MAT2500-02 08S 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.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRi8=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The parametrized curve 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
is shown in the figure together with the vectors LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYjNiVGKy1JJm1vdmVyR0YkNiUtSSNtaUdGJDYnUSJyRicvJSVib2xkR0Y3LyUnaXRhbGljR0Y3L0YwUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1GLDYuUS0mUmlnaHRBcnJvdztGJy8lLHBsYWNlaG9sZGVyR0Y3Ri8vRjNRJnVuc2V0RicvRjZGam4vRjlGNy9GO0Zqbi9GPUZqbi9GP0Zqbi9GQUZqbkZCL0ZGRkQvJSdhY2NlbnRHRjdGLy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNi1RKiZ1bWludXMwO0YnRi9GMi9GNkY0RjhGOkY8Rj5GQC9GQ1EsMC4yMjIyMjIyZW1GJy9GRkZecC1JI21uR0YkNiRRIjFGJ0YvRi9GLy1GLDYtUSIsRidGL0YyRjVGOEY6RjxGPkZARkJGRUZILUZlbzYkLUYjNiQtRmFwNiRRIjBGJ0YvRi9GL0ZkcEZILUZlbzYkLUYjNiRGYHBGL0YvLUYsNi1RIn5GJ0YvRjJGXHBGOEY6RjxGPkZARkJGYW9GLw==.
a) Evaluate and simplify 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 .b) Evaluate 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRi8=.
c) This is a plane curve which coincides with the plane containing the first and second derivatives. Write an equation for this plane picking any point on the curve and using a normal to the plane of the first and second derivatives at that point: simplify to a linear condition among the three coordinates.d) Write the parametrized equations of the line containing the points on the curve for which LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GV0Y5and 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i.e., 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
e) What is the length of the straight line segment connecting the tips of 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and 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 exactly and numerically?
f) Write down an integral formula for the length of the curve 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 from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GV0Y5to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk=, and use technology to evaluate it to two decimal place accuracy. How should it compare to part e) using common sense?g) Evaluate the scalar tangential projection 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 and the vector projections 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 and 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 of the acceleration LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYjNiotSSVtc3ViR0YkNiUtRiM2JkYrLUYjNiVGKy1JJm1vdmVyR0YkNiUtSSNtaUdGJDYnUSJhRicvJSVib2xkR0Y3LyUnaXRhbGljR0Y3L0YwUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1GLDYuUS0mUmlnaHRBcnJvdztGJy8lLHBsYWNlaG9sZGVyR0Y3Ri8vRjNRJnVuc2V0RicvRjZGYW8vRjlGNy9GO0Zhby9GPUZhby9GP0Zhby9GQUZhb0ZCL0ZGRkQvJSdhY2NlbnRHRjdGL0YrRi8tRiM2JEYrRi8vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMUYnRi9GL0YvLUYsNi1RIj1GJ0YvRjIvRjZGNEY4RjpGPEY+RkAvRkNRLDAuMjc3Nzc3OGVtRicvRkZGXnEtRiM2JUYrLUZSNiUtRlU2J1EickYnRlhGWkZmbkZobkZbb0Zpb0YvLUYsNi1RIidGJ0YvRjJGXHFGOEY6RjxGPkZAL0ZDUSwwLjExMTExMTFlbUYnRmhvRmdxRmBwRi9GK0Yv parallel (tangential) and perpendicular (normal) to 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRi8=. How does the length of the orthogonal (normal) vector projection of 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 compare to the scalar normal projection LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRIk5GJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1JI21uR0YkNiRRIjFGJ0Y9Rj1GPS1JI21vR0YkNi1RIj1GJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZRLyUpc3RyZXRjaHlHRlEvJSpzeW1tZXRyaWNHRlEvJShsYXJnZW9wR0ZRLyUubW92YWJsZWxpbWl0c0dGUS8lJ2FjY2VudEdGUS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmpuLUZDNiYtRiM2Ky1GTDYtUSFGJ0Y9Rk8vRlNGNEZURlZGWEZaRmZuL0ZpblEmMC4wZW1GJy9GXG9RLDAuMzMzMzMzM2VtRictRiM2JUZhby1JJm1vdmVyR0YkNiUtRi82J1EiVEYnLyUlYm9sZEdGNEYyL0Y2USxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1GTDYuUS0mUmlnaHRBcnJvdztGJy8lLHBsYWNlaG9sZGVyR0Y0Rj0vRlBRJnVuc2V0RicvRlNGXnEvRlVGNC9GV0ZecS9GWUZecS9GZW5GXnEvRmduRl5xRmVvL0Zcb0Zmby8lJ2FjY2VudEdGNEY9RkItRkw2LVEoJnRpbWVzO0YnRj1GT0ZSRlRGVkZYRlpGZm4vRmluUSwwLjIyMjIyMjJlbUYnL0Zcb0Zcci1GIzYlRmFvLUZccDYlLUYvNidRInJGJ0ZhcEYyRmNwRmVwRmhwRmZxRj0tRkw2LVEiJ0YnRj1GT0ZSRlRGVkZYRlpGZm4vRmluUSwwLjExMTExMTFlbUYnRmVxRmVyRkJGPUY9LyUlb3BlbkdRInxnckYnLyUmY2xvc2VHRlxzRj0=?h) Optional. To do only if you finish early. Evaluate the scalar tangential and normal projections 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 and 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 to 3 decimal place accuracy, and the angle between 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 and 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 in degrees to the nearest degree. Then use these three numbers to make a rough diagram of the projection rectangle representing 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, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRIk5GJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1JI21uR0YkNiRRIjFGJ0Y9Rj1GPUY9 (the sides) and 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 (the diagonal). Label the sides with their numerical lengths, and indicate the angle too. Is the point on the curve speeding up or slowing down? Why?solutiona) b)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) h)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Here is the whole rectangle whose sides are the two scalar projections and whose diagonal is the acceleration vector length, the angle looks like about 20 degrees.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYpLUY2NiYtRiM2Ly1GNjYmLUYjNictSSNtbkdGJDYkUSIwRicvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRkYvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGTi8lKnN5bW1ldHJpY0dGTi8lKGxhcmdlb3BHRk4vJS5tb3ZhYmxlbGltaXRzR0ZOLyUnYWNjZW50R0ZOLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGQi8lK2V4ZWN1dGFibGVHRk5GRkZGLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRkgtRjY2Ji1GIzYnLUYsNiVRI2FURidGL0YyRkhGQkZbb0ZGRkZGXW9GYG9GSC1GNjYmLUYjNidGZ29GSC1GLDYlUSNhTkYnRi9GMkZbb0ZGRkZGXW9GYG9GSC1GNjYmLUYjNidGQkZIRl5wRltvRkZGRkZdb0Zgb0ZIRj5GSEZqb0Zbb0ZGRkZGXW9GYG9GSC1GLDYlUShzY2FsaW5nRidGL0YyLUZJNi1RIj1GJ0ZGRkwvRlBGTkZRRlNGVUZXRlkvRmZuUSwwLjI3Nzc3NzhlbUYnL0ZpbkZdcS1GLDYlUSxjb25zdHJhaW5lZEYnRi9GMkZbb0ZGRkZGW29GRg==c)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)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e)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)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 the 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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: