{"cells":[{"metadata":{},"cell_type":"markdown","source":"PCSI1 Informatique\n\n# TP01 Expressions et calculs\n#### Objectifs :\n- notions élémentaires : expression, type, affectation, variable\n- exprimer en python des formules mathématiques"},{"metadata":{},"cell_type":"markdown","source":"## A. Expressions avec flottants et entiers\nUne **expression** permet de créer un objet, une donnée. Ces objets sont nécessairement **typés**. Nous nous interessons aux types principaux permettant de coder des nombres : `int`et `float`.\n\n**A faire :** exécuter les cellules ci-dessous en utilisant le raccourcis clavier majuscule+entrée. Analyser les résultats, en particulier le type de l'objet.\n\nLa fonction `print` affiche un objet (sous forme textuelle, lisible donc) ou des objets séparés par une virgule.\n"},{"metadata":{"trusted":false},"cell_type":"code","source":"print(1) # entier 1\nprint(-1023) # entier -1023\nprint(type(1)) # type de 1 : int","execution_count":null,"outputs":[]},{"metadata":{"trusted":false},"cell_type":"code","source":"print(1.) # flottant 1. Le point le distingue de l'entier de même valeur.\nprint(-1023.) # flottant -1023\nprint(3.56e-3) # définition avec notation scientifique\nprint(type(1.)) # type de 1. : float","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"`1` et `3.56e-3` sont des expressions élémentaires qui indiquent à l'interpréteur de créer un entier ou un flottant comprenant les valeurs 1 et 0.00356. Le résultat est ensuite affiché sous forme de texte par la fonction `print`.\n"},{"metadata":{},"cell_type":"markdown","source":"**A faire :** écrire les expressions correspondant aux calculs ci-dessous dans l'interpréteur Python **sans utiliser les parenthèses** et en gardant la structure des calculs (par exemple, ne pas remplacer $2 \\times 5$ par 10). Remarquer que sans l'utilisation de l'instruction **`print`**, seul le dernier résultat est affiché. Repérer le type du résultat : entier ou flottant ?\n\n\n|   |   |  |  |  |\n| ------:| :-----------:| :--: | :--: |:--: |\n| Expressions :| $$3 \\times 2^{3}$$ | $$\\frac{1}{2^4}$$ | $$\\frac 3 {2 \\times 5} $$ | $$\\frac {3 \\times 2}{5 \\times 3^2}$$ |\n| Résultats : | 24| 0,0625 | 0,3 | 0,133 | \n\n*Par convention on place un espace autour des opérateurs principaux.*"},{"metadata":{"trusted":false},"cell_type":"code","source":"","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"**A faire :** déterminer les résultats des expressions ci-dessous dans l'interpréteur Python. Vous devez **minimiser l'utilisation des parenthèses** tout en gardant les notations scientifiques et la structure des expressions (par exemple, ne pas remplacer $5^2-1$ par 24).\n\n*Mettre des espaces autour des opérateurs principaux*\n\n|   |   |  |  |  |\n| ------:| :-----------:| :--: | :--: |:--: |\n| Expressions :| $$\\frac{30+1,5 \\times 10^3} {5 \\times 2}$$ | $$\\frac{(8 \\times 2 + 3)(-7+3,5)}{16 \\times 3^2}$$ | $$\\left(\\frac{7+8,5}{5^2-1}\\right)-\\left(\\frac {10^{-3}} {8\\times 10^{-3} + 0,03}\\right)$$ | $$\\left( 2^3 - \\frac 1 4 \\right) ^2$$ |\n| Résultats : | 153 | -0,4618 | 0,6195 | 60,0625 | \n| nombre de paires de parenthèses : | 1 | 2 | 3 | 1 | \n"},{"metadata":{"trusted":false},"cell_type":"code","source":"","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"## B. Affectation du résultat d'une expression\nDans les exemples précédents, les résultat des expressions étaient affichés (`print`) puis *oubliés*. L'affectation permet de de *sauvegarder* le résultat pour le réutiliser ensuite.\n\n**Dans le suite du sujet, toutes les cellules contenant du code doivent être éxécutées et le résultat analysé et compris.** Les raccourcis clavier sont :\n- **Ctr+Entrée** pour éxécuter la cellule courante\n- **Majuscule+Entrée** pour exécuter la cellule courante et passer à la suivant\n- Entrée pour modifier une cellule\n- les flèches haut/bas pour changer de cellule"},{"metadata":{"trusted":false},"cell_type":"code","source":"x = (3 + 2) / 10  # le nom x est donné au résultat de l'expression (3+2)/10, un flottant puisqu'il y a une division\nprint(x) # affichage de l'objet de nom x\nprint(2*x + 1) # affichage du résultat d'une expression utilisant x\nprint(type(x)) # affichage du type de l'objet de nom x\n\ny = x     # y et x sont deux noms d'un même objet\nprint(y)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"En pratique, pour les flottants, les entiers et tous les objets non modifiables (ont dit, non muables), l'affection `y = x` peut être vu comme la recopie de la valeur de `x` dans `y`. Mais le mécanisme sous-jacent est différent : il s'agit de donner 2 noms à un même objet."},{"metadata":{"trusted":false},"cell_type":"code","source":"x = 100 # création de l'entier 100 et affectation du nom x\ny = x # affectation du nom y à l'entier 100 -> x et y sont deux noms d'un même objet, \"presque une recopie\"\nx = 300 # création de l'entier 300 et affectation du nom x -> x et y ne nomment plus le même objet\nprint(x)\nprint(y)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"Remarque : les noms de variables ne doivent pas correspondrent aux 34 **mots réservés** ci-dessous (ils sont utilisés par le langage lui-même) :\n```\nand  as  assert  break  class  continue   def  \ndel  elif   else   except   False   finally   for\nfrom   global   if   import   in   is   lambda\nNone   nonlocal   not   or   pass   print   raise\nreturn   True   try   while   with   yield```"},{"metadata":{},"cell_type":"markdown","source":"## C. Utilisation de fonctions mathématiques\n\n**A faire :** \n- importer le module math et excécuter la cellule. Le module math est importé dans l'**espace des noms**\n- taper sur une nouvelle ligne `math.` puis appuyer sur la touche *tabulation* du clavier. La liste des objets du module math doit s'afficher. Ce processus est appelé **autocomplétion**. Parcourir rapidement la liste avec les flèches haut/bas."},{"metadata":{"trusted":false},"cell_type":"code","source":"import math\n\n","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"**A faire :**\n- importer tous les objets de la bibliothèque `math` \n- calculer $\\tan(\\pi/4)$, $\\tan(\\pi/2)$ (qu'en déduire ?)"},{"metadata":{"trusted":false},"cell_type":"code","source":"from \n","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"## D. Calculs avec valeurs intermédiaires"},{"metadata":{},"cell_type":"markdown","source":"### Exemple d'utilisation : dégradation d'une boisson dans l'organisme\n\nLa cinétique de dégradation d'une boisson alcoolisée dans l’organisme donne une évolution temporelle de sa concentration dans le sang régie par l'équation :\n\n$C_2(t)=\\frac{V_1}{V_2}C_{01} (1-e^{-k_1 t})-k_2 t$ en mol/L, $t$ en min,\n\navec :\n\n- $C_{01}=0,90$ mol/L, concentration initiale dans l'estomac,\n- $V_1=1,0$ L, le volume de boisson absorbé,\n- $V_2=40$ L, le volume total de liquide et de sang dans le corps humain,\n- $k_1=0,17$ /min, la constante de vitesse caractéristique de la 1ère phase,\n- $k_2=71 \\times 10^{-6}$ mol/L/min, la constante de vitesse caractéristique de la 2ème phase.\n\nOn rappelle qu'en France, une personne ne peut conduire que si le taux d’alcool dans son sang ne dépasse pas $C_{2max}=0,50$ g/L, soit $0,011$ mol/L.\n\nLe tracé de $C_2$ en fonction du temps donne la figure ci-dessous.\n![concentration-3.png](attachment:concentration-3.png)\n\n**A faire :** \n- définir des variables correspondant à $C_{01}$, $V_1$, $V_2$, $k_1$, $k_2$. Puis, déterminer la concentration résiduelle au bout d'une heure (*par calcul direct, ne pas écrire de fonction, même si vous savez le faire*). Vérifier votre résultat avec la courbe. Cette concentration est-elle acceptable pour pouvoir conduire ?