MAT2705-02/06 10F Quiz 7 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).
1. 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 .a) Verify that the general solution 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 actually solves the DE.b) Using 2x2 matrix methods find the solution which satisfies the initial conditions, showing all work.c) Use technology to plot your result for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5LUY2Ni1RIy4uRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZOUSYwLjBlbUYnLUZQNiRRIjVGJ0Y5Rjk= and make a rough sketch of what you see, labeling the axes with variable names and key tickmarks on your sketch.d) Use calculus to determine exactly by hand (rules of exponents and logs! simplify your result for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= to a simple radical expression) the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= values of the obvious maximum point on the graph and then their approximate values to 4 decimal places, but if you get stuck on solving the derivative condition exactly, use technology to find the approximate values to 4 decimal places in any way you can. Do the numbers you found agree with what your eyes see in the technology plot? [Yes or no, with an explanation would be a good response.]solution1. 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a)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b)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The maximum is at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUScwLjYxMDlGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGNC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYkUSc0LjQyMDhGJ0Y0RjRGNC1GODYtUSIuRidGNEY7L0Y/Rj1GQUZDRkVGR0ZJRksvRk9GTUY0 Clicking on the peak of the graph below gives about (.6,4.4) which agrees with this hand calculation: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 initial conditions in matrix form are: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with solution:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtSShtZmVuY2VkR0YkNigtRiM2JUYrLUknbXRhYmxlR0YkNjYtSSRtdHJHRiQ2Jy1JJG10ZEdGJDYoLUYjNiMtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUpcm93YWxpZ25HRi4vJSxjb2x1bW5hbGlnbkdGLi8lK2dyb3VwYWxpZ25HRi4vJShyb3dzcGFuR0ZFLyUrY29sdW1uc3BhbkdGRUY9RklGS0ZNLUY7NictRj42KC1GIzYkLUkjbW9HRiQ2LVEqJnVtaW51czA7RidGRi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGaW4vJSlzdHJldGNoeUdGaW4vJSpzeW1tZXRyaWNHRmluLyUobGFyZ2VvcEdGaW4vJS5tb3ZhYmxlbGltaXRzR0Zpbi8lJ2FjY2VudEdGaW4vJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Zoby1GQzYkUSIzRidGRkZJRktGTUZPRlEtRj42KC1GIzYkRllGQkZJRktGTUZPRlFGSUZLRk0vJSZhbGlnbkdRJWF4aXNGJy9GSlEpYmFzZWxpbmVGJy9GTFEnY2VudGVyRicvRk5RJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR1EldHJ1ZUYnLyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGYHEvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGW3IvJSZmcmFtZUdGW3IvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR0Zpbi8lLWVxdWFsY29sdW1uc0dGaW4vJS1kaXNwbGF5c3R5bGVHRmluLyUlc2lkZUdRJnJpZ2h0RicvJTBtaW5sYWJlbHNwYWNpbmdHRmhxRitGRi9JK21zZW1hbnRpY3NHRiRRJ01hdHJpeEYnLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRl5zRmBwLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictRiM2J0YrLUkobWFjdGlvbkdGJDYkLUkobWZlbmNlZEdGJDYoLUYjNidGKy1JJ210YWJsZUdGJDY2LUkkbXRyR0YkNiYtSSRtdGRHRiQ2KC1GIzYmLUYsNiVRI0MxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxwbGFjZWhvbGRlckdGSS9GS1Enbm9ybWFsRicvJSlyb3dhbGlnbkdGLi8lLGNvbHVtbmFsaWduR0YuLyUrZ3JvdXBhbGlnbkdGLi8lKHJvd3NwYW5HUSIxRicvJStjb2x1bW5zcGFuR0ZmbkZURlZGWC1GPTYmLUZANigtRiM2Ji1GLDYlUSNDMkYnRkdGSkZNRlBGUkZURlZGWEZaRmduRlRGVkZYLyUmYWxpZ25HUSVheGlzRicvRlVRKWJhc2VsaW5lRicvRldRJ2NlbnRlckYnL0ZZUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGSS8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRl9wLyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmpwLyUmZnJhbWVHRmpwLyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGTy8lLWVxdWFsY29sdW1uc0dGTy8lLWRpc3BsYXlzdHlsZUdGTy8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0ZncEYrRk1GUkZSL0krbXNlbWFudGljc0dGJFEqQ29sVmVjdG9yRicvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGXXIvJSthY3Rpb250eXBlR1EucnRhYmxlYWRkcmVzc0YnRitGTUZSLUkjbW9HRiQ2LVEiPUYnRlIvJSZmZW5jZUdGTy8lKnNlcGFyYXRvckdGTy8lKXN0cmV0Y2h5R0ZPLyUqc3ltbWV0cmljR0ZPLyUobGFyZ2VvcEdGTy8lLm1vdmFibGVsaW1pdHNHRk8vJSdhY2NlbnRHRk8vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZddC1GMjYkLUYjNidGKy1GMjYkLUYjNiktSSVtc3VwR0YkNiUtRjU2KC1GIzYmRistRjo2Ni1GPTYnLUZANigtRiM2JC1JI21uR0YkNiRGZm5GUkZSRlRGVkZYRlpGZ25GY3VGVEZWRlgtRj02Jy1GQDYoLUYjNiUtRmpyNi1RKiZ1bWludXMwO0YnRlJGXXNGX3NGYXNGY3NGZXNGZ3NGaXMvRlx0USwwLjIyMjIyMjJlbUYnL0ZfdEZkdi1GaHU2JFEiM0YnRlJGUkZURlZGWEZaRmduLUZANigtRiM2JUZgdkZndUZSRlRGVkZYRlpGZ25GVEZWRlhGYm9GZW9GZ29GaW9GW3BGXXBGYHBGYnBGZXBGaHBGW3FGXXFGX3FGYnFGZHFGZnFGaHFGW3JGK0ZSRlIvRl5yUSdNYXRyaXhGJ0ZgckZjckZddy1GIzYmRmB2Rmd1RkdGSi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRmpyNi1RIn5GJ0ZSRl1zRl9zRmFzRmNzRmVzRmdzRmlzL0ZcdFEmMC4wZW1GJy9GX3RGaHctRiM2J0YrLUYyNiQtRjU2KC1GIzYnRistRjo2Ni1GPTYmLUZANigtRiM2Ji1GaHU2JFEiMkYnRlJGTUZQRlJGVEZWRlhGWkZnbkZURlZGWC1GPTYmLUZANigtRiM2Ji1GaHU2JFEiNEYnRlJGTUZQRlJGVEZWRlhGWkZnbkZURlZGWEZib0Zlb0Znb0Zpb0ZbcEZdcEZgcEZicEZlcEZocEZbcUZdcUZfcUZicUZkcUZmcUZocUZbckYrRk1GUkZSRl1yRmByRmNyRl1yRmZyRitGTUZSRmR3LUYyNiQtRiM2JEZkd0ZSRmZyRitGUkZmckYrRkdGSkZmckYrRk1GUg==JSFHThese numbers agree with our approximate values above.TTdSMApJNVJUQUJMRV9TQVZFLzUyNDc4MjY4WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLCYlI0MxRyIiIiUjQzJHRiksJkYoISIkRiohIiJGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzEzNzg1MTMyNFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyIiIyIiJUYlTTdSMApJNlJUQUJMRV9TQVZFLzEzNzg1MDEyOFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyUiIyIjIyEiIiIiIyMiIiRGKUYnIyIiIkYpRiU=TTdSMApJNlJUQUJMRV9TQVZFLzEzNzg2OTcyMFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyUjQzFHJSNDMkdGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzEzNzg2OTc5MlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyEiJCIiJkYl