IM Alg1.7.1 Lesson: Finding Unknown Inputs
[size=150]A mechanical device is used to launch a potato vertically into the air. The potato is launched from a platform 20 feet above the ground, with an initial vertical velocity of 92 feet per second.[br][br]The function [math]h\left(t\right)=-16t^2+92t+20[/math] models the height of the potato over the ground, in feet, [math]t[/math] seconds after launch.[br][br]Here is the graph representing the function.[br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARkAAACkCAYAAACjM1oIAAAfiUlEQVR4nO2dW4wbVxnHh4JQVS0ZFwkKUuhYQkioFGyEQC0S2A9ICAnJFuIFpe1YSIiL1I5fSgsPjCVA6tuseABRSGYhqZpL29nNbjabtLuzIZvsdpN00txKLu2kuapJm5OWsKGl8OdhOdOx1+PrOWdt5/tJR1F27fl81p6fz/U7GgiCICSirfYLIAhisCHJEAQhFZIMQRBSWVXJBEFQ9+e+72N2dhZhGEY/C8MQs7Ozic8hCKI3WRXJhGGIXC6HXC5X9XPGGLLZLCzLguM48H0/erxhGLBtG4VCAa7rKn/NBEF0xqpIxrIsBEGwQjKWZdUViGma8Dwv+r9hGHJfIEEQwljV7lKtZHRdB2NsRbeo9nG5XC5q5XDOnDmDEydORGV2dhYTExNR8X0fBw8elFL279+PF198Udr14+XAgQPYt2+fklgHDx7E/Pw81U1QmZubU1q3hYUFZfFeffXVxPu8pyRjGAZM04y6RY7jAAAymUzV4wqFwgrJXL9+HW+99VZUfvWrX+HUqVNROXfuHN544w0p5W9/+xuOHj0q7frxcu7cOUxMTCiJ9cYbb2Bubk5Z3c6fP4/x8XFlddu3bx8OHz6sJNaFCxcwNjamrG7z8/MIgkBJrIsXL2LHjh2J93nPSSaOrut1H1evJRMnCAKk02kBr7A1Dh8+jAsXLiiJtbS01LDuojly5Iiyut28eRMzMzNKYgHA0aNH8frrryuJ9e677+L5559XEgsATpw4UTVxIpP33nsPu3fvTvx9T0mmtsXCJVMoFKq6T4ZhNPwDWpYFTdOqxnFkQpIRA0lGHCSZ/1MrGdu2UalUEIYhKpUKTNMEsDylzUUzPDyMQqHQ8Lqf+tSncNttt+Ghhx6S9MqrIcmIgSQjDpLM/6k3k+Q4DkzTjMZjOJ7nReM1jLHEawZBgI9+9KPQNA1DQ0OiX3JdBkUyfC0SL4wxkowgSDIDxCOPPIIPfehD+PCHP6ysy9RvkpmdnUWlUkGxWEQ+n4emaU1LPp9HqVTC8PCwtAWRJBlxkGQkctddd0HTtEgyKrpMvS4ZxhhGRkZQLBaRSqWgaRpyuRxs24bruvB9P/EDuXPnTmzbtg2u68K2beRyOWiahlQqhWKxiJGRkYYty3YgyYiDJCOJIAigaRp++ctf4s4778QPfvADrFmzRnrcXpWM7/solUrQNA2GYUSLINshqbvk+z4sy4JhGEilUiiVSl23cEgy4iDJSIKvGJ6bm8Odd94JYOVqYRn0mmRGRkaQTqeh6zpM0+zq5m9lTMb3fZimGXWrRkZGOopFkhEHSUYS/OaLSyb+c1n0imS4XAzDgOM4Qrox7Qz8MsZg2zZ0XUc2m237706SEQdJRjK1kpHNakvG933k83nour5iVq5bOpldissmn