\n- déterminer graphiquement et très approximativement la durée nécessaire pour descendre en dessous du taux légal. Le vérifier par calcul.","attachments":{"concentration-3.png":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAcIAAAEsCAYAAABQVrO3AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAuJAAALiQE3ycutAAA8hklEQVR4nO3dd3hUVfrA8e87mRQgtFCkhF6NCqhUpcUoYoF1saICK6uuK2tX1p/rdl1XcO2srgIW1EVF1nUFsYQuSFN6DTVBFOmYEEKS9/fHvaNjSJkMSSYz836eZx7m3nvOve+cZ8g7995zzxFVxRhjjIlWnlAHYIwxxoSSJUJjjDFRzRKhMcaYqGaJ0BhjTFSzRGiMMSaqWSI0xhgT1SwRGmOMiWqWCI0xxkQ1S4TGGGOimiVCY4wxUc0SoTHGmKhmidAYY0xUs0RojDEmqlkiNMYYE9UsERpjjIlqlgiNMcZENUuExhhjopolQmOMMVHNEqExxpioZonQGGNMVLNEaIwxJqpZIjTGGBPVLBEaY4yJapYIjTHGRDVLhMYYY6KaJUJjjDFRzRKhMcaYqGaJ0BhjTFSzRGiMMSaqWSI0xhgT1SwRGmOMiWqWCI0xxkQ1S4TGGGOimiVCY4wxUc0SoTHGmKjmDXUAla1OnTqanJwcdP2cnBxq1qxZgRGFJ2sHh7WDw9rBYe3g8G+HDRs2HFXVOiEOqVwiPhEmJyezfv36oOunp6eTlpZWgRGFJ2sHh7WDw9rBYe3g8G8HEckKcTjlZpdGjTHGRDVLhMYYY6KaJUJjjDFRzRKhMcaYqGaJ0BhjTFSzRGiMMSaqWSI0xhgT1SL+OcJwcjy/gK92HWL7vmwOZOdRWKjUTvDSpG4NzkquS7O6CYhIqMM0xpiIEnQiFJFUYAIQB8wHblXV/EDKiMgNwFhAgOPAA6o6163TAngLOA3YAwxX1a/dbdcBfwFigLdV9aFg469O1n99hH/N38on677l2ImCEss1TIynW4u6pHZuzEUpp9G4dkIVRmmMMZEpqEQoIjHAJGCIqq4TkXeAEcArAZbZDqSq6gEROQNIF5FmqloIPA5MUdWXROR24DFglIjUA8YDPYHvgPkikqqqc4L76KGXk5fPYzM3MuWLncTGCIPPbEpqp0Z0alKbxrUT8Agcyc0n80AOa3Yf5qtdh/hy10E+27CXh99fS49WSVxxdnOGdmtGYryd3BtjTDCC/evZA8hS1XXu8iTgN/glwtLKqOoiv3LrgQQgUUSOApcCo91trwGPuu8HA3NUdQ+AiLwGDAPCMhHuPZLLjZOWsPnb7xl2dnPGDu5Mk7onn+E1SIynTcNa9O/YCICCQmXFzoN8tHYPs9Z+w0P/WcMjM9YztGszbuzdijOb163qj2KMMWEt2ESYDGT6Le9y15W3DMD1wDpVPSIiDYFsVc0FUNVsEckTkbol7G9wkPGH1LdHchn+0hdkHszh2eFnM7Rrs4DrxniEnm2S6NkmiYcvS2H+lu+YunQX767IYuqyTM5r14Bb+rdlYMdGdj/RGGMCcCrX09TvfUl/cUstIyLnAI8Ag0qoU7RemccUkTHAGN9yUlIS6enpJYRXtuzs7FOqX1R+ofL48jx2HVHGdI2l1r4NpKdvOKV9XtMMLkqKY05WPnN27uemV/bTrJYwqFUMvZvGEOs59YRY0e0QrqwdHNYODmsHR7i3Q7CJMBNo6becDBQdcbzUMiLSEXgXuE5Vt7ir9+NcIk1Q1VwRqQnEquphEckEupRxTFR1Ak4HHQBSUlL0VEaHr+jR5f/yv/VsO7ydR39+Jjf0alVh+wW4Csg+ns87yzOZtHA7r64/xie7vdye2p6ruycT740Jet82yr7D2sFh7eCwdnCEezsE+xzhcqC5iKS4y6OB6YGWEZFkYAZwm6ou8VVQVXXXj3BXjQI+cN/PAgaKSBMR8QIjizlmtbZ8xwEmf76doV2bcX3PlmVXCEKteC83nd+GufcP5JnrulEz3svD769l4Pi5TPliJ8fzS+6Vaowx0SioRKiqBcAtwDQRyQBygCki0l1EZpZWxt3FH4HGwHgRWem+WrvbHgRGishmYDjwkLu/wziPXCwANgELwqnHaGGh8uf/radujVj+PPSMSr9/543x8LNuzfn47v48N/xsEuO9/N4SojHGnCToe4SqOhtIKbJ6OU6vz9LKoKq34CTJ4vabCfQrYdtUYGqQIYfU9K92s2b3Yf44JIX6teKq7LgxHmFI12ZcdlZTZq7dwzOfbeH376/lhTkZ3HVhB648JxlvjA0wZIyJXvYXsAoUFirPz95Cm4a1uLF3xd4XDJTHI1zepRkf392f568/m4S4GH773hoGPT2fGav3UFhYtI+SMcZEB0uEVSB941527M/hl33bEBvisy9fQvzk7v6Mu7ILuXkFjHnrS4ZOWMi8zd/h3KY1xpjoYYmwCkxcsI16NWO58pziHqMMDW+Mh2t6tGD2/QP5/eUpfH0ol1GTl3LdS1+wYufBUIdnjDFVxhJhJduw5whLth/ghl4tqREX/OMLlSUhNoZf9m3D/LGp3HNhR9Z9fYQrX1jEza8tY8OeI6EOzxhjKp0NUFnJ3l+5G4DrelTO4xIVJTHey10XdmBEn1a8MDeD1xbvJH3jXoZ2bca9F3UMdXjGGFNpLBFWosJC5cNVezinZT1aJNUMdTgBSaoVx+8uS2F03zY8m57BO8szmbF6D/2be+ja6zgNE+NDHaIxxlQouzRaib7KPMjuQ8cYUo6xRKuLpnVr8Niws/js3gFcfGYTZmcWMGDcHJ75bAvZx/PL3oExxoQJS4SV6IOVX+MRuKxL01CHErQ2DWsx4fpzeLhnHGcl1+WpzzYzYPwcpizewYmCwlCHZ4wxp8wSYSVRVT5e9y092yRFxAS6bep6+PctvXnlph40TIzn9/9dx0VPzmPG6j32yIUxJqxZIqwkGXu/55sjuaR2ahzqUCqMiJDaqTEz7uzHk9d05USBMuatL7liwucs2rov1OEZY0xQLBFWkvlbnMTQr0OjEEdS8WI8wrBzkkm/bwAPX3Y6Ow/kcP3LSxg1eSnrv7ZHLowx4cUSYSVZsOU7GibG07lJ7VCHUmkSYmO4uV9b5j2Qyu0D27Fk+34ue24B9769kqyDOaEOzxhjAmKJsBIczy9gybYD9G3fAE8FTIpb3dWtEcvYwZ2Ze38q13Zvwfsrd3PBE/N45MP1HMzOC3V4xhhTKkuElWDFzoMcO1EQkZdFS9OkbgJ/v7ILn9zTnwGdGjFx4Xb6j5vDhDkZHMuzaZ+MMdWTJcJKsGTbAQDOb98wxJGERvvGtXl5ZHem3daHjk1qM/7jTQx8Yg5Tl+4i3x65MMZUM5YIK8HKzEM0q5tAk7rh/9jEqejeOolpt/Xh5ZHdqZ0Qy4PT1zD4mQV8su4be+TCGFNtWCKsYKrKysxDdGtZL9ShVAsiwkUppzHrrn48fuVZHM09wa1TVnDVi4tZvuNAqMMzxpjgE6GIpIrIehHJEJHJInLSuKUllRGR1iIyX0SyRWRikTozRWSl+8oQkYN+29Rv20oRqRds/JVl+75sDh87QbcW9UIdSrXijfFwbY+WzL0/lbGDO7H526Nc9eJibn5tOVu+PRrq8IwxUSyoRCgiMcAk4GpVbQ8kAiPKUeYI8CBwX9F9q+qlqtpNVbsBrwLv+m0u8G1zX4eCib8yfbXrEABnt6wf2kCqqRpxMdw+sD3zH0jl5r5tmL/5Oy5+ej6/nbaaPYePhTo8Y0wUCvaMsAeQparr3OVJwLBAy6jqAVVdBOSWcZwbgClBxhgSKzMPEeMRzmxWN9ShVGv1a8Xx8OUpzL5/AFec3Zx3VmQycPxc/v7RRg4fOxHq8IwxUSTYRJgMZPot73LXlbdMiUSkB5AALPRb7RGRZSKyQkTuLV/IVeOrzIN