Luku 5 lisää funktioista ja kuvaajien piirto.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5 Lisää funktioista ja kuvaajien piirto"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rekursio\n",
    "Rekursio tarkoittaa sitä, että funktio kutsuu itseään. Näin saadaan toistorakenne ilman silmukkaa.\n",
    "\n",
    "Yleinen rekursiolla määritelty lukujono on Fibonaccin lukujono. $F_1 = 1, F_2 = 1, F_n = F_{n-1} + F_{n-2}$\n",
    "\n",
    "Pythonissa tämän voi ohjelmoida rekursiivisesti:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def fibonacci(n):\n",
    "    if n == 1:\n",
    "        return 1\n",
    "    if n == 2:\n",
    "        return 1\n",
    "    return fibonacci(n - 1) + fibonacci(n - 2)\n",
    "\n",
    "\n",
    "fibonacci(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kuvaajien piirto pythonissa\n",
    "\n",
    "Pythonissa määritellyistä funktioista voi piirtää kuvaajia matplotlib-kirjastolla:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 4;\n",
       "                var nbb_unformatted_code = \"import matplotlib.pyplot as kuvaaja\\n\\n#kuvaaja = matplotlib.pyplot\\n\\nx_lista = []\\ny_lista = []\\n\\ndef f(x):\\n    return x ** 2\\n\\nx = -3 # start\\nwhile x <= 3: #end\\n    x_lista.append(x)\\n    y = f(x)\\n    y_lista.append(y)\\n    \\n    x = x + 0.01\\n    \\n#matplotlib.pyplot.plot(x_lista, y_lista)\\n#matplotlib.pyplot.grid()\\n#matplotlib.pyplot.show()\\nkuvaaja.plot(x_lista, y_lista)\\nkuvaaja.xlabel(\\\"x\\\")\\nkuvaaja.ylabel(\\\"y\\\")\\nkuvaaja.grid()\\nkuvaaja.show()\";\n",
       "                var nbb_formatted_code = \"import matplotlib.pyplot as kuvaaja\\n\\n# kuvaaja = matplotlib.pyplot\\n\\nx_lista = []\\ny_lista = []\\n\\n\\ndef f(x):\\n    return x ** 2\\n\\n\\nx = -3  # start\\nwhile x <= 3:  # end\\n    x_lista.append(x)\\n    y = f(x)\\n    y_lista.append(y)\\n\\n    x = x + 0.01\\n\\n# matplotlib.pyplot.plot(x_lista, y_lista)\\n# matplotlib.pyplot.grid()\\n# matplotlib.pyplot.show()\\nkuvaaja.plot(x_lista, y_lista)\\nkuvaaja.xlabel(\\\"x\\\")\\nkuvaaja.ylabel(\\\"y\\\")\\nkuvaaja.grid()\\nkuvaaja.show()\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as kuvaaja\n",
    "\n",
    "# kuvaaja = matplotlib.pyplot\n",
    "\n",
    "x_lista = []\n",
    "y_lista = []\n",
    "\n",
    "\n",
    "def f(x):\n",
    "    return x ** 2\n",
    "\n",
    "\n",
    "x = -3  # start\n",
    "while x <= 3:  # end\n",
    "    x_lista.append(x)\n",
    "    y = f(x)\n",
    "    y_lista.append(y)\n",
    "\n",
    "    x = x + 0.01\n",
    "\n",
    "# matplotlib.pyplot.plot(x_lista, y_lista)\n",
    "# matplotlib.pyplot.grid()\n",
    "# matplotlib.pyplot.show()\n",
    "kuvaaja.plot(x_lista, y_lista)\n",
    "kuvaaja.xlabel(\"x\")\n",
    "kuvaaja.ylabel(\"y\")\n",
    "kuvaaja.grid()\n",
    "kuvaaja.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tehtäviä"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tehtävä 5.1\n",
    "Ohjelmoi kaksi funktiota, joista toinen laskee kertoman rekursiivisesti ja toinen silmukalla. Kertoma on määritelty $n! = n\\cdot(n-1)!$ tai $n! = 1 \\cdot 2\\cdot \\ldots \\cdot n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "funktiota kutsuttiin parametrillä 5\n",
      "funktiota kutsuttiin parametrillä 4\n",
      "funktiota kutsuttiin parametrillä 3\n",
      "funktiota kutsuttiin parametrillä 2\n",
      "funktiota kutsuttiin parametrillä 1\n",
      "120\n",
      "120\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 5;\n",
