1.1.4.1. Average velocity from position.
Answer 1.
\(2.5\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut s}}\)
Answer 2.
\(3.5\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut s}}\)
\(x\) | \(f(x)\) |
\(2.1\) | \(-8.41\) |
\(2.01\) | \(-8.0401\) |
\(2.001\) | \(-8.004001\) |
\(1.999\) | \(-7.996001\) |
\(1.99\) | \(-7.9601\) |
\(1.9\) | \(-7.61\) |
\(x\) | \(g(x)\) |
\(-2.9\) | \(-1\) |
\(-2.99\) | \(-1\) |
\(-2.999\) | \(-1\) |
\(-3.001\) | \(1\) |
\(-3.01\) | \(-1\) |
\(-3.1\) | \(-1\) |
\(h\) | \(0.1\) | \(0.01\) | \(0.001\) | \(0.0001\) | \(-0.1\) | \(-0.01\) | \(-0.001\) | \(-0.0001\) |
\(\sqrt{|h|}/h\) | \(3.162\) | \(10\) | \(31.62\) | \(100\) | \(-3.162\) | \(-10\) | \(-31.62\) | \(-100\) |
\(h\) (feet) | \(0\) | \(1000\) | \(2000\) | \(3000\) | \(4000\) | \(5000\) | \(6000\) | \(7000\) | \(8000\) | \(9000\) | \(10{,}000\) |
\(c\) (ft/min) | \(925\) | \(875\) | \(830\) | \(780\) | \(730\) | \(685\) | \(635\) | \(585\) | \(535\) | \(490\) | \(440\) |
\(m\) (min/ft) | \(\frac{1}{925}\) | \(\frac{1}{875}\) | \(\frac{1}{830}\) | \(\frac{1}{780}\) | \(\frac{1}{730}\) | \(\frac{1}{685}\) | \(\frac{1}{635}\) | \(\frac{1}{585}\) | \(\frac{1}{535}\) | \(\frac{1}{490}\) | \(\frac{1}{440}\) |
\(x\) | \(-1\) | \(0\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) |
\(A(x)\) | \(0\) | \(1\) | \(1.5\) | \(1\) | \(0\) | \(-0.5\) | \(0\) | \(1\) |
\(B(x)\) | \(-1\) | \(0\) | \(0.5\) | \(0\) | \(-1\) | \(-1.5\) | \(-1\) | \(0\) |
\(C(x)\) | \(-1.5\) | \(-0.5\) | \(0\) | \(-0.5\) | \(-1.5\) | \(-2\) | \(-1.5\) | \(-0.5\) |
\(h\) (feet) | \(0\) | \(1000\) | \(2000\) | \(3000\) | \(4000\) | \(5000\) | \(6000\) | \(7000\) | \(8000\) | \(9000\) | \(10{,}000\) |
\(c\) (ft/min) | \(925\) | \(875\) | \(830\) | \(780\) | \(730\) | \(685\) | \(635\) | \(585\) | \(535\) | \(490\) | \(440\) |
\(m\) (min/ft) | \(\frac{1}{925}\) | \(\frac{1}{875}\) | \(\frac{1}{830}\) | \(\frac{1}{780}\) | \(\frac{1}{730}\) | \(\frac{1}{685}\) | \(\frac{1}{635}\) | \(\frac{1}{585}\) | \(\frac{1}{535}\) | \(\frac{1}{490}\) | \(\frac{1}{440}\) |
\(t\) | \(T_A(t)\) |
\(0.0\) | \(100\) |
\(0.1\) | \(98.5\) |
\(0.2\) | \(97.12492\) |
\(0.3\) | \(95.86801\) |
\(0.4\) | \(94.72237\) |
\(\vdots\) | \(\vdots\) |
\(49.6\) | \(65.56715\) |
\(49.7\) | \(65.48008\) |
\(49.8\) | \(65.43816\) |
\(49.9\) | \(65.44183\) |
\(50\) | \(65.49103\) |
\(t\) | \(T_A(t)\) |
\(0.0\) | \(100\) |
\(0.1\) | \(99.7\) |
\(0.2\) | \(99.41298\) |
\(0.3\) | \(99.13872\) |
\(0.4\) | \(98.87689\) |
\(\vdots\) | \(\vdots\) |
\(49.6\) | \(69.39515\) |
\(49.7\) | \(69.33946\) |
\(49.8\) | \(69.29248\) |
\(49.9\) | \(69.25467\) |
\(50\) | \(69.22638\) |
Day | Pay on this day | Total amount paid to date |
\(1\) | \(\dollar0.01\) | \(\dollar0.01\) |
\(2\) | \(\dollar0.02\) | \(\dollar0.03\) |
\(3\) | \(\dollar0.04\) | \(\dollar0.07\) |
\(4\) | \(\dollar0.08\) | \(\dollar0.15\) |
\(5\) | \(\dollar0.16\) | \(\dollar0.31\) |
\(6\) | \(\dollar0.32\) | \(\dollar0.63\) |
\(7\) | \(\dollar0.64\) | \(\dollar1.27\) |
\(8\) | \(\dollar1.28\) | \(\dollar2.55\) |
\(9\) | \(\dollar2.56\) | \(\dollar5.11\) |
\(10\) | \(\dollar5.12\) | \(\dollar10.23\) |