb0Zmby8lK2ZvcmVncm91bmRHUSxbMjAwLDAsMjAwXUYnRjktRiM2Ji1Gam82JUZccEZocUY5Ri9GaHFGMkZdcEZgcEZjcEZlcEZocS1GNjYuUSIrRidGaHFGOUY7Rj5GQEZCRkRGRkZIRmpwRlxxLUZQNiktRiw2JkZhcUZmb0ZocUY5RltyRl1wRmBwRmNwRmVwRmhxRjkvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUvc3Vic2NyaXB0c2hpZnRHRmhyLUZVNidGVy1GIzYkLUZqbzYkRmhyRjlGOS1GIzYkLUYsNiVRJyYjOTYxO0YnRmZvRjlGOUZmckZpci1GLDYlUSJyRidGL0YyLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGXG9GXm8tRiw2JVEkc2luRidGZm9GOS1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJyYjOTUyO0YnRmZvRjkvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkhGXG9GXm9GZnNGaXMtRjY2LVEwJkRpZmZlcmVudGlhbEQ7RidGOUZaRmZuL0ZBRmVuRmhuL0ZFRmVuRmpuRltvRlxvRl5vRmZzRmlzRlx1RmR0Rmd0RjktRiM2KS1GUDYoLUZqbzYkRl9wRjlGZ29GXXBGYHBGY3BGZXBGaXMtSSVtc3VwR0YkNiVGY3NGZ29GZnJGaXNGX3FGL0YyRl1wRmBwRmNwRmVwLUY2Ni1RIjtGJ0Y5RjsvRj9GMUZARkJGREZGRkhGXG9GTS1GLDYlUSVzdWJzRidGL0YyLUZgdDYkLUYjNi1GY3MtRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tSSZtc3FydEdGJDYjLUYjNiQtRmpvNiRRIjVGJ0Y5RjktRjY2LVEiLEYnRjlGO0ZddkZARkJGREZGRkhGXG8vRk5RLDAuMzMzMzMzM2VtRidGX3FGZXYtRmB0NiQtRiM2KC1GUDYoLUYsNiVRJyYjOTYwO0YnRmZvRjlGZ29GXXBGYHBGY3BGZXBGZ3AtRiw2JVEnYXJjdGFuRidGZm9GOS1GYHQ2JC1GIzYlRmlvRmd0RjlGOUZndEY5RjlGYHdGK0ZndEY5RjlGanUtRiw2JVEmZXZhbGZGJ0YvRjItRmB0NiQtRiM2JS1GLDYlUSIlRid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