       "                var nbb_unformatted_code = \"def kertoma_rekursiivinen(n):\\n    print(\\\"funktiota kutsuttiin parametrill\\u00e4\\\", n)\\n    if n == 1:\\n        return 1\\n    return n * kertoma_rekursiivinen(n - 1)\\nprint(kertoma_rekursiivinen(5))\\n\\n\\n# 5! = 1*2*3*4*5\\n\\ndef kertoma_silmukka(n):\\n    tulo = 1\\n    for luku in range(1, n+1):\\n        tulo = tulo * luku\\n    return tulo\\nprint(kertoma_silmukka(5))\";\n",
       "                var nbb_formatted_code = \"def kertoma_rekursiivinen(n):\\n    print(\\\"funktiota kutsuttiin parametrill\\u00e4\\\", n)\\n    if n == 1:\\n        return 1\\n    return n * kertoma_rekursiivinen(n - 1)\\n\\n\\nprint(kertoma_rekursiivinen(5))\\n\\n\\n# 5! = 1*2*3*4*5\\n\\n\\ndef kertoma_silmukka(n):\\n    tulo = 1\\n    for luku in range(1, n + 1):\\n        tulo = tulo * luku\\n    return tulo\\n\\n\\nprint(kertoma_silmukka(5))\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def kertoma_rekursiivinen(n):\n",
    "    print(\"funktiota kutsuttiin parametrillä\", n)\n",
    "    if n == 1:\n",
    "        return 1\n",
    "    return n * kertoma_rekursiivinen(n - 1)\n",
    "\n",
    "\n",
    "print(kertoma_rekursiivinen(5))\n",
    "\n",
    "\n",
    "# 5! = 1*2*3*4*5\n",
    "\n",
    "\n",
    "def kertoma_silmukka(n):\n",
    "    tulo = 1\n",
    "    for luku in range(1, n + 1):\n",
    "        tulo = tulo * luku\n",
    "    return tulo\n",
    "\n",
    "\n",
    "print(kertoma_silmukka(5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tehtävä 5.2\n",
    "Piirrä funktion $f(x)=2x-7$ kuvaaja. Merkitse kuvaajan funktion nollakohta."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 6;\n",
       "                var nbb_unformatted_code = \"import matplotlib.pyplot as kuvaaja\\n\\nx_lista = []\\ny_lista = []\\n\\ndef f(x):\\n    return 2*x - 7\\n\\nx = 0 # start\\nwhile x <= 5: #end\\n    x_lista.append(x)\\n    y = f(x)\\n    y_lista.append(y)\\n    \\n    x = x + 0.1\\n    \\n\\nkuvaaja.plot(x_lista, y_lista)\\nkuvaaja.xlabel(\\\"x\\\")\\nkuvaaja.ylabel(\\\"y\\\")\\nkuvaaja.plot([3.5], [0], marker='o', markersize=5, color=\\\"red\\\")\\nkuvaaja.grid()\\nkuvaaja.show()\";\n",
       "                var nbb_formatted_code = \"import matplotlib.pyplot as kuvaaja\\n\\nx_lista = []\\ny_lista = []\\n\\n\\ndef f(x):\\n    return 2 * x - 7\\n\\n\\nx = 0  # start\\nwhile x <= 5:  # end\\n    x_lista.append(x)\\n    y = f(x)\\n    y_lista.append(y)\\n\\n    x = x + 0.1\\n\\n\\nkuvaaja.plot(x_lista, y_lista)\\nkuvaaja.xlabel(\\\"x\\\")\\nkuvaaja.ylabel(\\\"y\\\")\\nkuvaaja.plot([3.5], [0], marker=\\\"o\\\", markersize=5, color=\\\"red\\\")\\nkuvaaja.grid()\\nkuvaaja.show()\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as kuvaaja\n",
    "\n",
    "x_lista = []\n",
    "y_lista = []\n",
    "\n",
    "\n",
    "def f(x):\n",
    "    return 2 * x - 7\n",
    "\n",
    "\n",
    "x = 0  # start\n",
    "while x <= 5:  # end\n",
    "    x_lista.append(x)\n",
    "    y = f(x)\n",
    "    y_lista.append(y)\n",
    "\n",
    "    x = x + 0.1\n",
    "\n",
    "\n",
    "kuvaaja.plot(x_lista, y_lista)\n",
    "kuvaaja.xlabel(\"x\")\n",
    "kuvaaja.ylabel(\"y\")\n",
    "kuvaaja.plot([3.5], [0], marker=\"o\", markersize=5, color=\"red\")\n",
    "kuvaaja.grid()\n",
    "kuvaaja.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tehtävä 5.3\n",
    "Piirrä funktion $f(x)=2x-6$ kuvaaja. Onko piste (2,4) suoran piste?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X:n arvolla 0 funktion arvo on -6\n",
      "X:n arvolla 1 funktion arvo on -4\n",
      "X:n arvolla 2 funktion arvo on -2\n",
      "X:n arvolla 3 funktion arvo on 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "piste on kuvaajalla\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 7;\n",