0blK7Wk7CWx0l16/Jk9d0Y+ad/ejTrgEvzttK/3FzeHn+NnJP2CMXxpjKdyrzEfp3+yvpqfFAypTkRuBN/Wn3wpaqmiUijYEPRGS3qr7tX0lExgBjfMtJSUmkp6eX89A/ys7ODrj+iUJlw9fH6dc85pSOWR2Vpx2CNaIl9EiMZdqWfB6duYEXZm/g5+1i6d3Ug0eqx8AEVdEO4cDawWHt4Aj3dgg2EWYC/lOuJwNZQZQpltup5lpggP96Vc1y/90rIm8AvYG3i5SZAEzwLaekpGhaWloghy1Weno6gdbfsOcIBekLuLD76aT1bhX0Mauj8rTDqUgDbldlxpo9jP94E5PW5bDoQB1+O7gTAzo2QkKcEKuqHao7aweHtYMj3Nsh2Eujy4HmIpLiLo8GpgdRpiSDgF2qusm3QkTqi0iC+74GMBRYHWT8lWLTN07vx04RPL5oVRARLu/SjE/vGcBffnYGe4/k8otXlnHDxCWsyToc6vCMMREmqESoqgXALcA0EckAcoApItJdRGaWVgZARGqKSBbwJDBcRLJExP/nxI3AG0UO2xlYJiKrcJLsCuC1YOKvLJvcxwA6NrZEWBHivB5G9mnNvLGp3JXWgZWZhxjy/ELu+PdX7NyfHerwjDERIuh7hKo6G0gpsno5cGkZZVDVHErpOKOq1xezbjFwVrDxVoXN3xylad0E6taMDXUoESUx3ss9F3Xkht4teTZ9C/9emsmstXu4oVcr7rigPQ0S40MdojEmjNnIMhVo07dH6XianQ1Wlsa1E3jkirP49J7+XHj6aby6aAcDxs/lufQt5OTlhzo8Y0yYskRYQb4/nk/WwWN2f7AKtG2UyAs3nsv0288jpVkd/vHpZgaMn8ubS3baoN7GmHKzRFhBNvvuD9oZYZU5p2V93r61N5NGdad+zVh+95+1DHp6PrPW2qDexpjAWSKsIJt9PUYtEVYpESHt9NP46K7+jLuyCznHC7jtDRvU2xgTOEuEFWTzt98jAu0bJ4Y6lKgU4xGu6dGCuQ8M5LeDO9ug3saYgFkirCA79mfTrG4NG1otxBJiY/j1wHbMfyCVW/r9OKj3g++t5pvDZQ1ta4yJRpYIK8iO/dm0alAz1GEYV/1acfzuMndQ727NeXt5JgOfmMO4WRs5kmuDehtjfnRSIhSRi0IRSDgrKFSyDhyzRFgNJdevyZPXdmPGHf3o2aYB/5y7lQHj5jBp4XaO59ug3saY4s8IJ1V5FGHumyO55BUU0jKpVqhDMSVIaVaH10f35M2be9G8fg3++uF60v4xj/e/2k1hofUwNSaaFZcIq8cw/2Fk5z5nuK/WdkZY7Z3fviEfjOnLs8PPxiPC3W+vZMjzC1mw5btQh2aMCZHiEqH9PC6nnQdyAGhpiTAseDzC0K7N+OzeAfxpSAp7DucyYtJSRkxawtrdNqi3MdHGKyIv+S0LUD9UwYSrnfudRNiqgV0aDSdxXg+/OL8NV56bzEvztzFxwXYuf24hP+vWjPsHdaJFkv2wMSYaeIHPi6xbWFxBU7Kd+7NpmBhHYvypzHNsQqV2Qiz3DerEiN6teOqzLbyzPJOP1nzDjb1b8ZsL2pNUKy7UIRpjKpFXVavVVEbhaOf+HDsbjACN6yTw2LCz+GXfNoz/eCOTP9/Ou8szuW1gO0af38aeETUmQnlE5F8iMsSd7NaUk6qyc382rewyWsRo3ziRf43oznu/7kOnJrUZ//EmBj4xh6lLd1FgPUyNiTge4G1gIPCFiMwUkTEi0iq0YYWP/dl5ZOcV2BlhBDq3VRLv3taHl0acS2K8lwenr+GPX+TxyTob1NuYSOJR1dmqep+qdgXuAGKAf5VVUURSRWS9iGSIyGQROekGWUllRKS1iMwXkWwRmVikzqsislNEVrqvkX7brhORzSKyVUT+dsqfvgJkHTwGQIskO6GORCLCoDOa8PHd/fn7sLM4lq/cOmUFV7+4mBU7bVBvYyKBR0Sa+V7AMWCaqg4urZKIxOA8eH+1qrYHEoER5ShzBHgQuK+EQ/xOVbu5r9fd/dUDxgMDgE7AQBFJLfcnrmB7DjmJsGldS4SRzBvj4bqeLfnb+fE8cHEnNn1zlCtfWMyvpiwnY+/3oQ7PGHMKPDi9Rv1fgfQa7QFkqeo6d3kSMCzQMqp6QFUXAeUZBXkwMEdV96hqPvBaMcescnvcgZyb1k0IcSSmKsTHCGNS2zNvbCqjz2/D7I17ufjp+fzf9DXsPWKDehsTjjyq2qbIq20A9ZKBTL/lXe668pYpyR9FZLWITBGRJhWwv0qz57BzRtjEEmFUSaoVxx+GpDD7voFc3qUp/166iwHj5/KPTzZx1Ab1NiaseEVkEHABzogys1X10wDr+vcWKGlYtkDKFPUQsMct/xDwCnBJoPsTkTHAGN9yUlIS6enpAR76ZNnZ2aXWX7k5j8RY+Hz+3KCPEQ7KaodoUVw7DG0EXXvFMW1LPs/NzuCVBRkMaetlYHIMXk9kjlho3weHtYMj3NvBC/wVeMtdfkREeqrqo2XUywRa+i0nA1lBlDmJqn7teysiT/PjfcRMoEtZ+1PVCcAE33JKSoqmpaWVddgSpaenU1r9f25eRKtGBaSl9Qv6GOGgrHaIFqW1w2hgwZbv+PtHG/n3piN8/l0c91/cicvPaoonwhKifR8c1g6OcG8HD9BfVZ9R1WdwOqJcF0C95UBzEUlxl0cD04MocxK3047PdcBq9/0snA4yTdzepyMD2V9l23PomHWUMT/o16ER//tNX56+thuFqtz576/42YTP+TxjX6hDM8aUwAMU+i0XllTQn6oWALcA00QkA8gBpohIdxGZWVoZABGpKSJZwJPAcBHJEhHfz4nXRWSNiKwCrsRJoKjqYWAssADYBCxQ1Tmn8NlPWUGh8u3R49ZRxvyExyNccXZz0u8bwO8vTyHrYA43TFzCyMlLWf/1kVCHZ4wpwgvMEZE33eUbgfcCqaiqs4GUIquXA5eWUQZVzaGEji6qemEpx5wKTA0kvqrw3dHjFBQqTetZIjQni/fG8Mu+bbi6ezIvzt3K5M+3c9lzC7iiW3PuG9SR5Po2GpEx1YEXGIdzSVSAv6vq/0IbUvjw9Ri1M0JTmjoJsYwd3JmRfVrz9GebeWd5JjNW72Fkn1aMSW1PfRvU25iQ8qrqB8AHoQ4kHP34DKHdIzRla1I3gb9f2YVf9m3D47M2MXHhdt5ensntA9tz0/mtSYi1Qb2NCQWPiMwWkW0isktEMkVkV6iDChf2ML0JRofTajNxVHfeva0PHRon8visjQwcP5d3lmXaoN7GhIAHZ9iy83FGgunu/msC4Bte7bQ6lghN+fVoncR7vz6PF288l5rxMYx9bzWXPDOf9A3f2qDexlQhr6p+FOogwtWeI7k0qBVnl7RM0ESEwWc24cLTG/PO8iye+mwzv3xtOT3bJPF/l3Tm7Jb1Qx2iMRHPKyJPAB8Dx30rVXV+6EIKH98ezrWh1UyF8MZ4uL5XS644uxmTFmznX/O38fN/LuKSM5vwwMWdaNsoMdQhGhOxvDgPrZ/Nj88QKjAoZBGFke++P06bhjYPoak4NeO83JHWget7teS52Rm8uWQnn6z/luE9W3BnWgca17YfXsZUNC/QTlWPl1nSnGTf0eN0b5UU6jBMBGqQGM+fhp7BTee35olPNvPGF7uY/uVubu7Xllv7tyUx/qTpP40xQfIA8aEOIhwdyysgO6+AhrXtGTBTeVo1qMVzw8/mg9+cT7cW9Xg2fQsDx8/h9cU7OFEQ0EBQxpgyeIA1IvKaiLzke4U6qHCw73vnJLpRov2OMJWvS3I93ry5F6/e1IOGifH84b/ruOjJeXy4+mvrYWrMKfICfwh1EOHoOzcRNrREaKqIiDCwU2P6d2jE+yt3849PNvObt77i5eRtPHjJ6fRp1yDUIRoTlryq+lqogwhH+45aIjSh4fEIw85J5tKzmjJl8U6en5PB8Je/YGCnRjx4SWc6N6kT6hCNCSueUAcQrvZ9nwdg9whNyCTExnBL/7bMH5vKbQPasXjrfi55ZgH3vbOK3e5gD8aYslkiDNI+uzRqqom6NWJ58JLOzLl/IFedk8x/vsoi9Ym5PDZzA4dzToQ6PGOqPUuEQdr3/XE8AvVr2hmhqR6a1avB+Ku78tFd/enXviH/mr+NfuNm8695W8k9URDq8IyptrwiMhxog9NxBgBV/UvoQgoP+74/TlKteGI8EupQjPmJTk1qM+kXPfhi237+/tFGHvtoI68t2sG9gzrx87Ob23fWmCI8wPU4SbDA71UmEUkVkfUikiEik0XkpCd8SyojIq1FZL6IZIvIxCJ1pojIJhFZJSLvikg9v20qIiv9XvUIkX1H82iYaGeDpvrq3bYB/7n9PF644RziY2O4/91VXPbsAuZs3GuPXBjjx6OqQ1T1L6r6qO9VViURiQEmAVeransgERhRjjJHgAeB+4rZ/VTgdFXtCmTw08c7ClS1m9/rULk+bQXa9/1xGtW2+4OmehMRLjmrKZ/c05+/XnEm+77P46ZXlzH85S9YlXko1OEZUy14RKRVEPV6AFmqus5dngQMC7SMqh5Q1UVAbtEdq+oMVfUNmbEcCCa+Svfd98eto4wJG7ExHkb0bsW8BwZy94UdWJ11mJ9N+Jwxb33Jjn3ZoQ7PmJDyAmtF5Et+OvtEWYNuJwOZfsu73HXlLVMiERHgVmCa32qPiCzDuaT7pqo+Gej+KlLuiQKO5ubbpVETdmrFe7n7wo7c0KsVz83ewltLdvHx2m+4vldL7kzrYD/uTFTyApcHWdf/JkNJd98DKVOSR4EcwP8eYktVzRKRxsAHIrJbVd/2ryQiY4AxvuWkpCTS09PLeegfZWdnn1R//zHnYx36JpP09D1B7zucFNcO0SiS2mFAInTuHcv0rfm8vngnby/dyeBWXga1iiHBW/p/10hqh1Nh7eAI93bwAquAtqr6ZTnqZQIt/ZaTgawgyhRLRO4G+gIXq99dfVXNcv/dKyJvAL2BnyRCVZ0ATPAtp6SkaFpaWiCHLVZ6ejpF66/KPAQLP6d3tzNIOzfgk9ywVlw7RKNIbIfrgZWZh3hs5gb+u+0An++N4a4L23NdjxbExhT/hFUktkMwrB0c4d4OHmAZ7uVHEekqIjMDqLccaC4iKe7yaGB6EGVOIiKjgJHAEFU95re+vogkuO9rAEOB1QHEWuF+eJjeOsuYCNGtRT2m3tqbV37Rgwa14vj9+2u5+Kn5fLRmj/UwNRHPg9Op5TCAqq7ip2dxxVLVAuAWYJqIZOBcwpwiIt19ibSkMgAiUlNEsoAngeEikiUivp8TE4H6wDz3EYnX3fWdgWUisgonya4AQjJO6oFsZ3i1BrXsHqGJHCJCaufGzLyrH+Ov6sKxEwX8+s0v+fk/F7Fk2/5Qh2dMpfGq6iGnX8oPAprkTFVnAylFVi8HLi2jDKqaQwkdZ1Q1toT1i4GzAomtsh1yh62qV7PYUI0JazEe4eruLRjStRmvLdrBhDkZXPvSF6R1bsxvL+lMx9NqhzpEYyqUV0QuAlRE6uA817cqxDFVe4eOOWeE9Wx4NRPBEmJj+NWAdlzbowX/nLuVVxftYM7T87nq3GR61LDLpSZyeIEbcc7OtgIfAXeGNKIwcDDnBLExQq24mFCHYkylq1czjocuPZ1R57XmyU828+6KLP4jsNWzkV8PbEfdGnZlxIQ3j6qOUtXGqtpIVUeq6sFQB1XdHc45Qb2acRS5pGxMRGterwb/uKYrM+/sR+f6Hl6ct5UB4+cwccE2jufboN4mfNnsE0E4mJNHPfsVbKLU6U3rcPc5cbx1Sy9aJdXkkRkbuOCJeUz/MovCQrtkasKPJcIgHMw5YdMvmah3XruGvD/mfJ6//my8McK976zisucWMm/zd/bIhQkrlgiDcDgnj7rWY9QYRITLuzTj03sG8OehZ7D3SC6jJi/lholLWJN1ONThGRMQr4g0A1rz0/kI54csojDgnBFaIjTGJ87rYdR5rRl2TnNeXrCdiQu2MeT5hQzp2owHBnWiZYOaoQ7RmBJ5cR5M38CP8xAqUNag21Er90QBx04U2KVRY4pROyGWey/qyI29W/LMZ1uYuiyTWWv3cEOvVtxxQXsa2KDephryAu3cB9xNAA4fcx6mt0ujxpSsce0EHv35WYzu24YnPt7Eq4t2MG1FFr/q35Zf9mtDzbiT5vE2JmQ8QH6ogwgnvlFl7IzQmLK1a5TICzeey/TbzyOlaR3+8elmBo6fy1tLdpFfENAgVsZUOi+wSERm8NP5CP8WupCqt4M57qgy9viEMQE7p2V93v5Vb2Zv3Mvjszby0H/WMHHhNsZe3JmLzzjNnsk1IeUB/oczvmis38uU4FCODa9mTDBEhLTTT+Oju/oz7sou5Bwv4LY3VnDVi4tZvuNAqMMzUcyrqn8OdRDh5IdLo7Xs94IxwYjxCNf0cAb1fmXRdl6Yu5WrXlzMRSmn8dvBnWjf2Ab1NlXLIyL/FpFvRGSPiLzlzv5uSnDQN/NEDTsjNOZU1IiL4faB7Zn/QCo3923DvE3fMeip+Tz43mq+PZIb6vBMFPFNzNsJZ76/FcDkkEZUzf0484SdERpTEerXiuPhy1NIv28AP+vWnLeXZzJg/BzGf7yRI7knQh2eiQIeVX1SVQ+7r39QwjyBxnEo+wQJsR4SYm3mCWMqUoukmjx1bTc+vKMvPds0YMKcrQwYN4dJC7fboN6mUnlEpKtvQUS6AQH9BBORVBFZLyIZIjJZRE56MKikMiLSWkTmi0i2iEwsUqeFiCwQkc0iMs8d+ca37Tp3/VYRCUnP1kPH8uzRCWMq0RnN6vL66J68eXMvmtevwV8/XM+FT87jvyt326DeplJ4gP+JyBIRWQr8F7i7rEoiEgNMAq5W1fZAIjCiHGWOAA/iTARc1OPAFFXtCLwNPOburx4wHhiAcyl3oIiklufDVoSD7hRMxpjKdX77hnwwpi/PXNcNgLumrmTI8wtZsOW70AZmIo4HaA/c7L46qOrnAdTrAWSp6jp3eRIwLNAyqnpAVRcBP7kjLs7DRJcCr7urXgOGuu8HA3NUdY+q5rvbih6z0h2yKZiMqTIej/Czbs1Jv3cgfxySwp7DuYyYtJQRk5awdrcN6m0qhgdoCOwH9gEN/S9FliIZyPRb3sXJ9xYDKVNUAyBbVXMBVDUbyBORukHur8IdyjlhHWWMqWJxXg83nd+GeQ8M5Dep7Vm24wCXP7eQu6d+ReYBGyHSnBovsBDwH9ZBgbYB1PW/WF/SsBCBlCmtTtF6Ze5PRMYAY3zLSUlJpKenB3jok2VnZ/+k/sHs43x/8LtT2mc4KtoO0crawRHKdjjbC4/0juV/2/L5YNXXfLjqa1JbxHBZGy+146p2hBr7PjjCvR28qhpI0isqE2jpt5wMZAVRpqj9QKKIJKhqrojUBGJV9bCIZAJdytqfqk4AJviWU1JSNC0trazPU6L09HR89fPyCznx6Ud0btuStLSUoPcZjvzbIZpZOziqQztcBWTs/Z5xszbyyfpv+eJb4baB7Rh9fhtqxFVNr+7q0A7VQbi3w0kT84rIzADqLQeai4gvG4wGpgdR5ifUmdZ6Bj92qhkFfOC+n4XTQaaJ2/t0ZFn7q2hH3WeaaifYpVFjqoP2jRN5aWR33vt1Hzo1qc34jzcx8Ik5TF1qg3qbwP0kEYpIDaBFWZVUtQC4BZgmIhlADjBFRLr7EmlJZdzj1BSRLOBJYLiIZImI7+fEg8BIEdkMDAcecvd3GBgLLAA2AQtUdc4pffpyOprrTNRRO8GmkDGmOjm3VRLv3taHl0acS2K8lwenr+GSZxbw6fpvcX5fG1Myr4jkue8FyAaeCaSiqs4Gil4fXI7T67O0MrjzHxbb0UVVM4F+JWybCkwNJL7K8GMitDNCY6obEWHQGU24oHNj3l2RxVOfbuaW15fTo3V9HrzkdM5tVT/UIZpqyquq9lBcgH68NGpnhMZUV94YD8N7tuRn3Zrxyuc7eHHuVq58YREXn3EaYwd3pl2jxFCHaKoZ30gvSUCCb6Wqfh2yiKqxI3Zp1JiwUTPOy5jU9gzv2ZLnZm/hjS928tmGvVzbowV3p3WgcZ2EsndiooJHRLYCXwOrcXp6BvJAfVTynRHWsUujxoSNpFpx/HHIGaTfO5DLuzTlrSW7GDB+Lv/4ZNMP/6dNdPPg3I/boKoNgWup4p6Y4cQ6yxgTvlo2qMkz153Nh3f05dxW9XludgYDxs/l1c+3k5dvPUyjmce9DOoFUNVpQO/QhlR9WWcZY8Lfmc3r8sbNvXh9dE+a1EngT/9zBvX+YNXXNqh3lPK4g2OvF5GxInIDYF2rSmCdZYyJHP07NuLDO/ry9LXdKFTlzn9/xc8mfM6ijH2hDs1UMQ9QA2fGic7AFTgPqptiHM3NJyHWQ2zMSeMQGGPCkMcjXHF2c9LvG8DDl51O5sEcrp+4hFGTl7L+6yOhDs9UEa+qfg98jzPyiynF0eMn7LKoMREo3hvDzf3acnX3Fvxr3lYmLdzOZc8t4OfdmnPvoI4k168Z6hBNJbJTm3I4mptvl0WNiWB1a8QydnBn5j2QyjXntuD9lbu54Il5PDpjPYdy8sregQlLHhF5RUQGich5vleog6qujuTm2xmhMVGgSd0EHr+qCx/f3Z/+HRvx8oLt9Bs3hxfmbiX3REGowzMVzAu0Bv7Pb50CF4QkmmruaO4JmterEeowjDFVpMNptZk4qjtLtx/gsY828Pisjby+eAf3XNSRK8+p8ulQTSXxqmqq/woRsVOeEtilUWOiU882SUz/9Xl8vO4bxs3axNhpq5m4YBuDmxZwgSoiVTsPoqlYxd0jtJFlSnA09wS14+13gjHRSEQYfGZTPrmnP4/+/EwO5pzg2ZUnuPalL/hq18FQh2dOgUdEmopIM/fVGbARaYtxoqCQ3BOFdkZoTJTzxni4oVcr5j0wkCvaeVm3+zA//+cibn9zBdv3ZYc6PBMEL84ZoO+8/jABTsMUbWxUGWOMv5pxXoa09fLw8L48PzuDN77YySfrvuW6ni24K60jjWrHhzpEEyCvqrYNdRDhwEaVMcYUp2FiPH8aegY3nd+a8R9v4o0vdjH9y93c0q8tt/RvS2K8/c2o7jzuJdHzRKS/7xXqoKojG3DbGFOaVg1q8fz15/DBb86nW4t6PJO+hYHj5/D64h2cKLBBvaszD7ACeAT4vft6OJCKIpIqIutFJENEJovISRmitDIiMs5dv1lErvJbP1NEVrqvDBE56LdN/batFJF6wX/08jnywxmhXRo1xpSsS3I93ry5F6/e1IOGifH84b/ruOjJecxYvQdVG9S7OvIC7VQ1pzyV3IG6JwFDVHWdiLwDjABeCaSMiAzCmeWiM3Aa8IWIfKyqR1X1Ur99PAy09Dt0gap2C+aDnqojx5wzwjp2RmiMKYOIMLBTY/p1aMT7X+3myU83M+atL+naoh4PDu5Mn3YNQh2i8eMB8oOo1wPIUtV17vIkYFg5ygwDXlXVfFXdDSwEBhVznBuAKUHEV+GO2hmhMaacYjzClecmk37fAH536ens2JfN8Je/4KZXlrLxGxvUu7rwAotEZAZw3LdSVf9WRr1knNnsfXa56wItkwy8V1p9EekBJOAkSR+PiCzDSeBvquqTZcRZYeweoTEmWAmxMdzSvy3XdG/BP+dl8MrnO7jkmQVceU4y917UkWY2YlVIeYH/ue/Le6rjf7G7pGEVSitTVv0bcZKdf7mWqpolIo2BD0Rkt6q+7V9JRMYAY3zLSUlJpKenl/QZypSdnU16ejqrtjqJcOWyxWyNi75RJHztEO2sHRzWDo5g2qFnHLTvE8v7W/N5b0UW73+VxYUtYri0jZdaseH5tyXcvw9eVf1zEPUy+em9u2Qgqxxlitu2xLfgdqq5Fhjgv0NVzXL/3Ssib+DcZ3y7SJkJwATfckpKiqalpQX6uU6Snp5OWloaS49vgG3buOSiVOK9MUHvL1z52iHaWTs4rB0cp9IOVwObvjnK47M2MmvjXhbv9TAmtR0j+7QmITa8/saE+/fBIyJfiMh2ABHpKiJ/CaDecqC5iKS4y6OB6eUoMx0YJSIxItIM6At84ld3ELBLVTf5VohIfRFJcN/XAIYCqwP9oKfq++P5eD1CnE3Ka4ypIJ2a1GbyL3ow9dbetG5Yi7/N3MgFT8xl2oosCgqth2lV8QB3AocAVHUVJ3d6OYmqFgC3ANNEJAPIAaaISHcRmVlaGXfbpzhngJuAecB9qnrU7xA3Am8UOWxnYJmIrMJJsiuA14L4zEHJySugVrzXBtc1xlS43m0b8P7t5/HPG84hPjaG+99dxWXPLmDOpr32yEUV8Krq0iJ/3E8EUlFVZwMpRVYvBy4to4xv21hgbAnbri9m3WLgrEBiqwzZx/OpFRdelyuMMeFDRLj0rKZclHIaU5fu4pn0Ldz0yjL6tG3A/13amS7J9UIdYsTyiEhT3I4rIpIG2DDqxcjJK6CmDZVkjKlksTEeRvRpzdwHUrn7wg6syjrE0Oc/Z8xbX7LDBvWuFF6c+3XtReRLoDZwRUgjqqay8+yM0BhTdRLjvdx9YUdu6NWKZ9O38O+lu/h47Tfc0Ksld6R1oGGiDepdUbxAP6ATziMMG1U1mAfsI1728Xwa1LIvnjGmajWqHc9frziT0X3b8MTHm3ht8U6mrcji1v7tuLlfG2rZlapT5gFqq+o6VV0L1BaR4aEOqjrKPl5gXzhjTMi0aViLCTecw/tjzufM5nV56rPNDBg/lze+2GmDep8ij6r+cE/QfV9sB5Zol5OXT614uzRqjAmtbi3qMfXW3kz+RXca1Irj4ffXcvFT8/lojQ3qHaziHoqz055iZOcVUDPOmsYYE3oiwgWdT2PmXf0Yf1UXjp0o4NdvfsmwFxaxdPuBUIcXdjwi8jsRSRSRWu5sD+tDHVR1c6KgkLz8QussY4ypVmI8wtXdWzDn/oE8eElntu79nmv+tZibX1vGlm+Plr0DAzhnhKcD291XJ+D2kEZUDeUcLwCwxyeMMdVSQmwMtw1ox/yxqdzavy3zt+zj4qfnM3baKvYcPhbq8Ko9r6reGOogqrvsPKcjbaLdIzTGVGP1asbx0KWnM7JPK578dDPvrsjivyu/ZnTfNtw2oB11a9g0csXxur1E2+B3b1BVAxlvNGrkuInQ7hEaY8JBcv2aPHlNN27u25ZxH2/khblb+ffSXfwmtT0j+rSKyokDSuMBrsdJggV+L+Mn2700ar1GjTHhJKVZHV69qSdv3dKLlkk1eWTGBi54Yh7/+SqLQhvU+wdeVR0S6iCqu2w7IzTGhLHz2jXk/dvPZ8aaPYz/eBP3vL2Kl+Zv58FLOtO/Q8Oon0zAIyKtQh1EdffDGaElQmNMmPJ4hCFdm/HZvQP489Az2Hskl1GTl3LjpCWsyToc6vBCygusdccZPe5bqaqDQhdS9eO7R2iXRo0x4S7O62HUea0Zdk5zXp6/jZcXbGfI8wsZ2rUZ9w/qRMsGNUMdYpXzApeHOojq7sd7hHZGaIyJDLUTYrl3UCdu7NOKZz7bwtRlmXy0dg839GrF2MGdoupWkBdYCHTAmYopw51Q1/j5sdeonREaYyJL49oJPPrzsxjdtw3jZ21i8db9Uder1ANkAG8BU4EtItIzkIoikioi60UkQ0Qmi8hJPx9KKyMi49z1m0XkKr/1r4rIThFZ6b5G+m27zi2/VUT+diofvDzsHqExJtK1a5TIiyPOZfrt5xHjia7OMx7galU9R1XPBq4FniurkojEAJPcuu2BRGBEoGVEZBDQG+gMpAJPiUhtv+q/U9Vu7ut1t049YDwwAGcEnIEikhr0Jy+HH3qN2j1CY0yEi8ZbQB5VXe5bUNVlQEIA9XoAWaq6zl2eBAwrR5lhwKuqmq+qu3Euz5bVQWcwMEdV97hzJr5WzDErRfbxfGJjJOouFxhjTDTwiMgYEanpvu4Evg6gXjKQ6be8y10XaJmy6v9RRFaLyBQRaVKOY1aKHJt5whhjIpYXuAD4C05nmbnAzQHW9R+WoKQLyqWVKWnbQ8Aed91DwCvAJYEeU0TGAGN8y0lJSaSnp5cQXtmys7PZkZVHjBae0n7CXXZ2dlR/fh9rB4e1g8PawRHu7eBV1SuDqJcJtPRbTgayylGmuG1LAFTVd0aqIvI0cJ9fnS5lHBNVnQBM8C2npKRoWlpamR+oJOnp6dSqm0iS5JKWNiDo/YS79PR0TqUdI4W1g8PawWHt4Aj3dvjJxLwicquIXBdAveVAcxFJcZdHA9PLUWY6MEpEYkSkGdAX+MSNoZnfPq4DVrvvZ+F0kGni9j4dWcwxK0V2Xr7NRWiMMRGq6Az1U/nxDKxE7rOGtwDTRCQDyAGmiEh3EZlZWhl326c4Z4CbgHnAfarqm0XydRFZIyKrgCtxEiiqehgYCyxw6y1Q1TlBf/JyyD6eH5U9qYwxJhr85K+7qh4RkbhAKqrqbCClyOrlwKVllPFtG4uT2Iquv7CUY07FSdZVKvt4AS2TLBEaY0wkKnppNB6oXULZqJWTl2/jjBpjTIT6IRGKSCLwEvBh6MKpnrLt8QljjIlYHhH5UkRWALtxEuNvQxxTtZJfqOTlF1pnGWOMiVBe4A84z+StVdXtIY6n2nGHGbXOMsYYE6G8qmqXQkvhS4Q17IzQGGMiUtHHJ0wReQXOYDY2BZMxxkQmS4RlyCt0/k2ItURojDGRyBJhGfJ8l0YtERpjTESyRFgG36VRS4TGGBOZLBGWwXdp1DrLGGNMZLJEWAbfpVG7R2iMMZHJEmEZ7NKoMcZENkuEZfix16g1lTHGRCL7616GPHug3hhjIpolwjIct8cnjDEmolkiLENeoXOP0DrLGGNMZAo6EYpIqoisF5EMEZksIieNSl1aGREZ567fLCJX+a2fIiKbRGSViLwrIvX8tqmIrPR71aOS5RWACMR77TeDMcZEoqD+uotIDDAJuFpV2wOJwIhAy4jIIKA30BlIBZ4SEd+EwFOB01W1K5CBMzuGT4GqdvN7HQom/vI4UeBcFhWRyj6UMcaYEAj2NKcHkKWq69zlScCwcpQZBryqqvmquhtYCAwCUNUZqur21WQ50CrIGCtEXqHa/UFjjIlgwSbCZCDTb3mXuy7QMmXWF+cU7FZgln+8IrJMRFaIyL1Bxl4uxwvs/qAxxkSyU5ltVv3el3TdsLQyZdV/FMgBJvqta6mqWSLSGPhARHar6tv+lURkDDDGt5yUlER6enoJ4ZXtWF4Bhfm5p7SPSJCdnR31bQDWDj7WDg5rB0e4t0OwiTATaOm3nAxklaNMcduW+BZE5G6gL3Cxqv6QMFU1y/13r4i8gXOf8SeJUFUnABN8yykpKZqWllaOj/ZTjy2bScN6dUhL6xv0PiJBeno6p9KOkcLawWHt4LB2cIR7OwR7aXQ50FxEUtzl0cD0cpSZDowSkRgRaYaT9D4BEJFRwEhgiKoe8+1MROqLSIL7vgYwFFgdZPwByyuwZwiNMSaSBZUIVbUAuAWYJiIZOJcwp4hIdxGZWVoZd9unOGeAm4B5wH2qetTd/USgPjDPfUTidXd9Z2CZiKzCSbIrgNeCib888gog3oZXM8aYiBX0PUJVnQ2kFFm9HLi0jDK+bWOBscWsjy2h/GLgrGDjDZb1GjXGmMhmpzplyCuwcUaNMSaSWSIsg90jNMaYyGaJsBSqSl6hPUdojDGRzBJhKY7nOwPc2KVRY4yJXJYIS3HMnYzQLo0aY0zkskRYimMnLBEaY0yks0RYCl8iTLBLo8YYE7EsEZbCLo0aY0zks0RYilzfGaGNLGOMMRHL/sKXIveE22vUzgiNMSZiWSIshXWWMcaYyGeJsBTWWcYYYyKfJcJS5FpnGWOMiXiWCEthl0aNMSbyWSIsxQ+J0C6NGmNMxLJEWArfc4Q26LYxxkSuoBOhiKSKyHoRyRCRySJy0iS/pZURkXHu+s0icpXf+hYissBdP09Emvltu85dv1VE/hZs7IHKtUujxhgT8YJKhCISA0wCrlbV9kAiMCLQMiIyCOgNdAZSgadEpLZb9XFgiqp2BN4GHnPr1APGAwOATsBAEUkNJv5A5Z4owCMQGyOVeRhjjDEhFOwZYQ8gS1XXucuTgGHlKDMMeFVV81V1N7AQGCQiAlwKvO6Wew0Y6r4fDMxR1T2qmu9uK3rMCnXsRAFxHnDCMsYYE4mCTYTJQKbf8i53XaBlStrWAMhW1VwAVc0G8kSkboDHrFDHThRi/WSMMSaynXRfrxzU731Jp0yllSlpmxYpV9K2Yo8pImOAMb7lpKQk0tPTSwivdF/vySNWNOj6kSQ7O9vaAWsHH2sHh7WDI9zbIdhEmAm09FtOBrLKUaa4bUuA/UCiiCSoaq6I1ARiVfWwiGQCXco4Jqo6AZjgW05JSdG0tLTyfLYfpKXBZ599RrD1I0l6erq1A9YOPtYODmsHR7i3Q7CXRpcDzUUkxV0eDUwvR5npwCgRiXF7hfYFPlFVBWbwY8ebUcAH7vtZOB1kmri9T0cWc8wKZ/cHjTEmsgWVCFW1ALgFmCYiGUAOMEVEuovIzNLKuNs+xTkD3ATMA+5T1aPu7h8ERorIZmA48JBb5zAwFljg1lugqnOCid8YY4zxCfoeoarOBlKKrF6O0+uztDK+bWNxElvR9ZlAvxLqTAWmBhmyMcYYcxIbWcYYY0xUs0RojDEmqlkiNMYYE9UsERpjjIlqlgiNMcZENUuExhhjopo4z7BHLhE5QjEj0JRDfeBgBYUTzqwdHNYODmsHh7WDw78dklW1TiiDKa+IT4SnSkTWq2qxz0JGE2sHh7WDw9rBYe3gCPd2sEujxhhjopolQmOMMVHNEmHZJpRdJCpYOzisHRzWDg5rB0dYt4PdIzTGGBPV7IzQGGNMVLNEWAIRSRWR9SKSISKT3TkQo4KI7BCRdSKy0n2luOvHue2xWUSuCnWcFU1EnhORLBHJL7K+2M8tIi1EZIG7fp47t2bYK64dRGSgiBz1+05M89sWqe3QQkTSRWSDiKwVkUf8tkXNd6Kkdoio74Sq2qvIC4gBtgFnuMvvADeFOq4q/Pw7cJ4F8l83CJiPM3VXcyATqB3qWCv4c/cFTgPyA/ncwFvAre7724HXQv0ZKrEdBgKflVA+UtuhKdDdfR+HM3fq0Gj7TpTSDhHznbAzwuL1ALJUdZ27PAkYFsJ4qoNhwKuqmq+qu4GFOH8QIoaqLlTVb4usLvZzi4jgzL35ulvuNZw/DmGvhHYoVoS3wx5VXe6+zwNWA62Isu9EKe1QrHBsB0uExUvG+ZXns8tdF03+JyKrROQR97JwtLZJSZ+7AZCtqrkAqpoN5IlI3aoPscqc614Cmy8iF7vroqIdRKQBcAXwGVH8nSjSDhAh34moue8VBP/utBKyKEKjr6pmiUht4A3gPnd9tLZJSZ+7aJfrSG6TL4FWqnpERLoBM0WkD5BNhLeDiMQD04AnVXWDc8ITfd+JYtphNxHynbAzwuJlAi39lpM5tfFKw4qqZrn/HgVeBnoTvW1S0ufeDySKSAKAiNQEYlX1cNWHWPlU9YiqHnHfrwQWAd2I8HYQkRjgTWC5qj7lro6670Rx7RBJ3wlLhMVbDjT39ZYERgPTQxhPlRGRWiJSx33vBa7EuScwHRglIjFuD7C+wCehi7TKFPu51ekFMAMY4ZYbBXwQohgrnYg0de/9ICLJQC9gfRS0w0vAEWCs37po/E6c1A6R9J2wB+pLICIXAM/j9JKaj9MDKr/0WuFPRNri/Ef34PSe/Ry4S1WPicg4nI4CCjykqu+GLtKKJyL/Ai7D6Qm4G5ihqr8q6XOLSAuc3nGnAd8Aw93OE2GtuHYA1gC/Bk64xcap6ltu+Uhth/NxOsKsBQrc1ZNV9dlo+k6U1A5AIRHynbBEaIwxJqrZpVFjjDFRzRKhMcaYqGaJ0BhjTFSzRGiMMSaqWSI0xhgT1SwRGlMKEannN7r+LhHZ77ecGsK4/ioVNAOIiHhEZKGI1KuI/RkTbuzxCWMCJCK/wBl+7uYQx1EH5/nOLlpB/4FF5FfAaar6l4rYnzHhxM4IjSknEakhIi+KyFIRWSMiv3HXtxaRbSIyQUS+EpHZItJNRD5119/jt49896xutYh8KSJnuevPF5EV7hnnWhHpVUwIVwGzfElQRF4VkRdE5DMR2Ski14nIw24My0SkiVvuT27Zz0Rkq4j8zW+f7+GMAGJM1LFEaEz5/R/wlar2xJmy6ya/4fha48y9djZwCGd0oqFuud+7AxeDM2rPblXtAvwBeMVdPxa4W1W74Yzb6JsKzF8/nGEA/TXHmRZrCM60YRluDHOAX/mV6+KW6QKMdofGQlX3AYhI83K0gzERwRKhMeV3KXCniKwEvgDqA53cbbtVdan7fiWwQFWPqep+YB/OJKc+UwBU9UOgrYjUwhnO7x8ici/QTlW/L+b4zYC9Rdb9V1ULcYZCSwD+4xdDG79yM9x4soENOInb5xt338ZEFUuExpSfADeoajf31VZVfYnnuF+5wmKWS536TFX/gTNYcT7wXxG5tphix4D4IuuOu/XV/cd33KLH9I+noMi2Gu6+jYkqlgiNKb+PgLvcqWkQkfbu3I3lNcKtfzmwTVWzRaSDqm5S1WdxZvjuXky9dUCHIGMvloh4cKYTyqjI/RoTDiwRGlN+jwDfA6tEZA0wkZPP0MpSACSJyFLgLzhTfQHcLSLrROQr4ELg2WLqfuBuq0i9gCW+WcWNiSb2+IQxISAi+apa6mXSMurPpwKnthGRl4GpqppeEfszJpzYGaEx4ekOoFVF7Mi9LLrckqCJVnZGaIwxJqrZGaExxpioZonQGGNMVLNEaIwxJqpZIjTGGBPVLBEaY4yJav8PMywrL/6f9yoAAAAASUVORK5CYII="}}},{"metadata":{"trusted":false},"cell_type":"code","source":"C01 = \nV1 =\nV2 = \nk1 = \nk2 = \n\nt =\nC2 =\n\n","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"### Exemple d'utilisation : circuit RLC\nEn physique, vous étudierez le comportement temporel d'un circuit électrique constitué d'un condensateur, d'une résistance et d'une bobine placés en série. Le tracé de la tension aux bornes du condensateur en fonction du temps est donné ci-dessous. Il s'agit d'un relevé expérimental d'un TP que vous ferez très probablement.\n![tension.png](attachment:tension.png)\n\nLes caractéristiques du circuit (en USI) sont :\n- résistance électrique de la résistance : $R=400 ~\\Omega$\n- capacité du condensateur : $C=105 \\times 10^{-9}$ F\n- inductance de la bobine : $L=0,9$ H.\n\nLa tension initiale est $U_0=9,8$ V.\n\nL'évolution temporelle de ce circuit peut être modélisée par une équation différentielle de degré 2 dont la solution est donnée ci-dessous.\n\nAvec : $z=\\frac R 2 \\sqrt{\\frac C L} $ le facteur d'amortissement, $\\omega_0=\\frac 1 {\\sqrt{LC}}$ la pulsation propre\n\net aussi $\\omega_a = \\omega_0 \\sqrt {1-z^2}$ et $\\phi = \\arctan \\frac{\\sqrt{1-z^2}} z$ \n\n$$u(t) = U_0 \\frac 1 {\\sqrt {1-z^2}} e^{-\\omega_0 z t} \\sin \\left(\\omega_a t + \\phi \\right)$$\n\n**A faire :**\n- définir les constantes et commenter (caractère `#` en indiquant l'unité et/ou la grandeur physique)\n- définir les variables intermédiaires associées à $z$, $\\omega_0$, $\\omega_a$ et $\\phi$. Ne pas utiliser de lettres grecques, $\\omega$ peut s'écrire `omega`. \n- calculer la tension aux instants $t=0,005$ s et $t=0,0075$ s. Les résultats de ce modèle correspondent-ils aux résultats expérimentaux ?\n\n*Remarques : dans un prochain TP, nous tracerons les courbes.* Ne pas oublier les espaces autour des affectations et des opérateurs principaux.\n","attachments":{"tension.png":{"image/png":"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"}}},{"metadata":{"trusted":false},"cell_type":"code","source":"R = \n","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"### NSI et amateurs\n\n* Définir une fonction retournant $C_2(t)$ telle que définie précédemment.\n* l'utiliser pour créer 2 listes $t$ et $c2$ permettant de tracer la courbe\n* tracer la courbe avec le code donné"},{"metadata":{"trusted":false},"cell_type":"code","source":"","execution_count":null,"outputs":[]},{"metadata":{"trusted":false},"cell_type":"code","source":"import matplotlib.pyplot as plt\nplt.plot(t, c2)\nplt.show()","execution_count":null,"outputs":[]}],"metadata":{"kernelspec":{"display_name":"Python 3 (ipykernel)","language":"python","name":"python3"}},"nbformat":4,"nbformat_minor":2}