8+3/GEnyYiDJCOZW0UyjDGUy2VomtZ0ar9TupnCZoxF3ahKpdL09ZFkxEGSkcytIBnf95FOp5HL5aTm2BGxTsb3fWQyGaTT6YavlSQjDpKMBN5++21cu3YN165dw86dO6HrOs6cOROVc+fO4cqVK1LK3r17cfToUWnXj5fz58+jUChA0zT8+te/lh6Pb5AUca1HH30Umqbh0UcfTazbxMSEkr/jlStXsG/fPrz88stKYl28eBFjY2PK6rawsIAgCJTEunTpEiYnJxPvzYGRzOnTp3Hs2DEcO3YMGzduxMc+9jGMjY1F5YUXXsDi4qKU4nkenn/+eWnX52V0dBSf+9zncPfdd2PTpk3S4/GYIuv2hz/8AZ/+9Kfxla98BdPT01W/279/v7J6LS4uYmxsDLt27VISa35+Hhs3blRWt+3bt2NqakpZ3UZHRxPvzYGRTJxB7C55nodUKoUHHngA4+PjUmPFkbGtgDGGQqGAVCpV1X2i7pI4qLskmUGTzPDwMDRNg+u6A7VB0rbtqF4ASUYkJBnJDJJkSqUSdF2PxDJIkgGWN8nquo5KpUKSEQhJRjKDIBnGGEqlEjKZTFWXYtAkAyxvB9F1HQ8++CBJRhAkGcn0u2T4qQ2ZTGbF2pJBlAywLJovfelL+Pa3vy09FockIwaSjAJESqaRYIDBlQwAXL58GZ/97GeRz+elLCyshSQjhq4kE08RkE6nq3KLlMtlpR/2duhXyTQTDDDYkrl58ya2b9+OTCaDbDYrXTQkGTF0LBnHcZBKpaJTA/gqU9/34XletM1f1bdOO/SjZFoRDDD4kpmZmQFjDJlMBvl8Xmo8kowYOpZMoVBo6UU6jiN8U1639JtkWhUMcGtIBkAkmlKpJC0eSUYMXY/JBEFQ94MfhqGySrRLv0kmn8+3JBjg1pEMIF80JBkxdC2ZpDOOHMeBbdsdvzDG2IpE4nwMqFKprIgZBAEqlUpLCZH6STJ8mrrVLuetJBlg+ctM13VYliU8HklGDB1Lhh8Xm81mMTw8XJXFfnZ2Fvl8vuNuEj8Hu/ZIlEKhEOWczWQyUUa7+P8ty2r6gesXyViWBV3X2/ow3GqSAT5YR1PvdItuIMmIoWPJhGEI0zSh6zoymUwkBV74mUidYJomGGMrJBPH87yopVSbQrPZN38/SIavdG03TcOtKBlg+YtG9OkTJBkxdN1dsm1b2oe6kWR4Jv16j6vXhTt+/DgOHTqEQ4cOYf369RgaGsLTTz8dlfHxcezZs0dK2bJlCyYmJlp+PN+L9Jvf/KbtWNPT0xgZGZFWl9qydevWturWTWlWt8cffxxDQ0P485//LCTetm3bsH37diV1m5mZwYYNG5S9b8888wzGxsaUxPJ9H88991zivdzyYjzefRJJkmR4d4q3VmrPyK4nmZs3b2JpaQlLS0uYnp5GKpXC1atXo8IYwz/+8Q8pZWFhAadPn27psceOHUMqlcITTzzRUayrV69i165d0upSWxYXF1uuW7flzTffxNTUVMPH/OxnP4NhGDh//nzX8Q4cOIC///3vSup27do17NixQ9n79tJLL+HEiRNKYjHGMDU1lXifN5UMYwzFYjFaiMep3VPTCfUkEwTBiu5QKy2ZOL3aXeJT1d10NW/V7lKcQqEgZA0NdZfEIKS7VG8MxbbtrmaXgJXyqG3BcEzTrLqxDMPoyzEZPpPUDSSZD6a2u51xIsmIQcgUNm+xyJRMGIZIpVIol8uoVCpRAT6Qz+joKEqlUl/OLjmOA13Xu14dTZJZRsSME0lGDF1LxjTNugOwuVyu65H++AckDMNIXPFS+/tWPlS9Jhl+sqUIOZBkPsB13RXZ9dqBJCMGISt+DcNAuVxGOp3G8PAw8vl8w5mh1aaXJMMYQzqd7rrVxyHJVGOaZsebKUkyYhCS6oEf1pXL5aINk71ML0mmWCwKFTJJZiWdbj0gyYiB8skoIEkyosZh4pBkVsLHZ9rtvpNkxCBEMr7vo1gsVk0buq7bcykeOL0gGZHjMHFIMvXh4zPt3FgkGTF0LRnP82AYBmzbrpp+tSxL+F4SUfSCZLLZrJRNfSSZZNpdP0OSEUPXkikUClEzVPQUtixWWzKWZbW1s7odSDLJMMag63rLY4YkGTFIWydDLZkPiEuGb+STdT41SaYx7fz9STJiENJdyuVyCMMwkgzvQlHSqmW4ZERPV9eDJNMcy7KQzWabPo4kIwYhA7+2bUPX9Wj/kmEYPZdEnB/8fenSJYyOjkLX9WhX9qFDh3DixAmcPXtWSpmensbBgwfxwx/+EPfcc4+0OGfPnsXJkycxOjoqNUa8zMzM4ODBg0pinTp1Cp7ndX2dI0eOYO3atSiXyw0f5/s+FhcXldTtzJkzePbZZ5W9b3v27MHCwoKyuk1MTCTem3Ul4/t+3eYmY6xnZ5TOnTuHV199Fa+++iq2bt2KNWvWYGZmJiovvvgijh8/LqVMTk7id7/7HTRNw7PPPistzvHjxxEEAbZt2yY1Rrzs3LkTe/fuVRLr8OHD2Lp1q5Brua7b9P2YmprCnj17lNTt5ZdfxubNm5W9b7t378bs7KySWEeOHMHY2FjivVlXMvFdzs12PPciqrtLe/fuxWc+8xklA+HUXWody7IazjZRd0kMHXWXHMdBqVRqmH5zdnaWxmT+z09+8hPcc889SmKRZFqHMQbDMBJnm0gyYuhIMowxmKYJwzCicZh6haawP1h0t23bNiXxSDLt4Xle4iI9kowYuh74tSyLuksNyOfzWLdunbIbkSTTPoVCAcViccXPSTJi6Oq0Av5vs8HeXhsMViUZvjdp7969JBkByJIMP1aldm8TSUYMHUvGMIymZxyFYYhSqdRzu7JVSIYxhlQqBc/zhJ2F3Qokmc5wHAfpdLrqC5EkI4aOJcOz0aXTaRSLxapsdeVyGdlsFrqu9+S4jArJmKYZLU4kyYhBpmSA5ZQQ8c8rSUYMQpJWOY6DQqEQnbnEtxT0WjeJI1syfOk6fxNJMmKQLZna940kIwbKJyOBbDZb9Y1IkhGDbMkAyy1QvnaGJCMGkoxg+MmP8VYcSUYMKiTDB4F93yfJCKKvJMMYQ6VSQbFYxPDwcNWN7HkeSqUShoeHm15HlmT4YG/t7nOSjBhUSAZY3ouXTqdJMoLoK8nEc9fE89V4nodCoRCNDzU7HE2WZHie41pIMmJQJRlgefb05z//OUlGAELyydT7UDuOI3zqOn5om+/7KBQKABAJpt7j6iFDMmEYJqbTJMmIQaVkPM/DmjVrcOTIESXxSDINSJKMaZrCp69d10Uul8PIyEiVWFo5pvbQoUOYm5vD3Nwcfv/732NoaAjr16+PypYtWzA5Odlxuf/++/Gtb32r7u/++te/YuvWrV1dv9Wyfft2/OlPf1ISa3JyEhs3blRatyeffFJZ3T7/+c/jO9/5jpJY4+Pj+OMf/6isbps2bcLmzZuV1e2ZZ55JvK8brpOJ55CpLTKSVvG1OXwNCm+t6Lpe9TjVZ2HXTn3WQi0ZMahsyQDAhg0bGr6vIqGWTANM04TjOPB9PyqyXnw8Ly4XDtBaSyaOaMnk8/mGrTaSjBhUS+bo0aP4/ve/X3dfk2hIMg1Qlagqnt6Tw1swpmlW7TsxDKPhtURKpt6UdS0kGTGshmTm5uakHF1TC0mmCZ7nVW0r4EX0G5PL5VAulzE8PIxisRi1HsIwhGEY0fR2swFnkZJpJWcvSUYMqyGZ119/HbZtt3WUSieQZBrgum507lJtkfFh512y2vSfYRgmpgWtRZRkeN2bQZIRw2pJhh+l0u4JlO1AkmlALpeT+seXgQjJ8JMHWjn2hSQjhtWSDPDBAj1ZkGQaED93qV8QIRnbtltqxQAkGVGspmR4