       "                var nbb_unformatted_code = \"import matplotlib.pyplot as kuvaaja\\n\\nx_lista = []\\ny_lista = []\\n\\ndef f(x):\\n    return 2*x - 6\\n\\nx = 0 # start\\nwhile x <= 5: #end\\n    x_lista.append(x)\\n    y = f(x)\\n    y_lista.append(y)\\n    \\n    x = x + 0.1\\n\\nprint(\\\"X:n arvolla 0 funktion arvo on\\\", f(0))\\nprint(\\\"X:n arvolla 1 funktion arvo on\\\", f(1))\\nprint(\\\"X:n arvolla 2 funktion arvo on\\\", f(2))\\nprint(\\\"X:n arvolla 3 funktion arvo on\\\", f(3))\\n\\n\\nkuvaaja.plot(x_lista, y_lista)\\nkuvaaja.xlabel(\\\"x\\\")\\nkuvaaja.ylabel(\\\"y\\\")\\nkuvaaja.plot([4], [2], marker='o', markersize=5, color=\\\"red\\\")\\nkuvaaja.plot([5], [3], marker='o', markersize=5, color=\\\"red\\\")\\n\\nkuvaaja.grid()\\nkuvaaja.show()\\n\\nif f(4) == 2:\\n    print(\\\"piste on kuvaajalla\\\")\\nelse:\\n    print(\\\"ei oo kuvaajalla\\\")\";\n",
       "                var nbb_formatted_code = \"import matplotlib.pyplot as kuvaaja\\n\\nx_lista = []\\ny_lista = []\\n\\n\\ndef f(x):\\n    return 2 * x - 6\\n\\n\\nx = 0  # start\\nwhile x <= 5:  # end\\n    x_lista.append(x)\\n    y = f(x)\\n    y_lista.append(y)\\n\\n    x = x + 0.1\\n\\nprint(\\\"X:n arvolla 0 funktion arvo on\\\", f(0))\\nprint(\\\"X:n arvolla 1 funktion arvo on\\\", f(1))\\nprint(\\\"X:n arvolla 2 funktion arvo on\\\", f(2))\\nprint(\\\"X:n arvolla 3 funktion arvo on\\\", f(3))\\n\\n\\nkuvaaja.plot(x_lista, y_lista)\\nkuvaaja.xlabel(\\\"x\\\")\\nkuvaaja.ylabel(\\\"y\\\")\\nkuvaaja.plot([4], [2], marker=\\\"o\\\", markersize=5, color=\\\"red\\\")\\nkuvaaja.plot([5], [3], marker=\\\"o\\\", markersize=5, color=\\\"red\\\")\\n\\nkuvaaja.grid()\\nkuvaaja.show()\\n\\nif f(4) == 2:\\n    print(\\\"piste on kuvaajalla\\\")\\nelse:\\n    print(\\\"ei oo kuvaajalla\\\")\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as kuvaaja\n",
    "\n",
    "x_lista = []\n",
    "y_lista = []\n",
    "\n",
    "\n",
    "def f(x):\n",
    "    return 2 * x - 6\n",
    "\n",
    "\n",
    "x = 0  # start\n",
    "while x <= 5:  # end\n",
    "    x_lista.append(x)\n",
    "    y = f(x)\n",
    "    y_lista.append(y)\n",
    "\n",
    "    x = x + 0.1\n",
    "\n",
    "print(\"X:n arvolla 0 funktion arvo on\", f(0))\n",
    "print(\"X:n arvolla 1 funktion arvo on\", f(1))\n",
    "print(\"X:n arvolla 2 funktion arvo on\", f(2))\n",
    "print(\"X:n arvolla 3 funktion arvo on\", f(3))\n",
    "\n",
    "\n",
    "kuvaaja.plot(x_lista, y_lista)\n",
    "kuvaaja.xlabel(\"x\")\n",
    "kuvaaja.ylabel(\"y\")\n",
    "kuvaaja.plot([4], [2], marker=\"o\", markersize=5, color=\"red\")\n",
    "kuvaaja.plot([5], [3], marker=\"o\", markersize=5, color=\"red\")\n",
    "\n",
    "kuvaaja.grid()\n",
    "kuvaaja.show()\n",
    "\n",
    "if f(4) == 2:\n",
    "    print(\"piste on kuvaajalla\")\n",
    "else:\n",
    "    print(\"ei oo kuvaajalla\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tehtävä 5.4\n",
    "Funktio f(x) kuvaa sähkönkulutusta Suomessa (kWh). Missä muuttuja x on kulunut aika vuosissa vuodesta 1970. Piirrä funktion kuvaaja."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eXkRKagZ/vf4cBnVr4r+SMSEUaBLZAlQETimJiEgC0A+4y6f4OWC6iIwEtgGDXPnnwOVACt5IrhEALlk8DSxyxz1V2MkO3ANMBCrjdahbp7qJWOv2pDPi7UVkHM/j7RHduLClLSBlwq/EJCIir+DdtsoClovIHHwSiao+UFJ9Vc0Ezjih7CDeaK0Tj1Xg3mLOMwGYUET5YqBDSTEYEwm+2+iNwKoaF8sHd/eibYPq4Q7JGMD/lchi93MJ3u0mY8xpNn3xDp6csYoW9ary9ohutgKhKVP8JZE04AdVTfVznDGmlKkqY2Zv5OW5KVzYsg6vDe1iU7ibMsdfErkFeFVEsoAfgO/xksrqkEdmTBTLySvg8Y9WMmPZLgYlNebZazvaEramTPL3sOENACLSDDjPve4SkTOBRap6ecgjNCbKpB3L5b+mLOGHzQd5pF8r7uvTApsWzpRVAY3OUtWtIhKPNwqqMlD43hhTivalZzN8wkI278/gxUGduK5LY/+VjAkjf6OzngR6AXWBDXiTMP4DGKWq+SXVNcacms37Mxg2fiFHsnJ4+7buXNCyTrhDMsYvf1ciw4BM4FO8PpEFqpoW8qiMiTLLdxxhxNsLiakgvH9XLzo0qhHukIwJiL8+kTZuKvbz8KYeeVxEqgIr8DrY3w59iMZEtuQNqfzXlKXUrRbH5Nu708xWITTliN8+Efd0+Gci8iXeuiAX4T2BfjtgScSYX2HG0p08+uFKWiVWY+Lt3ahXLT7cIRlzSvz1iVyNdxVyPtAeWIM3zPcRvNtbxpggjftuC89+vo5eZ53B2GFd7RkQUy75uxK5DS9pPAosUdWckEdkTIQrKFCe+3I9Y7/bwuUd6zPmps7ExcaEOyxjguKvT+S60xWIMdEgN7+Axz70HiK8tWdT/nh1+3IxjbsxxfG3xvpIEfm9z/YuN/36URG5O/ThGRM5snLyuHPyYmYs28XD/Vrx1EBLIKb883c7626gv892qqo2cg8ezgLeCFlkxkSQtKxcbp+0iGXbD/PnazsypMeZ4Q7JmFLhL4mIm7q90AcAqpotIvbEujEB2H/0OLeOX8Dm/Rm8OqQLAzo2CHdIxpQaf0mkpu+Gqv4ZQEQqAPY4rTF+7Dycxa3jF7I3LZu3hnfjN61sISkTWfxNC/qViDxTRPlTwFchiMeYiJGSmsGNb/zIgYzjTLmjuyUQE5H8XYn8HnhLRFLwnlIH6IS3WNUdoQzMmPJs9a40hk9YiAhMG9WT9g1tGhMTmfwN8c0EbhaRs/AeNgRYq6qbQx6ZMeXUhkP53D92PtXiY5lyRw/Oqls13CEZEzL+nlhvpqpbVXULsKWI/QI0UtWdoQrQmPIkeUMq/7c4m8ZnJDBlZA8a1rTxJyay+bud9YLrRP8Eb531/XhribQALgb6AqMBSyIm6n22cjcPvb+cBgkVmH5XL+pUjQt3SMaEnL/bWTeKSDtgKN6Eiw2ALGAd8DnwrKpmhzxKY8q4aQu388THq0hqWovbzj5uCcREDb+LNqvqWlX9b1XtraqtVfVcVR2iqlP8JRARqSkiH4rIehFZJyK9RKS2iMwWkU3uZy13rIjIyyKSIiIrRaSLz3mGu+M3ichwn/KuIrLK1XlZbA1REwbjvtvC4zNWcVHLuky+vQcJFe3X0EQPv0nkV3oJ+FJV2+CN6loHPA7MUdWWwBy3DTAAaOleo4DXAdx6JqOBHkB3YHRh4nHH3OlTz/fpemNCSlUZM3sjz36+jis6NmDcsCQqV7KJFE10CVkSEZEaeGuPjAdQ1RxVPQIMBCa5wyYB17j3A4HJ6pkP1BSRBsBlwGxVPaSqh4HZQH+3r7qqzldVBSb7nMuYkFJVnv9yAy/N2cSNXRvz8s3nUik21H+TGVP2+F2U6ldojtcR/7aIdMLrmH8QSFTVPe6YvUCie98I2OFTf6crK6l8ZxHlJxGRUXhXNyQmJpKcnBzUF8rIyAi6bqSKxjZRVaauz+GrbXlc3CSWAXUOMe+7b3/eH41tEghrl5NFQpsElERE5HxguapmisgtQBfgJVXd5ufcXYD7VXWBiLzEL7euAFBVFRENMvaAqepYYCxAUlKS9u7dO6jzJCcnE2zdSBVtbVJQoIyeuYavtm3jtvOaMfqqdpzYFRdtbRIoa5eTRUKbBHr9/TqQ5a4oHgE2490+KslOYKeqLnDbH+IllX3uVhTuZ6rbvwto4lO/sSsrqbxxEeXGhERBgfLkx6t4Z/427rrorCITiDHRJtAkkuf6HQYC/1DVV4FqJVVQ1b3ADhFp7Yr6AmuBmUDhCKvheM+g4MqHuVFaPYE0d9trFnCpiNRyHeqXArPcvnQR6elGZQ3zOZcxpSq/QPndhyuYtmgH9/dpweMD2lgCMYbA+0SOisgTwC3ARe4BxEAWhL4feFdEKuE98T4CL3FNF5GRwDZgkDv2c+ByIAXvWZQRAKp6SESeBha5455S1UPu/T3ARKAy8IV7GVOqcvMLeHj6Cj5dsZuH+7Xigb4twx2SMWVGoEnkJmAIMFJV94rImcAL/iqp6nIgqYhdfYs4VoF7iznPBGBCEeWLgQ7+4jAmWDl5BTwwdRlfrtnL4wPacPdvzg53SMaUKQElEXdr6kWf7e347xMxplw7npfPve8u5et1qfzhynaMvKB5uEMypswJdHTWUaBwFFUlvFtZGapq81ubiJSdm8+od5bw3cb9PH1NB27t2TTcIRlTJgV6JfJzJ7rrxB4I9AxVUMaEU1ZOHndMWsyPWw7y/PUduambrYduTHFO+RFb90T5P/GeJDcmomQcz+O2txcxf8tB/u/GTpZAjPEj0NtZ1/lsVsDrLLfZe01ESc/O5bYJC1mxM42XBp/LVZ0ahjskY8q8QEdnXeXzPg/YindLy5iIkJaVy7AJC1i7J51Xh5xL/w4Nwh2SMeVCoEnkLVX93rfATYWSWszxxpQbhzJzuOWtBaSkZvDGLV3p2zbRfyVjDBB4n8grAZYZU67sP3qcm8fOZ/P+DMYNT7IEYswp8rfGei/gPKCuiDzss6s6YAsnmHJtX3o2Q8bNZ/eRbN6+rRvntagT7pCMKXf83c6qBFR1x/nOlZUO3BCqoIwJtd1HjjFk3Hz2Hz3OpNu707157XCHZEy55G+N9W+Bb0Vkop9p340pN3YcymLIW/M5kpnL5JE96Nq0lv9KxpgiBdqxPrGodT9UtU8px2NMSG09kMmQcfPJzMnn3Tt7cE7jmuEOyZhyLdAk8juf9/HA9XhDfY0pN1JSMxj61nxy85X37uxB+4Y2a48xv1ag054sOaHoexFZGIJ4jAmJDXuPMvQtb320qXf2pHX9EpfDMcYEKNAn1n17HSsAXQH7M86UC2t3p3PL+AXEVhDeu7MnLepVDXdIxkSMQG9nLcGbxVfwbmP9BIwMVVDGlJaVO49w6/iFJFSK4b07e9KsTkK4QzImogR6O8sWUjDlztLthxk+fiE1qlRk6p09aVK7SrhDMibi+HvY8LqS9qvqjNINx5jSsfCnQ4x4eyF1q8Xx3p09aVizcrhDMiYi+bsSuaqEfQpYEjFlzg8pBxg5aTENa8bz3p09SaweH+6QjIlY/h42HHG6AjGmNHy7cT+jJi+m2RkJTLmjB3WrxYU7JGMiWqCjs/63qHJVfap0wzEmeHPW7eO/piylRb2qTLmjB7UTKoU7JGMiXqCz+Gb6vPKBAUAzf5VEZKuIrBKR5SKy2JXVFpHZIrLJ/azlykVEXhaRFBFZKSJdfM4z3B2/SUSG+5R3dedPcXUl4G9uIsqXq/dy95QltGlQjffutARizOkS6Ois//PdFpG/AbMC/IyLVfWAz/bjwBxVfU5EHnfbj+Elppbu1QN4HejhnlEZjbeaogJLRGSmqh52x9wJLAA+B/oDXwQYl4kQn67YzW/fX06nxjWYeHt3qsdXDHdIxkSNU15j3akCNA6y7kBgkns/CbjGp3yyW8N9PlBTRBrgreU+W1UPucQxG+jv9lVX1fmqqsBkn3OZKDFj6U4enLaMrk1rMXlkD0sgxpxmgfaJrMK7CgBvHZG6wNMBVFXgKzd545uqOhZIVNU9bv9eoHAVoEbADp+6O11ZSeU7iygvKv5RwCiAxMREkpOTAwj9ZBkZGUHXjVThbJPvduby9uoc2tSuwMizs1n847/DEseJ7PekaNYuJ4uENgn0ifWBeH0h4D2xvo/AFqW6QFV3iUg9YLaIrPfdqapa1OzApc0lr7EASUlJ2rt376DOk5ycTLB1I1W42uSd+duYsHo1v2lVlzdv7Up8xbKzRpr9nhTN2uVkkdAmgd