MAT2500-01/04 16S Quiz 0. 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). Indicate where technology is used and what type (Maple, GC).Given the two points 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a) Take your best shot at drawing these two points on a system of Cartesian axes using rectangular coordinate boxes to locate each point with respect to those axes. Be sure you label each axis with its variable name and label their tickmarks.
b) The distance of the point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYsNiVRInhGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRInlGJ0YvRjJGPS1GLDYlUSJ6RidGL0YyRkFGQUZB from point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is twice the distance of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= from point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Show that the set of all such points LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is a sphere, and write down the standard equation for this sphere identifying its center LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYsNiNRJ2B4X18wYEYnLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYjUSdgeV9fMGBGJ0Y9LUYsNiNRJ2B6X18wYEYnRkFGQS1GLDYjUSFGJ0ZB and radius LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= .c) Are the three points LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiQkYnRi9GMkY1LUYsNiVRIkNGJ0YvRjJGOQ== collinear? If so, demonstrate this property. d) Which is the lowest point? Why? e) Which of the first two points lies inside the sphere? Why? solutiona) We copy the diagram from a previously available problem solution available to you. Stewart 12.1.45LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRictRjY2LVEifkYnRjlGOy9GP0Y9RkBGQkZERkZGSEZKL0ZORkwtRiw2JVEld2l0aEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdGPUY5RjktRjY2LVEiOkYnRjlGO0ZTRkBGQkZERkZGSC9GS0ZPRk1Gam5GOQ==LSUnUExPVDNERzYvLSUpUE9MWUdPTlNHNik3JjclJCIiISEiIiQiIiEhIiIkIiIhISIiNyUkISM1ISIiJCIiISEiIiQiIiEhIiI3JSQhIzUhIiIkIiNdISIiJCIiISEiIjclJCIiISEiIiQiI10hIiIkIiIhISIiNyY3JSQiIiEhIiIkIiIhISIiJCIiISEiIjclJCIiISEiIiQiI10hIiIkIiIhISIiNyUkIiIhISIiJCIjXSEiIiQiI0khIiI3JSQiIiEhIiIkIiIhISIiJCIjSSEiIjcmNyUkIiIhISIiJCIiISEiIiQiIiEhIiI3JSQiIiEhIiIkIiIhISIiJCIjSSEiIjclJCEjNSEiIiQiIiEhIiIkIiNJISIiNyUkISM1ISIiJCIiISEiIiQiIiEhIiI3JjclJCEjNSEiIiQiI10hIiIkIiNJISIiNyUkISM1ISIiJCIiISEiIiQiI0khIiI3JSQhIzUhIiIkIiIhISIiJCIiISEiIjclJCEjNSEiIiQiI10hIiIkIiIhISIiNyY3JSQhIzUhIiIkIiNdISIiJCIjSSEiIjclJCEjNSEiIiQiI10hIiIkIiIhISIiNyUkIiIhISIiJCIjXSEiIiQiIiEhIiI3JSQiIiEhIiIkIiNdISIiJCIjSSEiIjcmNyUkISM1ISIiJCIjXSEiIiQiI0khIiI3JSQiIiEhIiIkIiNdISIiJCIjSSEiIjclJCIiISEiIiQiIiEhIiIkIiNJISIiNyUkISM1ISIiJCIiISEiIiQiI0khIiItJS1UUkFOU1BBUkVOQ1lHNiMkIigzJz5dISIoLSUpUE9MWUdPTlNHNik3JjclJCIiISEiIiQiIiEhIiIkIiIhISIiNyUkIiNnISIiJCIiISEiIiQiIiEhIiI3JSQiI2chIiIkIiM/ISIiJCIiISEiIjclJCIiISEiIiQiIz8hIiIkIiIhISIiNyY3JSQiIiEhIiIkIiIhISIiJCIiISEiIjclJCIiISEiIiQiIz8hIiIkIiIhISIiNyUkIiIhISIiJCIjPyEiIiQhIz8hIiI3JSQiIiEhIiIkIiIhISIiJCEjPyEiIjcmNyUkIiIhISIiJCIiISEiIiQiIiEhIiI3JSQiIiEhIiIkIiIhISIiJCEjPyEiIjclJCIjZyEiIiQiIiEhIiIkISM/ISIiNyUkIiNnISIiJCIiISEiIiQiIiEhIiI3JjclJCIjZyEiIiQiIz8hIiIkISM/ISIiNyUkIiNnISIiJCIiISEiIiQhIz8hIiI3JSQiI2chIiIkIiIhISIiJCIiISEiIjclJCIjZyEiIiQiIz8hIiIkIiIhISIiNyY3JSQiI2chIiIkIiM/ISIiJCEjPyEiIjclJCIjZyEiIiQiIz8hIiIkIiIhISIiNyUkIiIhISIiJCIjPyEiIiQiIiEhIiI3JSQiIiEhIiIkIiM/ISIiJCEjPyEiIjcmNyUkIiNnISIiJCIjPyEiIiQhIz8hIiI3JSQiIiEhIiIkIiM/ISIiJCEjPyEiIjclJCIiISEiIiQiIiEhIiIkISM/ISIiNyUkIiNnISIiJCIiISEiIiQhIz8hIiItJS1UUkFOU1BBUkVOQ1lHNiMkIigzJz5dISIoLSUnUE9JTlRTRzYmNyUkISM1ISIiJCIjXSEiIiQiI0khIiItJSZDT0xPUkc2JiUkUkdCRyQiIzUhIiIkIiIhISIiJCIiISEiIi0lJ1NZTUJPTEc2JCUtX1NPTElEQ0lSQ0xFRyIjPy0lJlNUWUxFRzYjJSZQT0lOVEctJSdQT0lOVFNHNiY3JSQiI2chIiIkIiM/ISIiJCEjPyEiIi0lJkNPTE9SRzYmJSRSR0JHJCIjNSEiIiQiIiEhIiIkIiIhISIiLSUnU1lNQk9MRzYkJS1fU09MSURDSVJDTEVHIiM/LSUmU1RZTEVHNiMlJlBPSU5URy0lJ1BPSU5UU0c2JjclJCIiISEiIiQiIiEhIiIkIiIhISIiLSUmQ09MT1JHNiYlJFJHQkckIiM1ISIiJCIjNSEiIiQiIiEhIiItJSdTWU1CT0xHNiQlLV9TT0xJRENJUkNMRUciI0ktJSZTVFlMRUc2IyUmUE9JTlRHLSYlJl9BWElTRzYjIiIiNiYtJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lKkxJTkVTVFlMRUc2IyIiIS0lKlRISUNLTkVTU0c2IyIiIS0lLVRSQU5TUEFSRU5DWUc2IyQiIiEhIiItJiUmX0FYSVNHNiMiIiM2Ji0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIhLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0mJSZfQVhJU0c2IyIiJDYmLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiEtJSpUSElDS05FU1NHNiMiIiEtJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSUrTElHSFRNT0RFTEc2I1EoTElHSFRfMzYiLSUrUFJPSkVDVElPTkc2LCQiKVB5X1UhIikkISgvKil5JyEiKCQiKHBgKWYhIigkIilGTl9PISIpJCIpMTlRdCEiKSQiKHoiR2QhIigkIShfNEcpISIoJCEpZC0rRCEiKiQiKS9JK2MhIikkIiM1ISIiLSUpX1ZJU0lCTEVHNiMiIiItJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiQrIiEiIi0lKUJPVU5EU19ZRzYjJCIkKyIhIiItJS1CT1VORFNfV0lEVEhHNiMkIiUrUiEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiUrUiEiIi0lKUNISUxEUkVORzYiLSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZRzYjJCIiISEiIi0lLUJPVU5EU19XSURUSEc2IyQiJStTISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJStTISIiLSUpQ0hJTERSRU5HNiI=NiI=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The square of the distance from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= to the first point is 4 times the distance to the second point: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1JJm1mcmFjR0YkNigtRiw2JVEiYUYnRi9GMi1GIzYjLUkjbW5HRiQ2JFEiMkYnL0YzUSdub3JtYWxGJy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGTS8lKWJldmVsbGVkR1EmZmFsc2VGJ0ZGLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Nice.TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzI3NTg4MzAyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkISIiIiImIiIkRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzI4MTcwMzQyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkIiInIiIjISIjRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzI4MTcwNDk0WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkJSJ4RyUieUclInpHRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzI4MTcwNjMwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkIyIjRCIiJCIiIiMhIzZGKUYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzI4MTcwNzY2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkJCIrTExMTCQpISIqJCIiIiIiISQhK25tbW1PRilGJQ==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