a0bWWWIkmQZ4ntd0hW2v0a1k4rliWoEkI4bVlAyw3D2W1ZohydTgui7y+XxUUqkU0ul01c/y+fzAniCZtH0gCZKMGFZbMsDyzKWMzzVJpgY+yNqsDOJpBbwV086NTJIRQy9IRlZrhiTTgH4bjwG6k0y7rRiAJCOKXpAMgIbHqHQKSaYBfOC39pylIAiQSqWgaRpKpZKQFyuKTiXTSSsGIMmIolck47ouUqmU0EWoJJkG5HI56LqOXC4HwzCiwdBCoRD1XXttBqpTyXTSigFIMqLoFckAiNaGiYIk04BcLhe9WMZY1X4i/mH3PG/VE4p3exb2/Pw81qxZA9d12z4LeHJyUtl50UEQCDsvupXSr2dht1IanYX929/+FmvWrMH8/LyQWHQWdgPqbU7k/3LJ+L6/6pK5cuUKLl26hEuXLmF0dBS6ruPQoUNROXHiBM6ePZtYyuUy7rvvvoaPSSrT09M4ePBgR89tt5w8eRKjo6NKYp09exYzMzPK6nbq1Cl4nqesbr7vY3FxMfH3a9euRblcFhLrzJkzePbZZ5XVbc+ePVhYWFAS68yZMxgfH0+8N5tKxrZtlMtlzM7OolKpQNd1lMvlqoVLruv21NlL7XaXOh2L4VB3SQy91F0CxM40UXepAYwxWJaFTCaDQqEAxliU+iGTyaBYLErJLdMN7Uqm07EYDklGDL0mGUDcuhmSTIcwxuC6bk8JBmhPMt22YgCSjCh6UTKiWjMkmTrwDzKfvq5Xek0unHYk020rBiDJiKIXJQOIac2QZGrgqTf5bFJSCs7VHuxNolXJJB1x0i4kGTH0qmREtGZIMgNGq5JxHKflndaNIMmIoVclI2KHNkmmBXi3qR9oVTKt5otpBklGDL0qGWC5W53NZjuORZJpAGMM+XwemqZVnRrQa6t847QimVaz3rUCSUYMvSwZ3prp9G9PkmmAbduwLAtA9cK8+AmPvUYrkhHVigFIMqLoZckA6CoXMEmmAfEWy6BIxvO8picQtANJRgy9LplGp4g2gyTTANM0qzZCcmTm/uVdtHh3jH+LlEqlpnJoJplm5yi1C0lGDL0uGWD5fugkUyRJpgFhGELXdZRKJaTTaVQqFeTz+a7XljSiUCjAMIzoZnJdN3pjgyCIzshOopFk+GmQIrfxk2TE0A+S4a2Zdm9gkkwT+FYC0zRhWZbUtJuu60YL5PjNFN8JDlSfNMm5efMmlpaWsLS0hOnpaaRSKbz55ptRYYzhxo0bWLduHdatW4cbN24IKy+++CJOnz4t9JpJ5c0338Tu3buVxLpx4wYOHDigrG5vvfUWdu3apaxuBw8exMmTJ9t+3ne/+922P0OMMUxOTiqrWxAEeOWVV5TEun79OqamphLv6Z5aJxM/RTIumUwmU/W4esfUHj9+PNpxvX79egwNDWHz5s1RGR8fx+bNm6FpGjZv3ow9e/YIK1u2bMHExITQayaV6elpjIyMKIm1Z88ebN26dWDrtm3bNmzfvr3t5w0PD2NoaKitv8vMzAw2bNigrG7PPPMMxsbGlMTyfR/PPfdc4n3dkmSCIFBygmShUIhaLHGR1E41d3oWtmmaTbtanUDdJTH0Q3eJk8lk2hrXo+5SA/hMjGmaUk+QdBwH2Ww2Elg6nUapVIpaN/HuUbM1OvUkI2IjZBIkGTH0k2Ta3WpAkmmAqhMka09IyGQycBwnSjXBx4EYY00X0dWTjG3bK7pdoiDJiKGfJAO0t3GSJNOAZl0TWcTj8o2a5XK5pUV09SQjcvFdLSQZMfSbZNrZakCSaQCf7ekFWt3GUCsZ13WrtkSIhiQjhn6TTDtbDUgyNdSeIKlpGrLZbN+eICl68V0tJBkx9JtkgNYX55FkauCJwZuV1ehGtUJcMkEQCF98VwtJRgz9KJlWF+eRZAaMuGQ6XQbeDiQZMfSjZIDl8cNmLWWSzIDBJcMYg6Zp0lNSkGTE0K+S8TwPqVSq4WNIMgMGl4yI/L2tQJIRQ79KBmg+nU2SGTC4ZGROW8chyYihnyXDF5MmQZIZMObm5jA0NCR12joOSUYM/SwZ3jVPem9IMgPG3Nwcbr/9dmXre0gyYuhnyQCNJxlIMgPA6dOncezYMRw7dgwbN27ERz7yETz55JMYGxvD2NgYpqensbi4KKV4nofnn39e2vXjZd++fXjqqaeUxFpcXMTo6Kiyuu3fv19p3cbGxrBr1y5h19u0aRM0Tav7WZufn8fGjRuV1W18fBxTU1NKYi0sLDTcejQwknnnnXfAGANjDDt37sTtt9+O1157LSrnz5/H1atXpZS9e/fi2LFj0q4fLxcuXMCOHTuUxLp69Sr27duntG4TExPK6rZ//34cOXJE6DXvvfdePProoyt+funSJWzfvl1Z3RYWFnD48GElsS5fvozJycnEe3NgJBNnbm4Oa9asURaPukti6PfuEpC8O5u6SwNGO8fUioAkI4ZBkAwA6Lq+ovtAkhkwSDLiIMm0j2VZK5KjkWQGDJKMOEgy7VNvPxNJZsAgyYiDJNMZtfuZSDIDBklGHCSZzqgdACbJDBgkGXGQZDonPgBMkhkwSDLiIMl0TnwAmCQzYJBkxEGS6Zz4ADBJZsBQLZmpqSkcPXpUSSzGGJ566iklsQBg9+7dOHLkiJJYb7/9NjZt2qQkFgC88MILeOmll6TG4APAN27cwF/+8hepseL4vo8DBw4oibW0tISRkZHE35NkBECSEcMgSoYPAPerZBhjME0Tw8PDiS0jkowCSDJiGETJAMsDwE8//XRfSgZY/szde++90DQNX/jCF1YIZ2Als2HDhsTyi1/8AnfccUdLydBFlAceeAA//elPlcR67LHH8L3vfU9Z3R588EFldXv88ceV1u2hhx7Cj3/8Y+lxMpkMvvjFL6JYLCqrm2ma+NGPfiTseo899hg+/vGPQ9M03HHHHVXCeeWVVwZTMvfdd19iuffee/GJT3xixREusspXv/pVfP3rX1cS65vf/Ca+/OUvU90ElK997Wu4//77pcf5xje+gUwmU/dYIZl1u++++4Re86677oKmadA0Dbfddhs0TcPatWvx8MMPY2JiIvFe7VvJNEJ1d+nkyZO4cuWKklj/+te/lA3oAcCpU6fwxhtvKIn17rvvYnFxUUksADhz5gwuX76sJNZ7772HhYUFJbEA4LXXXsPFixeFXe+hhx6KBPPJT34SDz/8cJSg/9///jfm5+cTn9u3kuF9wiAIMDs7W3WuEklGHCQZMfSzZGzbxt13341HHnmk7skfAyeZIAhgWRbCMIRlWbDt5RMJUqlU9AcgyYiDJCOGfpUMY6zpkUIDJRkuGMYYcrlcVesll8tFqytVS+b69eu4efOmkljvv/8+rl69qiQWsFy3paUlJbHef/99ZbIGlmezVNXtP//5j9K6vfPOO/jnP/+pJNZ///vfhl9EfSMZxhgymQwYY7Bte8VRJ47jRGcsqZYMQRDJ9I1kLMuC4zgAULf55vs+SYYgepC+kYyu6w37hnxtAKBeMmEYKtsnwhjD7Oys0liq6sbxfb+qKywrxuzsLGZnZ6UfY8xR8ffkEyHxIvv9C8NwxeRLnL6RjKY1fqmFQiHaOHju3Dk88cQTCl7V8ofVMAzYti09Vi6Xg2masCwLmUxG6ofHcRxkMploYL1UKkmLFcd13YaHpImAMRa9Z/W63jLilUolFAoF2Lbd8PiQbnFdt2oRXS6Xi3oAsuLx/Vm5XK5u3fpCMs1O5wuCYEVOVRXwfR2e5ymRTPybwnEcJTE5mUxGeowwDFEoFJDL5aRKxvf9xEPYZGDbttQbvRF8HFPm9TnxIYs4fSEZYPlA83ofDH6jy25eN8L3faU3PLAsGVUfXMaYkiN/C4UCwjBUIhnLspR1BfnfTnW303Vd6TI1TTNqCSZ98fWNZDzPg6ZpqFQq0ZvleV40pb2aqJZMfKZNJq7rIp/PI5vNSs9hE++2yJZMGIYwTTNq4heLRWmxgOUvSN5VymQy0rtnHNldauCDz2I6nU4UWt9IBliWimmayOVysCxL2YBdM1RKhq8RUll3z/NgGIa0D2xtd1e2ZGqJj+fJwDCM6AtBVatQVZfQNE04jhOJ27KsFY/pK8n0KqokwwUjc+AwCdM0pd2IfPCQF13XkclklInUsiypf1PDMKr+32wSQwQqRM0/j3Hq1Y0kIwAVkmGMIZvNKrvx4tPIYRgqaXpzVIzJ8CnX0dFR6V3P+LiF53nSJymCIKg7ACuDeAs3KS5JRgBhGEr/1uBvYG2RBV9BzbdrqOy+uK4rfS2JbdvROInssS3GGCzLipYgqFgDpOr94l1dXrd67xtJhiAIqZBkCIKQCkmGIAipkGQIgpAKSYYgCKmQZAiCkApJhiAIqZBkCIKQCkmGIAipkGRuQYIgULrBMgiCVd8p3yo8WX0jwjDsmc25/QBJ5hagXtJ1VUmbgiCo2oXc6yQlXorDM+upzg/Tr5BkbgFUpBZIIpfLKcufIoJWJAOoFXW/Q5IZcHK5HDRNi84zBpZbNvzG590Dx3GQTqeRTqdRqVQQBAGKxSI0TUOxWKz61maMoVwuI51OI5vNJqZJCIKgSnA81206nUYqlUKxWKzKsxK/Zq2YPM9DPp+HpmnIZrNVO8SLxSJSqRTy+XzV83jdXNeN6lYqlapaVbye6XQaxWIxSjvBsW0b2Ww2uj7vJvGUsP3SQltNSDK3ALU5PniSaWD5mzuVSkX/D8MwyufCxWJZVlV6gkKhEI1bhGEIwzDq7vp1HKfqefETJXhsjmma0e9qr+n7PnRdj/4fv9FTqVQkFp6SgkuP141flzGGQqFQlbbUMIyq5xuGEUnG87yqQwRrx5bisYhkSDK3AM0kU/t7nn2eE+9ChGHY8HqNfu44DvL5/Ipvf94qqH0uF1mtGDiu665IcB5vifC6xePV/r72+TwlJ39sOp1OHHvhqSKIxpBkbgE6kUz8GzouGf742lJvHKPeTWjbNnRdR6lUilokza6ZlMQqLqL4a02lUol1i9clLhQOb71wHMeBYRjI5/MrXkOSXIlqSDK3AJ1IJn5D1UqG38TNsCwr8SZ0XRe6rkcH4zVKSZmUcpQnnopTT4hJv68dfwGqjzuO43kedF2veh08GTnRGJLMLYBIyQBIHIOppZ4EkuIYhpE4vmHbdt0TBfjAcrw7FE9m3UwyfPyp9vlJs0u1LZd+mzlbLUgytwD82I9KpQKge8nwgdhisYhyuZx4ZApfI8NxHCd6HaVSqSq3LhcGv2Y+n49eI09Ync1mUalUqrouvDvDnxO/ZjPJ8L+FYRjRdeOSsW0b+XwelUoF5XIZhmGsmF2itTLNIcncIsTzvsbP7maMrRBE7SwKY2zFClf+PN/3G65+rW2h8OfUk1Kzayb9judYrr1mvbrVq0sQBPB9H2EYrvg9/51fcz53va4WUR+SDCGV2oHUQYAxhnQ6TVsLWoQkQ0inn/YutUK91hCRDEmGIAipkGQIgpAKSYYgCKn8DwAKI+v9YXF1AAAAAElFTkSuQmCC[/img][br]For each question, be prepared to explain your reasoning.[/size][br][br]What is the height of the potato 1 second after launch?
8 seconds after launch, will the potato still be in the air?
Will the potato reach 120 feet? If so, when will it happen?
When will the potato hit the ground?
