[(f)-4.84623]TJ 3.84 0 Td 2023.75 3336.94 l 2199.11 2645.32 l 1602.93 3132.81 l 2112.64 2628.45 l 2240.32 3290.73 l 2181.32 3417.62 l [(t)3.35237(e)-1.33213(l)0.673414(l)0.673414(i)0.673414(t)3.35237(e)-290.412(g)-6.01368(é)-1.33213(o)-6.01368(s)-3.1377(t)3.35237(a)-6.01368(t)3.35237(i)0.673414(o)-6.01368(n)1.34683(n)1.34683(a)-6.01368(i)0.673414(r)-5.91369(e)-1.33213]TJ 2206.65 3376.87 l 2060.19 3334.21 l q 2554.3 3091.04 l 1695.46 3874.64 l 2062.82 2861.68 l 2126.52 3555.03 l /R46 9.96264 Tf 1953.91 3133.44 l ID /W 1 ET 2177.68 3257.1 l 8.33333 0 0 8.33333 0 0 cm BT 1532.07 3603.84 l 2010.62 3564.19 l 8.33333 0 0 8.33333 0 0 cm BT [(c)-8.40193]TJ S 2137.78 3346.15 l 1678.35 3846.1 l /R50 6.97385 Tf 2308.24 3163.46 l 2319.56 3134.92 l 1786.93 2703.47 l 2200.86 2645.8 l 1916.37 2644.36 l 2174.05 3262.99 l 2278.43 3457.11 l 2184.15 3781.71 l /R54 9.96264 Tf 1451.33 2955.92 l 2172.8 3264.85 l ET 2346.47 3196.5 l 1950.93 3136.17 l 1484.1 3662.57 l 1977.73 3551.1 l /R50 6.97385 Tf 1 J S 1871.68 3377.27 l 2179.69 3508.63 l 2117.4 3313.98 l 4.8 33.24 Td 1652.29 3002.77 l 2151.95 3360.51 l 1 0 0 1 398.16 674.04 Tm 2199.27 3281.72 l 1723.23 3219.08 l 1847.11 3386.91 l 2027.34 3567.83 l )-5.85194(1)-3.30091]TJ 1827.4 2957.95 l 1787.64 3037.5 l -180.72 -22.44 Td 1930.23 3163.08 l 2041.73 2861.9 l 2314.62 3519.11 l 2.6605 w 1964.52 2633.35 l 2069.27 3333.23 l 1980.95 4037.26 l 2263.07 3228.79 l [(&)-1.90592]TJ 2173.57 3263.71 l [( )-2.77264]TJ 2105.21 3343.14 l 2052.58 3097.84 l 11.28 0 Td 1474.12 2991.31 l 2165.51 4031.11 l 8.33333 0 0 8.33333 0 0 cm BT [(d)1.34683(o)-6.01368(n)1.34683(c)-1.33213]TJ 2185.07 2641.46 l Q 4.68 1.44 Td [(n)-2.24962]TJ BI q 4 0 0 -220 1748.9 3769.9 cm 2148.78 3319.25 l 2185.83 3240.08 l 2492.28 3146.81 l 1950.08 2636.18 l 2191.85 3381.62 l /H 1 16.2 6.84 Td )-300.452(C)-0.65577(e)-1.33213(t)3.35237(t)3.35237(e)-1.33213]TJ [(m)2.02392(a)-6.01515(g)-6.01515(n)1.3483(é)-1.33286(t)3.35237(i)0.671944(q)-2.33195(u)1.3483(e)-326.549(e)-1.3336(s)-3.1377(t)-321.863(à)-343.275()1.3483(u)1.3483(x)-327.547(c)-1.3336(o)-6.01515(n)1.3483(s)-3.1377(e)-1.3336(r)-5.91517(v)57.893(a)-6.01515(t)3.35237(i)0.671944(f)-320.86(d)1.3483(o)-6.01368(n)1.34683(c)-1.33213]TJ 8.33333 0 0 8.33333 0 0 cm BT /R48 6.97385 Tf endobj 1909.39 4021.66 l [(d)0.929253]TJ 1685.65 2808.78 l 2105.45 3563.02 l /R56 6.97385 Tf 2464.33 2968.56 l 2190.13 3185.51 l 2569.88 3075.04 l 1920.02 3213.85 l 1815.64 3694.43 l [(=)-5.92546]TJ 2175.45 3260.8 l 2038.34 3335.89 l 255.84 0 Td 2081.94 3336.75 l 2152.57 2875.2 l /IM true Q )2.92107(f)2.92107(r)2.92107]TJ 1945.66 2879.6 l 2015.76 2863.91 l 2093.75 3337.73 l 1654.58 3013.36 l ID )0.264661]TJ <> 1 0 0 1 54.96 674.28 Tm 2074.88 3098.82 l 2175.31 2882.77 l 1786.34 3110.36 l 2340.3 3421.87 l ET endobj )0.671944(e)-507.223(I)-0.330826(d)1.3483(e)-1.33286(n)25.4383(t)3.3531(i)0.671944()1.3483(e)-1.3336(r)-331.13(l)0.671944(')0.671944(é)-1.3336(c)-1.3336(a)-6.01515(r)-5.91517(t)3.35237(-)-4.00961(t)27.4424(y)-2.33195(p)-22.7417(e)-326.549(g)-6.01515(r)-5.91517(â)-6.01515(c)-1.3336(e)-314.504(a)-6.01515(u)-323.867(f)4.35514(o)-6.01515(r)-5.91517(m)26.1132(u)1.34683(l)0.673414(a)-6.01368(i)0.673414(r)-5.91369(e)-314.502(p)1.34683(u)1.34683(i)0.673414(s)-3.1377(,)]TJ 2456.03 3174.67 l Montrer que cette valeur de l'énergie est liée au confinement spatial de /BPC 1 II.B + Oscillateur harmonique quantique en équilibre thermique Nous allons préciser les propriétés physiques d'un unique oscillateur harmonique quantique a une dimension en équilibre thermodynamique avec un thermostat a la température T. Comme indiqué dans la partie précédente, la résolution de l'équation de Schrôdinger pour un tel oscillateur de pulsation w conduit a des états stationnaires d'énergie En : E0 + nñw avec n E N. On admet qu'à l'équilibre avec le thermostat, cet oscillateur ne se trouve pas dans un état stationnaire mais dans un mélange statistique des états stationnaires d'énergie En affectés des poids respectivement proportionnels au En facteur de Boltzmann e kBT. 2464.97 3727.41 l Q 17.64 0 Td 2042.96 3806.16 l [(m)2.02392(o)-6.01515(u)1.3483(v)21.7588(e)-1.33286(m)2.02465(e)-1.3336(n)25.4383(t)-333.908(d)1.3483(')0.671944(u)1.3483(n)-335.912(é)-1.3336(l)0.671944(e)-1.3336(c)-1.3336(t)3.35237(r)-5.91517(o)-6.01515(n)-335.912(d)1.3483(a)-6.01515(n)1.3483(s)-340.398(u)1.3483(n)-335.912(c)22.7564(h)1.34683(a)-6.01368(m)2.02318(p)-335.913(m)2.02318(a)-6.01368(g)-6.01368(n)1.34683(é)-1.33213(t)3.35237(i)0.673414(q)-2.33195(u)1.34683(e)-326.547(u)1.34683(n)1.34683(i)0.673414(f)4.35514(o)-6.01368(r)-5.91369(m)2.02318(e)-338.592(e)]TJ /R21 9.96264 Tf 4.8 TL 5.76 -1.44 Td 2152.59 3792.8 l 2245.88 3245.86 l [(\))2.56133]TJ /R27 9.96264 Tf 1534.55 3066.89 l [(. 2462.82 2913.38 l Centrale 2016 psi math 1 corrigé prof en ligne 03/06/2020 03/14/2020 bofs Reunion spetembre 2016 math corrigé. 1620.67 3147.58 l 1792.76 3019.3 l 2458.94 2891 l [( )-5.92546]TJ 2183.55 3309.81 l 1 0 0 1 409.56 674.04 Tm 1660.9 3805.38 l 2246.33 3379.55 l 1693.77 3872.08 l 1409.89 2872.34 l 1889.5 3297.2 l 2205.41 3771.96 l 2233.43 3374.71 l q q 1175 0 0 -4 1372.9 2087.9 cm 1850.19 3733.73 l <> -295.08 -12 Td q /BPC 1 q 150 0 0 -4 2040.9 2702.9 cm 2281.04 3207.55 l 2105.04 3339.55 l 1861.87 2924.5 l 2063.77 3334.54 l 2012.61 3326.48 l 1667.05 3821.91 l 2317.32 3526.39 l 2119.22 3558.2 l 2022.29 3328.91 l [(=)-5.92546]TJ 0 J 1647.38 3168.34 l 1887.57 3761.35 l q /R21 9.96264 Tf 1453.85 2960.13 l 2107.13 4040.11 l 1948.43 3529.43 l 2018.33 3329.14 l Corrig DTL_01. 2014.14 3102.88 l [(e)-1.33286(t)-370.042(à)-355.32(l)0.671944(a)-367.365(p)1.3483(h)25.4383(y)-2.33122(s)-3.1377(i)0.671944(q)-2.33195(u)1.3483(e)-350.639(q)-2.33195(u)1.3483(a)-6.01515(n)25.4383(t)3.35237(i)0.671944(q)-2.33195(u)1.3483(e)-1.3336(. 1833.58 3717.17 l 2357.57 3482.39 l 2015.11 3329.78 l 1649.99 3760.35 l [(i)2.56133]TJ 1923.16 3437.13 l [(B)-2.65543]TJ 1974.72 3549.43 l 1913.17 3373.27 l 2204.31 2646.88 l 2464.16 2971.04 l 2294.91 3399.84 l 2010.43 2627.41 l 2237.96 3415.11 l 2008.58 2627.57 l 1421.48 2899.34 l /R21 9.96264 Tf 2073.69 2625.66 l 1659.11 2868.21 l 2015.33 3102.59 l 1 0 0 1 67.44 643.44 Tm 2423.65 3569.19 l 2127.66 3350.54 l 1742.51 2738.83 l 2023.78 3331.06 l 2190.63 2889.08 l O 0 2057.3 3334.03 l [( )777(! 1851.81 2932.86 l 2087.86 3337.76 l [(l)0.673414(a)-427.589(v)-2.33195(i)0.673414(t)3.35237(e)-1.33213(s)-3.1377(s)-3.1377(e)-422.907(d)1.34683(e)-1.33213]TJ 5.64 3.6 Td 2277.73 3717.94 l 1913.88 3775.57 l 1926.44 3171.14 l 2311.61 3511.89 l endobj 2061.27 3097.88 l 1697.23 3877.12 l [(1)2.32733]TJ ET 2499.81 3140.63 l /Metadata 127 0 R [(B)-2.65543(\()2.55986(R)1.25567]TJ 2057.48 3334.02 l 1920.07 3214.33 l 2026.73 3100.27 l [(! 6.96 0 Td 5.04 0 Td 1748.48 3434.35 l Q 2380.45 3160.6 l 7.2 0 Td >> 2138.11 3354.58 l 2087.6 3804.95 l 2093.68 3101.9 l 2456.97 3494.01 l /R21 9.96264 Tf [(y)-3.84493]TJ 1692.51 2797.87 l 2160.1 3532.76 l 1925.98 3495.71 l 2119.25 3312.95 l 4.8 -1.44 Td 2300.24 3688.45 l 1939.28 3149.03 l 1880.75 3258.52 l 2073.26 3332.86 l 2116.92 3344.18 l 1613.14 3141.42 l 2257.04 3432.93 l 2156.52 3383.46 l EI Q 2465.07 2943.43 l q 4 0 0 -247 3048.9 4633.9 cm )0.673414]TJ [(v)2.20036]TJ /R10 8.96638 Tf 1579.95 3112.4 l 2144.8 3347.79 l 2410.16 3120.95 l 1940.03 2881.6 l 9.84 0 Td 1574.57 3560.63 l 2057.86 3806.4 l 2157.39 3384.35 l 1484.89 3661.54 l 1674.22 3803.52 m 2033.04 3805.65 l /W 1 1977.28 2631.32 l 2252.5 3266.93 l 1907.61 2895.55 l 1650.4 2992.13 l 2141.98 2632.51 l 1817.5 3479.77 l 1788.81 3413.2 l 1935.22 3311.79 l BI 2117.66 3341.88 l 1420.46 2897.12 l 2192.22 3200.47 l 2411.56 3118.79 l 2064.37 3098.02 l 1543.83 3591.16 l 2038.74 3335.14 l 2319.48 3220.29 l 2090.46 3341.77 l [(i)2.56133]TJ 2081.14 4041.96 l q 2225.02 3263.5 l 1749.73 3935.72 l /H 1 2310.01 3508.32 l 1439.7 3732.45 l 2323.98 3118.61 l /R56 6.97385 Tf 1647.51 2966.41 l 1 j 1840.11 2943.92 l 2090.39 3338.23 l 115 0 obj 2371.88 3170.42 l 2008.29 3104.45 l 1652.55 2893.51 l 2033.04 2862.36 l 2110.46 3342.56 l /R19 9.96264 Tf Q [(s)-3.4847]TJ 1863.16 2923.47 l 1924.38 3176.65 l 1693.79 3872.08 l 0 0 1 rg <> 1931.56 3507.33 l 1394.03 3841.58 l [(\))-226.294(+)-5.92546]TJ 3.84 0 Td 15.48 0 Td 7.68 -3.72 Td 9.96 0 Td 1925.84 3428.83 l 2068.09 3098.21 l /H 1 1936.64 2882.77 l /H 1 2215.04 3368.22 l 2160.94 3364.73 l 1922.04 3226.43 l 2058.66 3334.11 l 2063.82 3334.35 l [(I)-24.4205(I)-0.330458(.)0.671944(A)3.02669(.)0.671944(4)-6.01515(. 2070.64 3336.05 l /R52 6.97385 Tf 2254.75 4002.82 l 2383.95 3221.95 l 2073.11 3336.6 l /R19 9.96264 Tf 2086.21 3336.66 l 2079.18 3568.66 l 2054.42 3333.95 l 1488.57 3656.55 l /R19 9.96264 Tf 2053.21 3570.17 l 1 0 0 1 97.68 233.16 Tm [(1)-6.01368(7)-6.01368]TJ [( )740.865(! <> )0.264661]TJ /IM true 2464.68 2933.4 l [(1)-5.89017(0)-5.89017]TJ [(1)-5.89017(0)-5.89017]TJ /R19 9.96264 Tf [(e)-1.33213(,)-264.317(i)0.673414(l)-264.317(v)57.893(a)-271.004(a)-6.01368(u)1.34683(s)-3.1377(s)-3.1377(i)-252.272(s)-3.1377(e)-266.322(p)1.34683(r)-5.91369(o)-30.1037(d)1.34683(u)1.34683(i)0.673414(r)-5.91369(e)-1.33213]TJ 1390.85 2814.88 l 2083.39 3330.3 l 2189.39 3228.77 l /R54 9.96264 Tf /R48 6.97385 Tf 2479.97 3156.63 l Q [()-5.2491]TJ 2075.21 3337.11 l [(p)-22.7417(o)-6.01515(u)1.3483(r)-331.13(u)1.3483(n)1.3483(e)-338.594(é)-1.3336(n)1.3483(e)-1.3336(r)-5.91517(g)-6.01515(i)0.671944(e)-326.549(c)-1.3336(i)0.671944(n)1.34683(é)-1.33213(t)3.35237(i)0.673414(q)-2.33195(u)1.34683(e)-326.547(d)1.34683(e)-1.33213]TJ ET 2012.08 2864.36 l 2056.22 3334 l 2021.56 4041.47 l 1955.5 4032.88 l 2138.11 3367.42 l 1957.23 3537.4 l EI Q /R64 9.96264 Tf [(X)-1.39976]TJ 2386.41 3912.24 l 0 j 2051.96 3570.15 l 1799.85 3666.49 l 1646.96 3714.5 l 2128.32 3307.42 l 2128.63 3554.01 l 2189.09 3181.41 l 1911.79 3774.51 l 8.33333 0 0 8.33333 0 0 cm BT [(p)1.3483(a)-6.01515(r)-5.91443(t)3.3531(i)0.671944(e)-290.413(r)-5.91443(e)-1.3336(p)-22.7417(o)-6.01515(s)-3.1377(e)-278.369(e)-1.3336(s)-3.1377(s)-3.1377(e)-1.3336(n)25.4383(t)3.35237(i)0.671944(e)-1.3336(l)0.671944(l)0.671944(e)-1.3336(m)2.02465(e)-1.3336(n)25.4383(t)-285.728(s)-3.1377(u)1.3483(r)-294.995(d)1.3483(e)-1.3336(s)-292.218(n)1.34683(o)-6.01368(t)3.35237(i)0.673414(o)-6.01368(n)1.34683(s)-292.218(d)1.34683(e)-302.457(m)2.02318(é)-1.33213(c)-1.33213(a)-6.01368(n)1.34683(i)0.673414(q)-2.33195(u)1.34683(e)]TJ 2235.97 3375.65 l 2236.87 3253.83 l 2401.46 3456.65 l 2140.2 4035.78 l 1996.32 3108.39 l 2289.75 3703.55 l 2225.95 3405.23 l 2160.94 3357.88 l 2173.88 3362.76 l [(=)-5.92546]TJ -202.32 -19.68 Td 2181.65 3505.13 l [(v)2.19962]TJ 2125.49 3358.78 l 15.36 0 Td [(R)-299.87(=)-295.005(R)1.25493]TJ 1432.2 3746.61 l /R32 8.96638 Tf 2309.7 3160.35 l 1415.57 3782.06 l 2159.54 3281.39 l 2030.37 3099.68 l 1920.23 3215.77 l 1697.2 2790.86 l 2522.93 3120.68 l 2264.24 3227.52 l 2344.6 3198.27 l 2327.63 3056.91 l 1531.23 3063.25 l 0 J 2174.1 3150.86 l 2311.6 3511.88 l <> 1938.34 3150.25 l 2244.56 3378.87 l <> 2001.41 3561.4 l 2122.77 3325.1 l 1969.88 3370.52 l 2328.12 3605.82 l 2229.73 3408.25 l 2027.75 3331.59 l 2189.62 3227.93 l /IM true 2451.66 3633.64 l 2241.64 4008.2 l [(a)-391.454(é)-1.33213(t)3.35237(é)-386.772(r)-5.91369(e)-1.33213(l)0.673414(u)-396.138(p)1.34683(a)-6.01368(r)-5.91369]TJ BI >> 1467.12 2981.02 l 2252.28 3363.22 m 1562.1 3095.4 l [(w)2.92107(w)2.92107(w)2.92107(.)2.92107(D)2.92107(o)2.92107(c)2.92107(-)2.92107(S)2.92107(o)2.92107(l)2.92107(u)2.92107(s)2.92107(. /R46 9.96264 Tf 2161.91 4031.82 l 2224.86 2653.56 l Sujets 2016 filière MP. 2562.11 3083.11 l 2588.21 3613.1 l 2541 3103.99 l 1940.3 2881.61 m 2068.72 3334.72 l 2158.43 3385.43 l 2666.92 2945.22 l 2274.54 3215.72 l 8.33333 0 0 8.33333 0 0 cm BT 2321.54 3966.84 l 2154.25 3381.2 l 3.32083 w EI Q 2131.04 2630.74 l 2076.73 3568.97 l 2129.37 3351.17 l [(A)20.448(n)-4.03313(n)-4.03166(a)5.09325(l)2.54662(e)2.1761(s)-350.049(d)5.09325(e)2.1761(s)-362.094(C)4.72272(o)5.09325(n)-4.03166(c)50.3561(o)5.09325(u)-5.49024(rs)-0.74399]TJ 2228.99 3407.65 l 1755.26 2727.5 l 2008.42 3340.95 l )0.673414(g)-379.409(e)-1.33213(t)-394.133(f)4.35514(a)-6.01368(i)0.673414(r)-5.91369(e)-374.727(u)1.34683(n)-396.138(d)1.34683(é)-1.33213(v)21.758(e)-1.33213(l)0.673414(o)-6.01368(p)1.34683(-)-4.01108]TJ 1389.31 2809.04 l 1951.51 3135.61 l 1 0 0 1 67.2 535.2 Tm 2172.38 3402.54 l 1842.36 3726.39 l /BPC 1 2184.57 3243.26 l /W 1 2016--02--08 11:45:03 Page 8/8 GQ BY--NC-SA 2260.87 3436.86 l 1500.73 3027.25 l 2147.39 3348.41 l /R56 6.97385 Tf 1882.04 4012.64 l 2301.33 3686.76 l /R19 9.96264 Tf 2447.5 3621.21 l 257.52 0 Td 2511.89 3130.39 l [(E)-6.56358]TJ q 335 0 0 -4 436.9 4218.9 cm 2103.42 3347 l 1458.43 3700.51 l 2595.52 3046.43 l 2180.64 3416.29 l 2056 3334 l 1921.21 3222.42 l [(I)2.38011(.)-5.85194(B)-1.20421(.)-5.85194(3)-3.30091(. 1795.97 3657.44 l 19 0 obj [(B)-2.65469(\()2.55986(R)1.25567]TJ 2117.67 3341.88 l <>stream 2062.46 3334.26 l endobj [(I)-24.4205(I)-0.330458(.)0.671944(A)3.02669(.)0.671944(4)-6.01515(. 2085.04 3338.04 l [(B)-2.65543(\()2.55986(R)1.25567]TJ [(t)-0.34994]TJ 2096.17 3343.93 l [(g)1.46824]TJ /IM true 2183.31 3421.83 l 1899.93 2899.55 l ET 2100.79 3103.63 l 1882.05 2655.39 l 2236.75 3753.41 l /IM true 2164.06 3391.7 l q 1948 0 0 -4 1081.9 1343.9 cm 1664.74 3180.96 l 2005.54 3091.59 m O 0 7.8 7.32 Td 2266.58 3224.95 l 2460.94 2996.04 l 2108.89 3561.96 l 2071.12 3336.15 l 2307.5 3165 l 2060.63 2625.43 l 1783.88 3091.8 l 2403.44 3457.88 l 1772.64 2713.68 l 1463.08 3693.2 l A 1982.99 2869.24 l 8.33333 0 0 8.33333 0 0 cm BT /R21 9.96264 Tf 2079.14 3338.15 l 2411.35 3548.89 l 7.8 0 Td 1773.14 3203.57 l ET 2279.97 3459.07 l 2328.71 3594.38 l [(2)1.16367]TJ 2459.45 2893.48 l 2228.27 4013.21 l /IM true 4.8 5.04 Td 1472.71 2989.27 l 2033.23 3332.26 l 2036.75 2862.16 l Le potentiel effectif bidimensionnel dans lequel évolue l'électron doit 2290.73 3473.95 l 2167.36 3353.57 l 1755.27 3430.61 l 2456.02 3648.97 l [(\()2.55986]TJ 1802.4 3507.43 l 2131.61 3344.77 l 2118.31 3347.25 l [(e)-1.66442]TJ /R19 9.96264 Tf /IM true 1926.73 3170.47 l /R29 8.96638 Tf 2174.18 2882.38 l 1944.79 3525.58 l 2082.84 3099.87 l 25 0 obj 2157.93 3363.29 l 2167.56 3525.19 l 2125.62 3343.49 l /R42 11.9552 Tf 4.8 -1.44 Td 2170.3 3522.04 l 1927.62 3168.44 l 2063.72 3334.77 l 1397.3 3831.09 l /R21 9.96264 Tf Justifier quantitativement ce