7O+h9V3eZeu4A4vD6IErljUdVU4GOgO7DP3YrC/Sxcp30X0MSnemNXVlJ54yLKTYSb8O+f+MM/V3NJ23qMHVa2Eogx0SbQJLJTRF4DcKOpZgNTSqogIgkiUq3wPXApsBqYCRSOsBoOfOLezwSGuVFaPYE0d9trFnCpiNRyn30pMMvtSxeRnm5U1jCfc5kI9ca3m3nqs7UM6FCf14Z2JS7WEogx4RTo6Kz/FZG/isgbeDP4PqeqH/mplgh87EbdxgLvqeqXIrIImC4iI4FtwCB3/OfA5UAKkAWMcJ99SESeBha5455S1UPu/T3ARKAy3qgsG5kVwV6es4kXZ2/kqk4NGTOoE7ExwY4LMcaUllOZO2sB8AdgIaAicl1Jc2ep6hagUxHlB4G+RZQrcG8x55oATCiifDHQoaTvYMo/VeXF2Rt5ZW4K13VpxAs3dCKmgj0SZExZcKpzZy0DKrpymzvLhJyq8tyX63nz2y0M7taEP1/bkQqWQIwpM2zuLFNmqSpPfbaWt7/fyq09m/Knq9tbAjGmjAn0OZG6eE+GN/Oto6q3hyYsE+0KCpT/nbmaKfO3M/KC5vzPFW2xWW2MKXsCfU7kE2Ae8DW/PC9iTEjkFyhPzFjJ9MU7ufs3Z/NY/9aWQIwpowJNIlVU9bGQRmIMkJdfwCMfrOCT5bv57SUtebBvS0sgxpRhgY6R/ExELg9pJCbq5eQVcP/UZXyyfDeP9m/Nby9pZQnEmDIu0CuRB4EnRSQHyHVlqqrVQxOWiTbZufnc995Svl6Xyh+ubMfIC5qHOyRjTAACfdiwWqgDMdHrWE4+o95ZzLxNB3j6mg7c2rNpuEMyxgQo0CsRRORq4CK3mayqn4UmJBNNMo/nMXLSIhb8dIi/3nAOg5Ka+K9kjCkzSuwTEZFH3c/n8G5prXWvB0XkL6EPz0Sy9Oxchk1YyKKth/n7TZ0tgRhTDvm7Elnrfl4OdFbVAgARmYT39PoTIYzNRLAjWTkMn7CQNbvT+cfN5zKgY4Nwh2SMCYK/0VlJPu9r+ryvUfqhmGhxMOM4Q8YtYN2eo7xxS1dLIMaUY/6uROa5n38BlonIN4Dg9Y08HsrATGRKPZrN0HEL2H4oi3HDk/hNq7rhDskY8yv4mztrjns7C0gGurntx/CmXzcmYHvSjjF03AL2pmfz9ohunHd2nXCHZIz5lQJ92PBTIFNVZ6rqTKCWKzMmIDsOZTHozR9JPXqcybd3twRiTIQINIn8GfjUrVbYFfgQuCV0YZlI8tOBTG5680fSsnKZckcPkprVDndIxphSEujDhv8SkYp4y+JWA65V1Y0hjcxEhJTUowwZt4Dc/AKmjupJ+4Y2JsOYSOJvZcNX8BafKlQD2AzcJyKo6gOhDM6Ub6t3pTFswkIqiDBtVC9a17eJD4yJNP6uRBafsL0kVIGYyLJ46yFGTFxEtbhYptzRg7PqVg13SMaYEPA3OmvS6QrERI55m/YzavIS6teIZ8odPWhU0wbyGROpAl3Z8Hzgj0BTV0fwZvE9K3ShmfLoqzV7ue+9ZZxVN4HJI7tTr1p8uEMyxoRQoBMwjgcewrudZSsbmiL9c9kuHvlgBR0a1WDSiG7UrFIp3CEZY0Is0CG+aar6haqmqurBwlcgFUUkRkSWichnbru5iCwQkRQReV9EKrnyOLed4vY38znHE658g4hc5lPe35WliIg9QR9G7y7YxkPTl9OtWS3evaOHJRBjooS/WXy7iEgX4BsReUFEehWWufJAPAis89l+Hhijqi2Aw8BIVz4SOOzKx7jjEJF2wGCgPdAfeM0lphjgVWAA0A642R1rTrM3v93Mf3+8motb12PiiO5UjQt4hQFjTDnn7//2/zth23dCRgX6lFRZRBoDVwDPAg+Lt9ZpH2CIO2QSXl/L68BA9x68hxn/4Y4fCExT1ePATyKSAnR3x6Wo6hb3WdPcsYUzD5sQU1U+2pTDp5vXc8U5DRgzqDOVYgO9uDXGRAJ/o7Mu/pXn/zvwKN4DigBnAEdUNc9t7wQaufeNgB3uc/NEJM0d3wiY73NO3zo7TijvUVQQIjIKGAWQmJhIcnJyUF8mIyMj6LqRpkCVqetzmL0tj4sax3J9gzR++Pd34Q6rTLDfk6JZu5wsEtrkVFY2vALvltLPw21U9akSjr8SSFXVJSLS+1fE+Kup6lhgLEBSUpL27h1cOMnJyQRbN5LkFyhPzFjJ7G07ubRpLG/efSneRaMB+z0pjrXLySKhTfw9sf5HVf2jiLwBVAEuBt4CbgAW+jn3+cDVInI5XuKpDrwE1BSRWHc10hjY5Y7fBTQBdopILN7T8Qd9ygv51imu3ITI8bx8Hn5/Bf9atYcH+7akc+wuSyDGRDF/N7AL70/0UtVheB3ffwJ6Aa1KqqiqT6hqY1VthtcxPldVhwLf4CUhgOHAJ+79TLeN2z9XVdWVD3ajt5oDLfES2CKgpRvtVcl9xsxAvrQJTsbxPEZOXMy/Vu3hf65oy0P9WlkCMSbK+buddTUwFzjutrNEpCHeFUKwy9E9BkwTkWfwltgd78rHA++4jvNDeEkBVV0jItPxOszzgHtVNR9ARO7DW+skBpigqmuCjMn4cSgzhxFvL2T17nT+dmMnbujaONwhGWPKAH9J5B3383MRqQm8ACzFG5k1LtAPUdVkvEWtcKOpuhdxTDZwYzH1n8Ub4XVi+efA54HGYYKz68gxbh2/gF2Hj/HmLV25pF1iuEMyxpQR/kZnLXE//+iKPnIPDcaralqIYzNlQErqUW4dv5CM43m8M7IH3ZvbWiDGmF/4e9iwm4jU99keBkwHnhYR+9ckwi3bfpgb3viRvALl/VG9LIEYY07ir2P9TSAHQEQuAp4DJgNpuCGzJjLN27SfoW8toHp8RT66+zzaNawe7pCMMWWQvz6RGFU95N7fBIxV1Y/wbmstD2lkJmw+W7mbh95fTot61Zh0ezebidcYUyx/VyIx7pkNgL54I7UK2QRJEeidH7dy/9RlnNukFtNG9bQEYowpkb9EMBX4VkQOAMeAeQAi0gLvlpaJEKrKmK838fKcTVzSth7/GNKF+Iox4Q7LGFPG+Rud9ayIzMF7JuQr9/AfeFcw94c6OHN65OYX8OSMVXywZCc3dm3MX67rSGyMTaRojPHP7y0pVZ1fRNnG0IRjTrfM43nc8+5Svt24nwf6tuShS1raU+jGmIBZv0YU23/0OLdPXMTaPen85bqO3Nz9zHCHZIwpZyyJRKkt+zMY/vZCDhzNYdywrvRpY0+hG2NOnSWRKLRk22HumLSICiJMG9WTTk1qhjskY0w5ZUkkyny1Zi/3T11GgxrxTBzRnWZ1EsIdkjGmHLMkEkXemb+N0Z+spmPjmkwYnsQZVePCHZIxppyzJBIFCgqU52et581vt9C3TT1eGXIuVSrZf3pjzK9n/5JEuGM5+Tz0/nK+XLOXoT3O5E9Xt7dnQIwxpcaSSARLTc/mjsmLWbUrjT9c2Y7bz29mz4AYY0qVJZEItW5POiMnLuJwVi5jb02iny0kZYwJAUsiEeib9anc995SqsbH8sHdvejQqEa4QzLGRChLIhFm8o9b+ePMNbRtUJ3xw7tRv4bNwmuMCR1LIhEiv0B5+rO1TPxhK5e0rcdLg88lIc7+8xpjQsv+lYkA6dm5PDh1Gd9s2M/IC5rz5OVtialgHejGmNAL2VhPEYkXkYUiskJE1ojIn1x5cxFZICIpIvK+iFRy5XFuO8Xtb+Zzridc+QYRucynvL8rSxGRx0P1XcqyLfszuObV75m36QDPXNOBP1zZzhKIMea0CeUDA8eBPqraCegM9BeRnsDzwBhVbQEcBka640cCh135GHccItIOGAy0B/oDr4lIjIjEAK8CA4B2wM3u2KiRvCGVga9+z5GsXKbc0YNbejYNd0jGmCgTsiSingy3WdG9FOgDfOjKJwHXuPcD3TZuf1/xHmoYCExT1eOq+hOQAnR3rxRV3aKqOcA0d2zEU1XGfbeF2ycuolHNynxy7/n0POuMcIdljIlCIe0TcVcLS4AWeFcNm4EjqprnDtkJNHLvGwE7AFQ1T0TSgDNcue/CWL51dpxQ3qOYOEYBowASExNJTk4O6vtkZGQEXbe05OQrE9fk8MPuPJISY7izQz6bVy5kc5jiKQttUtZYmxTN2uVkkdAmIU0iqpoPdBaRmsDHQJtQfl4JcYwFxgIkJSVp7969gzpPcnIywdYtDXvTsrnrncWs2J3Fw/1acX+fFmF/Aj3cbVIWWZsUzdrlZJHQJqdldJaqHhGRb4BeQE0RiXVXI42BXe6wXUATYKeIxAI1gIM+5YV86xRXHnGWbDvMf01ZQubxPN68tSuXta8f7pCMMSako7PquisQRKQy0A9YB3wD3OAOGw584t7PdNu4/XNVVV35YDd6qznQElgILAJautFelfA632eG6vuEi6oy6YetDB77I/EVY/jonvMsgRhjyoxQXok0ACa5fpEKwHRV/UxE1gLTROQZYBkw3h0/HnhHRFKAQ3hJAVVdIyLTgbVAHnCvu02GiNwHzAJigAmquiaE3+e0y8rJ48kZq/jn8t30bVOPFwd1pkaViuEOyxhjfhayJKKqK4Fziyjfgjey6sTybODGYs71LPBsEeWfA5//6mDLoJ8OZHL3O0vYmHqUR/q14t6LW1DBnv8wxpQx9sR6GfTVmr08Mn0FsTHCpBHduahV3XCHZIwxRbIkUobk5Rfw4uyNvJa8mXMa1+C1oV1oXKtKuMMyxphiWRIpI/amZfPAtGUs/OkQQ3qcyeir2hEXGxPusIwxpkSWRMqAuev38cj0FRzPK+DFQZ24rkvjcIdkjDEBsSQSRjl5Bbwwaz3j5v1E2wbV+ceQczm7btVwh2WMMQGzJBImOw5lcd/UZazYcYRbezblv69oS3xFu31ljClfLImEweer9vDYRysBeH1oFwZ0bBDmiIwxJjiWRE6jjON5PP3pWt5fvIPOTWryys3n0qS2jb4yxpRflkROkyXbDvPQ+8vZcTiLe3qfzW8vaUWl2FAu52KMMaFnSSTEcvMLeHnOJl79JoWGNSsz/a5edGtWO9xhGWNMqbAkEkKb92fw0PvLWbkzjRu6Nmb0Ve2oFm9zXxljIoclkRAoKFAm/7iV575cT3zFGOs8N8ZELEsipeynA5k8+uEKFm09TO/WdXn++nNIrB4f7rCMMSYkLImUkvwCZcK/f+JvX20gLrYCf7uxE9d3aRT2lQeNMSaULImUgk37jvL7D1eyfMcRLmmbyLPXdrCrD2NMVLAk8iscz8tn3HdbeHlOClXiYnhpcGeu7tTQrj6MMVHDkkiQftx8kP/55yo278/k8o71+dPVHahbLS7cYRljzGllSSQQ+fnwxRc0nTGDtP2HeSrvTD5asZcmtSvz9m3duLhNvXBHaIwxYWFJxJ/8fLjsMnTBAppmZnLs3alc36A1DV97j3suaU3lSjZpojEmelkS8eeLL9D5C5DMDARIyMmm54EUzivYApXahTs6Y4wJK5u8yZ9lyyAr8z+KKmRlwfLl4YnHGGPKEEsi/px7LpKQ8J9lCQnQuXNYwjHGmLIkZElERJqIyDcislZE1ojIg668tojMFpFN7mctVy4i8rKIpIjIShHp4nOu4e74TSIy3Ke8q4iscnVellCMrR0wAHr0gKpVURGoWtXbHjCg1D/KGGPKm1BeieQBj6hqO6AncK+ItAMeB+aoaktgjtsGGAC0dK9RwOvgJR1gNNAD6A6MLkw87pg7fer1L/VvERMDs2bB1KlsHTECpk71tmOsQ90YY0LWsa6qe4A97v1REVkHNAIGAr3dYZOAZOAxVz5ZVRWYLyI1RaSBO3a2qh4CEJHZQH8RSQaqq+p8Vz4ZuAb4otS/TEwMXHkl26pWpXnv3n4PN8aYaHFaRmeJSDPgXGABkOgSDMBeING9bwTs8Km205WVVL6ziPKiPn8U3tUNiYmJJCcnB/U9MjIygq4bqaxNTmZtUjRrl5NFQpuEPImISFXgI+C3qpru222hqioiGuoYVHUsMBYgKSlJewd5NZGcnEywdSOVtcnJrE2KZu1yskhok5COzhKRingJ5F1VneGK97nbVLifqa58F9DEp3pjV1ZSeeMiyo0xxpwmoRydJcB4YJ2qvuizayZQOMJqOPCJT/kwN0qrJ5DmbnvNAi4VkVquQ/1SYJbbly4iPd1nDfM5lzHGmNMglLezzgduBVaJyHJX9iTwHDBdREYC24BBbt/nwOVACpAFjABQ1UMi8jSwyB33VGEnO3APMBGojNehXvqd6sYYY4ol3mCo6CEi+/GSVzDqAAdKMZxIYG1yMmuTolm7nKy8tElTVa1b1I6oSyK/hogsVtWkcMdRllibnMzapGjWLieLhDaxaU+MMcYEzZKIMcaYoFkSOTVjwx1AGWRtcjJrk6JZu5ys3LeJ9YkYY4wJml2JGGOMCZolEWOMMUGzJBIAEekvIhvcuiWP+68RmURkgoikishqn7Ii14eJFqe6bk40EJF4EVkoIitcm/zJlTcXkQXu/6P3RaRSuGM93UQkRkSWichnbrvct4klET9EJAZ4FW+9k3bAzW5dlGg0kZPXbClufZhocarr5kSD40AfVe0EdMZbuqEn8DwwRlVbAIeBkeELMWweBNb5bJf7NrEk4l93IEVVt6hqDjANb+2TqKOq3wGHTigeiLcuDO7nNaczpnBT1T2qutS9P4r3D0ThujlR2S7qyXCbFd1LgT7Ah648qtoEQEQaA1cAb7ltIQLaxJKIf8WtZ2I8xa0PE3UCXDcnKrjbNsvxZumeDWwGjqhqnjskGv8/+jvwKFDgts8gAtrEkogpNW5VyqgcM37iujm++6KxXVQ1X1U74y3R0B1oE96IwktErgRSVXVJuGMpbadlZcNyrrj1TIxnn4g0UNU9J6wPEzVKWjcnmtsFQFWPiMg3QC+gpojEur+8o+3/o/OBq0XkciAeqA68RAS0iV2J+LcIaOlGUVQCBuOtfWI8xa0PExWCWDcn4olIXRGp6d5XBvrh9RV9A9zgDouqNlHVJ1S1sao2w/s3ZK6qDiUC2sSeWA+A++vh70AMMEFVnw1vROEhIlOB3njTV+8DRgP/BKYDZ+LWh/FZ7yXiicgFwDxgFb/c634Sr18kKttFRM7B6ySOwftDdbqqPiUiZ+ENTKkNLANuUdXj4Ys0PESkN/A7Vb0yEtrEkogxxpig2e0sY4wxQbMkYowxJmiWRIwxxgTNkogxxpigWRIxxhgTNEsiJqKIyDUioiLSxqesoYh86N7fJiL/CF+EgRGRt4qa6FNE7nMzvqqI1PEpryUiH4vISjeDbgdX3lpElvu80kXkt25f0DMN28zWppAlERNpbgb+7X4CoKq7VfWG4quUPap6h6quLWLX98AleM+e+HoSWK6q5wDD8J6GRlU3qGpnNwVJVyAL+NjVCWqmYZvZ2viyJGIihpu/6gK86bQH+5Q3810Dxaf8ChH5UUTqiMidIrLIrYHxkYhU8fNZ80Wkvc92sogkicgfReR3PuWr3cSMiMjDbnu1z9VAgoj8y33uahG5yfd8J36uqi5T1a1FhNQOmOuOWQ80E5ETJ33sC2xW1cIEFOxMwzaztfmZJRETSQYCX6rqRuCgiHQt7kARuRbvL+/LVfUAMENVu7k1MNbhf12H94FB7lwNgAaquriEz+sKjAB64K07cqeInIu3PstuVe2kqh2ALwP8ridaAVznPqs70BRvLiZfg4GpPttFzjQsIhefcAus8PWDO9ZmtjY/syRiIsnNeH8V437eXMxxfYDHgCtU9bAr6yAi80RkFTAUaF9M3ULT+WXOo0H8siZEcS4APlbVTLfWxgzgQrzpUvqJyPMicqGqpvk5T3Gew5vMbzlwP94UGvmFO928b1cDHxRV2XemYVX9pvAW2Amv84KMzUQwm8XXRAQRqY2XHDqKiOLN26Qi8vsiDt8MnAW0AgqvHiYC16jqChG5DW+OsGKp6i4ROejmiboJuNvtyuM//ziL93OejSLSBbgceEZE5qjqUyXVKeY86XhXOoWTQv4EbPE5ZACwVFX3+ZQVOdOwiFwMjCniY7JcIrGZrc3P7ErERIobgHdUtamqNlPVJnj/kF5YxLHbgOuByT79GtWAPW5a96GFB4rItSLyl2I+8328RYZqqOpKV7YV6OLqdgGau/J5wDUiUkVEEoBrgXki0hDvH+cpwAuFdU+ViNSUX9bnvgP47oR1TW7mP29lQTEzDQdwJWIzW5ufWRIxkeJmfhl1VOgjirml5TqfhwIfiMjZwB/wZt79Hljvc+jZQPrJZwC8W1iD8W5t+X5mbRFZA9wHbHSftxTvameh+5y3VHUZ0BFY6G5DjQaeKelLisgDIrIT76//lSLyltvVFlgtIhvwrjoe9KmTgDcd+4wTTvcc3q20TXgjvp4r6bMLubUv7gNm4fUfTVfVNYHUNZHHZvE1pgQiMgV4SFX3hzsWY8oiSyLGGGOCZrezjDHGBM2SiDHGmKBZEjHGGBM0SyLGGGOCZknEGGNM0CyJGGOMCdr/A8qvsRSZd0b5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sähkönkulutus on 1970 21583.0\n",
      "sähkönkulutus on 2000 79885.0\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 8;\n",
       "                var nbb_unformatted_code = \"import matplotlib.pyplot as kuvaaja\\n\\nx_lista = []\\ny_lista = []\\n\\ndef f(x):\\n    return -1.3 * x**3 + 58.8 * x**2 + 1349.4 * x + 21583\\n\\nx = 0 # start\\nwhile x <= 44: #end\\n    x_lista.append(x)\\n    y = f(x)\\n    y_lista.append(y)\\n    \\n    x = x + 0.1\\n\\n\\nkuvaaja.plot(x_lista, y_lista)\\nkuvaaja.xlabel(\\\"Aika, vuosi 1970=0\\\")\\nkuvaaja.ylabel(\\\"S\\u00e4hk\\u00f6nkulutus (GWh)\\\")\\nkuvaaja.plot([0], [f(0)], marker='o', markersize=5, color=\\\"red\\\")\\nkuvaaja.plot([30], [f(30)], marker='o', markersize=5, color=\\\"red\\\")\\n\\nkuvaaja.grid()\\nkuvaaja.show()\\n\\nprint(\\\"s\\u00e4hk\\u00f6nkulutus on 1970\\\", f(0))\\nprint(\\\"s\\u00e4hk\\u00f6nkulutus on 2000\\\",f(30))\";\n",
       "                var nbb_formatted_code = \"import matplotlib.pyplot as kuvaaja\\n\\nx_lista = []\\ny_lista = []\\n\\n\\ndef f(x):\\n    return -1.3 * x ** 3 + 58.8 * x ** 2 + 1349.4 * x + 21583\\n\\n\\nx = 0  # start\\nwhile x <= 44:  # end\\n    x_lista.append(x)\\n    y = f(x)\\n    y_lista.append(y)\\n\\n    x = x + 0.1\\n\\n\\nkuvaaja.plot(x_lista, y_lista)\\nkuvaaja.xlabel(\\\"Aika, vuosi 1970=0\\\")\\nkuvaaja.ylabel(\\\"S\\u00e4hk\\u00f6nkulutus (GWh)\\\")\\nkuvaaja.plot([0], [f(0)], marker=\\\"o\\\", markersize=5, color=\\\"red\\\")\\nkuvaaja.plot([30], [f(30)], marker=\\\"o\\\", markersize=5, color=\\\"red\\\")\\n\\nkuvaaja.grid()\\nkuvaaja.show()\\n\\nprint(\\\"s\\u00e4hk\\u00f6nkulutus on 1970\\\", f(0))\\nprint(\\\"s\\u00e4hk\\u00f6nkulutus on 2000\\\", f(30))\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as kuvaaja\n",
    "\n",
    "x_lista = []\n",
    "y_lista = []\n",
    "\n",
    "\n",
    "def f(x):\n",
    "    return -1.3 * x ** 3 + 58.8 * x ** 2 + 1349.4 * x + 21583\n",
    "\n",
    "\n",
    "x = 0  # start\n",
    "while x <= 44:  # end\n",
    "    x_lista.append(x)\n",
    "    y = f(x)\n",
    "    y_lista.append(y)\n",
    "\n",
    "    x = x + 0.1\n",
    "\n",
    "\n",
    "kuvaaja.plot(x_lista, y_lista)\n",
    "kuvaaja.xlabel(\"Aika, vuosi 1970=0\")\n",
    "kuvaaja.ylabel(\"Sähkönkulutus (GWh)\")\n",
    "kuvaaja.plot([0], [f(0)], marker=\"o\", markersize=5, color=\"red\")\n",
    "kuvaaja.plot([30], [f(30)], marker=\"o\", markersize=5, color=\"red\")\n",
    "\n",
    "kuvaaja.grid()\n",
    "kuvaaja.show()\n",
    "\n",
    "print(\"sähkönkulutus on 1970\", f(0))\n",
    "print(\"sähkönkulutus on 2000\", f(30))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tehtävä 5.5\n",
    "Pesäpallon lentoa kuvaa pystysuunnassa funktio h(t), missä h on pallon korkeus (m) ajan t (s) funktiona. Laske milloin pallo osuu takaisin maahan ja piirrä korkeusfunktion h(t) kuvaaja."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pallo osuu maahan kun t= 3.1199999999999775\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h on hetkellä 0 1.7\n",
      "h on hetkellä 2 11.499999999999996\n",
      "d on hetkellä 0 0.0\n",
      "d on hetkellä 1 31.5\n",
      "d on hetkellä 2 63.0\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 11;\n",
       "                var nbb_unformatted_code = \"import matplotlib.pyplot as kuvaaja\\n\\nx_lista = []\\ny_lista = []\\n\\ndef h(t):\\n    return 1.7 + 14.7 * t - 4.9 * t ** 2\\ndef d(t):\\n    return 31.5 * t\\n\\nt = 0 # start\\nwhile h(t) >= 0: #end\\n    x_lista.append(d(t))\\n    y_lista.append(h(t))\\n    \\n    t = t + 0.01\\nprint(\\\"pallo osuu maahan kun t=\\\",t)\\n\\nkuvaaja.plot(x_lista, y_lista)\\nkuvaaja.xlabel(\\\"Pituus (m)\\\")\\nkuvaaja.ylabel(\\\"Korkeus (m)\\\")\\n#kuvaaja.plot([0], [f(0)], marker='o', markersize=5, color=\\\"red\\\")\\n#kuvaaja.plot([30], [f(30)], marker='o', markersize=5, color=\\\"red\\\")\\n\\nkuvaaja.grid()\\nkuvaaja.show()\\n\\nprint(\\\"h on hetkell\\u00e4 0\\\", h(0))\\nprint(\\\"h on hetkell\\u00e4 2\\\", h(2))\\nprint(\\\"d on hetkell\\u00e4 0\\\", d(0))\\nprint(\\\"d on hetkell\\u00e4 1\\\", d(1))\\nprint(\\\"d on hetkell\\u00e4 2\\\", d(2))\";\n",
       "                var nbb_formatted_code = \"import matplotlib.pyplot as kuvaaja\\n\\nx_lista = []\\ny_lista = []\\n\\n\\ndef h(t):\\n    return 1.7 + 14.7 * t - 4.9 * t ** 2\\n\\n\\ndef d(t):\\n    return 31.5 * t\\n\\n\\nt = 0  # start\\nwhile h(t) >= 0:  # end\\n    x_lista.append(d(t))\\n    y_lista.append(h(t))\\n\\n    t = t + 0.01\\nprint(\\\"pallo osuu maahan kun t=\\\", t)\\n\\nkuvaaja.plot(x_lista, y_lista)\\nkuvaaja.xlabel(\\\"Pituus (m)\\\")\\nkuvaaja.ylabel(\\\"Korkeus (m)\\\")\\n# kuvaaja.plot([0], [f(0)], marker='o', markersize=5, color=\\\"red\\\")\\n# kuvaaja.plot([30], [f(30)], marker='o', markersize=5, color=\\\"red\\\")\\n\\nkuvaaja.grid()\\nkuvaaja.show()\\n\\nprint(\\\"h on hetkell\\u00e4 0\\\", h(0))\\nprint(\\\"h on hetkell\\u00e4 2\\\", h(2))\\nprint(\\\"d on hetkell\\u00e4 0\\\", d(0))\\nprint(\\\"d on hetkell\\u00e4 1\\\", d(1))\\nprint(\\\"d on hetkell\\u00e4 2\\\", d(2))\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as kuvaaja\n",
    "\n",
    "x_lista = []\n",
    "y_lista = []\n",
    "\n",
    "def h(t):\n",
    "    return 1.7 + 14.7 * t - 4.9 * t ** 2\n",
    "def d(t):\n",
    "    return 31.5 * t\n",
    "\n",
    "t = 0 # start\n",
    "while h(t) >= 0: #end\n",
    "    x_lista.append(d(t))\n",
    "    y_lista.append(h(t))\n",
    "    \n",
    "    t = t + 0.01\n",
    "print(\"pallo osuu maahan kun t=\",t)\n",
    "\n",
    "kuvaaja.plot(x_lista, y_lista)\n",
    "kuvaaja.xlabel(\"Pituus (m)\")\n",
    "kuvaaja.ylabel(\"Korkeus (m)\")\n",
    "#kuvaaja.plot([0], [f(0)], marker='o', markersize=5, color=\"red\")\n",
    "#kuvaaja.plot([30], [f(30)], marker='o', markersize=5, color=\"red\")\n",
    "\n",
    "kuvaaja.grid()\n",
    "kuvaaja.show()\n",
    "\n",
    "print(\"h on hetkellä 0\", h(0))\n",
    "print(\"h on hetkellä 2\", h(2))\n",
    "print(\"d on hetkellä 0\", d(0))\n",
    "print(\"d on hetkellä 1\", d(1))\n",
    "print(\"d on hetkellä 2\", d(2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}