St. Louis Science Center Planetarium Mathematics I. or II.
PLANETARIUM SLOPES AND ANGLES
Name ____________________ Date __________
Complete the tables below and attach your calculations to this table page. Turn this in to your teacher. If you wish to email your work to the address below - please use your initials in place of your name. You will probably not get a return response other than a smile. For helpful suggestions link here. For resource equations or formulas related to the St. Louis Science Center Planetarium click here: 
Print this table page to fill out:
Use the function y = f(x) for the branch of the Planetarium Hyperbola above the x-axis. Find the value of x for each f(x) listed. Find the first derivative of f(x) to calculate data then complete that column below. For each derivative calculation determine the angle in degrees between the positive x-axis and the tangent line to the curve. Consider using another computer software program to construct this table.
| x = |
f (x) = |
f ' (x) = |
Angle = |
Comments |
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14.5 feet |
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14.0 |
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14.0 |
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13.5 |
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13.0 |
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12.5 |
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12.0 |
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11.5 |
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11.0 |
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10.5 |
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9.5 |
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9.0 |
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8.5 |
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8.0 |
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7.5 |
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7.0 |
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6.5 |
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6.0 |
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5.5 |
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5.0 |
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4.5 |
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4.0 |
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3.5 |
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3.0 |
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2.5 |
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2.0 |
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1.5 |
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1.0 |
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0.5 |
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0.0 |
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Use the function y = f(x) for the branch of the Planetarium Hyperbola below the x-axis. Find the value of f(x) for each x listed. Find the first derivative of f(x) to calculate data then complete that column below. For each derivative calculation determine the angle in degrees between the positive x-axis and the tangent line to the curve. Consider using another computer software program to construct this table.
| x = |
f (x) = |
f ' (x) = |
Angle = |
Comments |
| 0.5 feet |
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| 1.0 |
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| 1.5 |
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| 2.0 |
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| 2.5 |
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| 3.0 |
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| 3.5 |
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| 4.0 |
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| 4.5 |
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| 5.0 |
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| 6.0 |
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| 7.0 |
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| 8.0 |
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| 9.0 |
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| 10.0 |
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| 11.0 |
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| 12.0 |
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| 13.0 |
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| 14.0 |
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| 15.0 |
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| 18.0 |
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| 21.0 |
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| 24.0 |
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| 27.0 |
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| 30.0 |
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| 33.0 |
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| 36.0 |
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| 42.0 |
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| 48.0 |
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| 54.0 |
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| 60.0 |
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| 63.0 |
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| 66.0 |
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| 69.0 |
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| 70.0 |
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| 70.5 |
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| 71.0 |
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| 72.0 |
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| 75.0 |
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| 78.0 |
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| 81.0 |
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| 82.0 |
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| 82.5 |
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| 83.0 |
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| 83.5 |
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| 84.0 |
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