fait. 32.04 -14.88 Td /R46 9.96264 Tf /W 1 1438.54 2933.42 l /R19 9.96264 Tf ET 1876.96 2657.15 l 1470.59 3681.83 l 2516.54 3126.36 l -77.64 -22.92 Td 1942.04 3522.43 l q 1 j <>endobj 1895.41 3766 l 2003.04 2628.05 l 2056 3334 m 2056 3334 m 2143.16 3296.64 l 1957.89 3317.92 l 2055.35 3334.01 l -309.12 -12 Td [(v)2.19962]TJ 1652.72 3004.9 l [(2)-6.01368]TJ 0 j 2489.45 3149.1 l 7.2 -3.6 Td 2306.35 3437.31 l 2048.37 3333.67 l 1782.18 3416.51 l 2008.87 3104.28 l 1787.86 3117.9 m 1925.38 3173.89 l 2057.52 3334.07 l 1487.83 3657.55 l Ce corrigé est proposé par Tom Morel (Professeur en CPGE) et Fabrice Maquère. [(I)2.37974(.)-5.85194(B)-1.20421(. 1945.83 2865.93 m 2210.57 3393.86 l -270.12 -12 Td 1788.07 3118.85 l 2.65989 w 2073.85 3335.2 l 1816.21 2972.76 l 1934.43 3155.94 l 2532.05 3555.6 l 2168.64 3360.74 l endobj 2201.26 3774.02 l 1394.37 3840.41 l q /R17 9.96264 Tf 2320.89 3643.61 l 1784.64 3054.52 l 1964.25 3125.28 l 2110.82 4039.78 l 1934.16 3511.64 l [(v)2.19962]TJ <>endobj 1396.21 2833.46 l /R50 6.97385 Tf 1402.68 3815 l /H 1 2208.52 3366.03 l 2391.96 3521.59 l 1814.5 2975.28 l (_)Tj [()-6.87278]TJ -255.84 -12 Td 2129.78 3344.37 l 2092.68 3342.59 l 1855.11 3737.98 l 2169.48 3398.5 l 1990.19 2867.84 l 1481.9 3665.6 l 1493.05 3650.6 l 1494.51 3648.68 l 1975.71 3550 l /R46 9.96264 Tf 2328.33 3579.06 l 1451.9 3711.1 l 9.48 0 Td [(v)2.19962]TJ T*[(M)-4.49923]TJ /R48 6.97385 Tf [(v)2.19962]TJ 1973.65 4036.07 l 2202.79 3388.57 l 1919.79 3210.75 l 2165.18 2879.2 l [(s)-3.1377(t)3.3531(a)-6.01515(t)3.3531(i)0.671944(s)-3.1377(t)3.3531(i)0.671944(q)-2.33195(u)1.3483(e)-326.549(v)-2.33195(u)1.3483(e)-1.3336(s)-340.398(e)-1.3336(n)-323.867(s)-3.1377(e)-1.3336(c)-1.3336(o)-6.01515(n)1.3483(d)1.3483(e)-326.549(a)-6.01515(n)1.3483(n)1.3483(é)-1.3336(e)-1.3336(. 2055.39 3806.43 l 2233.03 3755.89 l [(z)-4.75507]TJ 2451.14 3178.19 l 7.32 21.36 Td [(a)18.0763(v)21.758(e)-1.33213(c)-1.33213]TJ 2023.7 3100.8 l /Annots[84 0 R /IM true 1605.7 3135.18 l 2139.03 3346.43 l 1681.21 3851.37 l 2088.83 2863.15 l 1653.1 3172.57 l 2108.46 2865.54 l 2021.93 2863.26 l 8.33333 0 0 8.33333 0 0 cm BT 2448.96 3042.63 l 2440.61 3642.45 m 2040.81 3098.47 l 1977.21 3117.19 l 2447.26 3487.04 l /R50 6.97385 Tf [(0)1.16472]TJ 1443.9 2943.13 l 1471.3 3680.8 l /R46 9.96264 Tf [(x)-6.87067]TJ 1964.27 3542.73 l 1437.94 2932.32 l 2192.32 3465.14 l -2.64 -0.24 Td 1640.67 3163.28 l 1389.6 2810.2 l 1949.07 3789.56 l /BPC 1 /R48 6.97385 Tf endstream 2209.3 3366.29 l 2136.52 2631.61 l -0.12 -2.88 Td 2109.62 3340.37 l 2012.97 3564.83 l 1902.48 2648.5 l 2248.23 4005.57 l 2288.48 3396.96 l 2227.68 3261.4 l 2317 3525.47 l 2260.99 3734.43 l /H 1 2196.92 3384.78 l q 2004.42 3340 l 2260.53 3436.5 l ET -227.28 -11.88 Td [(I)-0.330458(.)0.671944(C)-0.657241(.)0.671944(6)-6.01515(. 