Your teacher will give you a picture that is 7 inches by 4 inches, a piece of framing material measuring 4 inches by 2.5 inches, and a pair of scissors.[br][br]Cut the framing material to create a rectangular frame for the picture. The frame should have the same thickness all the way around and have no overlaps. All of the framing material should be used (with no leftover pieces). Framing material is very expensive![br]You get 3 copies of the framing material, in case you make mistakes and need to recut.[br][br]Han says, “The perimeter of the picture is 22 inches. If I cut the framing material into 9 pieces, each one being 2.5 inches by [math]\frac{4}{9}[/math] inch, I’ll have more than enough material to surround the picture because those pieces would mean 22.5 inches for the frame.”[br][br]Do you agree with Han? Explain your reasoning.
[size=150]Here is a diagram that shows the picture with a frame that is the same thickness all the way around. The picture is 7 inches by 4 inches. The frame is created from 10 square inches of framing material (in the form of a rectangle measuring 4 inches by 2.5 inches).[/size]
Write an equation to represent the relationship between the measurements of the picture and of the frame, and the area of the framed picture. Be prepared to explain what each part of your equation represents.
What would a solution to this equation mean in this situation?
IM Alg1.7.1 Practice: Finding Unknown Inputs
[size=150]A girl throws a paper airplane from her treehouse. The height of the plane is a function of time and can be modeled by the equation [math]h\left(t\right)=25+2.5t-\frac{1}{2}t^2[/math]. Height is measured in feet and time is measured in seconds.[/size][br][br]Evaluate [math]h\left(0\right)[/math] and explain what this value means in this situation.
What would a solution to [math]h\left(t\right)=0[/math] mean in this situation?[br]
What does the equation [math]h\left(9\right)=7[/math] mean?[br]
What does the model say about the airplane 2.5 seconds after the girl throws it if each of these statements is true?[br][br][math]h(2)=28[/math] [math]h(2.5)=28.125[/math] [math]h(3)=28[/math]
A square picture has a frame that is 3 inches thick all the way around. The total side length of the picture and frame is [math]x[/math] inches.[br][br]Which expression represents the area of the square picture, without the frame? If you get stuck, try sketching a diagram.
[size=150]The revenue from a youth league baseball game depends on the price of per ticket, [math]x[/math].[br][br]Here is a graph that represents the revenue function, [math]R[/math].[/size][br][img]data:image/png;base64,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[/img][br]Select [b]all[/b] the true statements.
A garden designer designed a square decorative pool. The pool is surrounded by a walkway. On two opposite sides of the pool, the walkway is 8 feet. On the other two opposite sides, the walkway is 10 feet.
[size=150]The side length of the square pool is [math]x[/math]. [/size][br][br]Write an expression that represents the total length of the rectangle (including the pool and walkway).
Write an expression that represents the total width of the rectangle (including the pool and walkway).
Write an expression that represents the total area of the pool and walkway.
[size=150]Write an equation of the form: [math]\text{your expression}=1,\!440[/math][/size][br][br]What does a solution to the equation mean in this situation?[br]
[size=150]Suppose [math]m[/math] and [math]c[/math] each represent the position number of a letter in the alphabet, but [math]m[/math] represents the letters in the original message and [math]c[/math] represents the letters in a secret code. The equation [math]c=m+2[/math] is used to encode a message.[br][/size][br][size=100]Write an equation that can be used to decode the secret code into the original message.[/size]
What does this code say: "OCVJ KU HWP!"?
An American traveler who is heading to Europe is exchanging some U.S. dollars for European euros. At the time of his travel, 1 dollar can be exchanged for 0.91 euros.
Find the amount of money in euros that the American traveler would get if he exchanged 100 dollars.
What if he exchanged 500 dollars?
Write an equation that gives the amount of money in euros, [math]e[/math], as a function of the dollar amount being exchanged, [math]d[/math].[br]
Upon returning to America, the traveler has 42 euros to exchange back into U.S. dollars. How many dollars would he get if the exchange rate is still the same?[br]
Write an equation that gives the amount of money in dollars, [math]d[/math], as a function of the euro amount being exchanged, [math]e[/math].
A random sample of people are asked to give a taste score—either "low" or "high"—to two different types of ice cream. The two types of ice cream have identical formulas, except they differ in the percentage of sugar in the ice cream.[br][br]What values could be used to complete the table below so that it suggests there is an association between taste score and percentage of sugar? Explain your reasoning.