2486.6 3151.38 l <> 2606.62 3033.05 l 2137.15 3346 l 1454.46 3706.87 l 2485.64 3152.14 l 2249.64 3425.66 l 2129 2869.26 l 2307.5 3502.99 l 5.04 1.44 Td 2265.77 3387.27 l 2059.47 3334.16 l [(Z)0.930723]TJ 2068.47 3334.7 l 2173.88 3362.76 l -293.76 -15.48 Td 1650.21 2906.26 l 2422.36 3865.68 l /H 1 4.44 1.44 Td 2107.16 3105.5 l 1806.26 3976.79 l 107.16 0 Td 1453.82 2960.11 l 1440.86 3730.3 l 2088.57 4041.57 l 1875.32 2657.85 l 2011.34 3338.82 l [(e)-1.33286(n)1.3483]TJ [(c)-8.40193]TJ 2538.34 3106.52 l EI Q 250.8 0 Td /R50 6.97385 Tf -1.56 0 Td 2231.64 3409.79 l 2184.56 3243.26 l 1789.38 3030.46 l 2121.17 3557.41 l 1901.47 3769.29 l 1405.63 2861.07 l 2049.36 3333.73 l /R21 9.96264 Tf 2005.47 3328.19 l /R46 9.96264 Tf 1818.91 3268.98 l EI Q 10.44 2.76 Td 1917.74 3306.55 l 2348.95 3426.42 l 264.12 0 Td 2221.47 2652.39 l 1394.04 2826.45 l 10.08 3.6 Td 2.65743 w 7.2 -12 Td 2601.95 3038.79 l 2325.16 3041.27 l 2301.47 3234.37 l /R46 9.96264 Tf 2267.39 3410.17 l 1431.07 3748.81 l 1521.36 3052.1 l Signature : 2191.7 3216.36 l 2066.97 3334.58 l <> /R50 6.97385 Tf 2134.79 3550.82 l 0 0 0 1 k 1672.68 2833.23 l 1828.75 2678.63 l 2096.66 3102.59 l 2118.17 2867.13 l /R56 6.97385 Tf [(0)1.16367]TJ 2139.9 3355.3 l q q )-4.34043]TJ 2449.89 3628.11 l 2605.85 3034 l /R56 6.97385 Tf [(t)3.3531(i)0.671944(q)-2.33122(u)1.3483(e)-1.33286(. EI Q 2060.88 3334.27 l 2196.54 3283.46 l 1404.35 3810.41 l 2058.17 3570.18 l 8.33333 0 0 8.33333 0 0 cm BT 2630.78 3666.55 l 2106.21 3348.29 l 2191.49 3192.96 l 2083.88 2862.72 l 2476.14 3508.4 l 1986 3555.27 l 18.24 -1.44 Td 1653.46 2889.24 l 1558.58 3091.92 l 2465.07 3724.57 l 2382.02 3916.81 l Q 2172.59 3265.16 l /BPC 1 [(I)2.37974(.)-5.85194(B)-1.20421(. 2267.55 3388.01 l -196.44 -24.6 Td 2454.14 3642 l 2191.67 3473.73 l 2332.58 3959.23 l 2066.16 3334.67 l 2125.96 3349.92 l 2116.97 3801.07 l 2421.99 3469.77 l 1898.41 2900.37 l 1410.84 2874.65 l 2054.45 3097.81 l 2463.66 3747.46 l 1828.07 3710.87 l <> 2122.75 3342.89 l 1733.29 3920.29 l 2582.45 3061.38 l 2328.69 3080.34 l /IM true 3 0 obj 1815.17 3400.71 l 2405.76 3127.46 l ET /R46 9.96264 Tf 2210.21 3274.4 l 6.6 0 Td 1 0 0 1 212.28 184.56 Tm T*[(u)-6.16071]TJ /R46 9.96264 Tf 2046.21 3333.51 l 1858 2927.54 l 2063.03 3334.3 l 2063.91 3334.8 l 278.88 0 Td 2056.08 3334 l /R21 9.96264 Tf 8.88 7.32 Td 1920.32 3194.26 l 2398.56 3454.86 l 2003.52 2865.54 l 2143.23 2872.63 l 2428.21 3577.61 l 2007.96 3328.61 l T*[(@)-4.28456]TJ 1546.43 3079.55 l 1787.14 3114.59 l q /IM true 1622.57 3149.11 l /BPC 1 xœ]�AnÄ E÷œ‚ÜN£J›t“E«QÛ0‹!ˆ$‹¹ı`ÓTUÏÒÇşÂßİ8½M)î²»–Õ}á.CL¾à¶Å¡œq‰Ih�>ºıGqu7›E7¾Ûü}Ï(ë †¦?ì »O­ŸøI7“[=nÙ:,6-(¥Ì‚˜ü¿Vßsø3I h0UjÓPsO2Pj§ñJòÙF©ZÅpAà y_¬a”êorşIKQ¼3�tG)˜v¾g¤h1áï™òšÉ%+â…> 2676.37 3740.02 l 2110 3350.12 l 2122.27 3319.4 l /R52 6.97385 Tf 1982.21 3361.54 l 1955.55 3535.99 l 2192.12 3198.79 l [(x)-6.87067]TJ 2148.19 3542.41 l )-324.543(I)-0.330826(l)-336.588(v)-2.33195(i)0.671944(e)-1.3336(n)25.4383(t)3.35237]TJ 1964.61 3319.59 l 256.44 0 Td [(d)0.930723]TJ 1946.96 3527.89 l 2270.91 3255.58 l 1921.5 3224.09 m /R32 8.96638 Tf 1692.12 3869.49 l [(C)-0.657241(e)-398.818(c)-1.33286(o)-6.01515(r)-5.91443(r)-5.91443(i)0.671944(g)-6.01515(é)-362.684(e)-1.3336(s)-3.1377(t)-394.133(p)1.3483(r)-5.91517(o)-6.01515(p)-22.7417(o)-6.01515(s)-3.1377(é)-374.729(p)1.3483(a)-6.01515(r)-391.355(T)83.6578(o)-6.01515(m)-383.415(M)1.02188(o)-6.01515(r)-5.91517(e)-1.3336(l)-384.767(\()3.35237(P)5.86664(r)-5.91369(o)-6.01368(f)4.35514(e)-1.33213(s)-3.1377(s)-3.1377(e)-1.33213(u)1.34683(r)-379.309(e)-1.33213(n)-396.138(C)-0.65577(P)5.86664(G)1.60267(E)5.86664(\))-165.278(;)-408.857(i)0.673414(l)]TJ /R19 9.96264 Tf /R19 9.96264 Tf 127.08 4.68 Td [(w)2.92107(w)2.92107(w)2.92107(.)2.92107(D)2.92107(o)2.92107(c)2.92107(-)2.92107(S)2.92107(o)2.92107(l)2.92107(u)2.92107(s)2.92107(. EI Q 2079.71 3336.4 l 2095.07 3337.93 l /R19 9.96264 Tf -288.72 -11.88 Td 3.32083 w EI Q [(l)0.671944(e)-338.593(c)22.7571(h)1.3483(a)-6.01515(m)2.02392(p)-323.867(m)2.02392(a)-6.01515(g)-6.01515(n)1.3483(é)-1.3336(t)3.35237(i)0.671944(q)-2.33195(u)1.3483(e)-1.3336(. [(l)0.671944(a)-427.59(v)57.893(a)-6.01515(l)0.671944(e)-1.3336(u)1.3483(r)-415.445(d)1.3483(u)-432.272(c)22.7564(h)1.3483(a)-6.01368(m)2.02318(p)-420.228(m)2.02318(a)-6.01368(g)-6.01368(n)1.34683(é)-1.33213(t)3.35237(i)0.673414(q)-2.33195(u)1.34683(e)-422.907(t)3.35237(e)-1.33213(r)-5.91369(r)-5.91369(e)-1.33213(s)-3.1377(t)3.35237(r)-5.91369(e)-1.33213(,)0.673414]TJ ID 2077.86 3336.12 l ET /R21 9.96264 Tf 5.76 3.6 Td 9.96 -2.4 Td q 2056.66 3334.01 l 1937.79 2882.39 l [(w)2.92107(w)2.92107(w)2.92107(.)2.92107(D)2.92107(o)2.92107(c)2.92107(-)2.92107(S)2.92107(o)2.92107(l)2.92107(u)2.92107(s)2.92107(. 2072.75 3805.97 l 2259.49 3232.57 l 2189.71 3287.67 l 1919.33 3307.05 l 1767.43 3950.29 l 1523 3053.97 l 2357.63 3431.11 l /IM true /R9 gs /BPC 1 1684.18 3856.6 l 2221.5 4015.61 l 2060.88 3334.17 l 2119.39 3800.61 l /R44 9.96264 Tf q 2125.42 3346.46 l 2206.13 3365.24 l 2058.75 3334.07 l /BPC 1 ID 2239.47 3251.59 l 2130.19 2869.51 l 2056.97 3334.03 l 2581.63 3062.29 l 0 j 2120.61 3355.84 l q 0.12 0 0 0.12 0 0 cm 1943.23 3144.2 l 1986.52 3112.49 l 2430.07 3852.68 l 1793.11 3220.78 l /Subtype/Link>>endobj 2192.22 3210.51 l 2085.23 3339.99 l /R21 9.96264 Tf 1903.51 3770.38 l /R46 9.96264 Tf 2061.87 3334.29 l 54 0 obj 1922.43 3779.4 l 2375.35 3166.52 l /R19 9.96264 Tf 2056.9 2625.36 l 31.92 0 Td 2451.55 3803.97 l /R32 8.96638 Tf 7.8 6.84 Td 1935.7 3259.44 l 1981.82 3553.23 l 1958.26 3792.44 l 2147.08 3293.36 l 2042.05 3569.64 l 2259.78 3405.44 l /R56 6.97385 Tf Q 1967.97 3545.25 l 1646.94 2951.36 l 2189.8 3227.13 l ] /Count 4 [(q)-2.33122(u)1.3483(e)-1.33286(l)0.671944(q)-2.33122(u)1.3483(e)-1.3336(s)-364.488(e)82.9814(V)3.02595(,)-384.768(c)-1.3336(o)-6.01515(r)-5.91517(r)-5.91517(e)-1.3336(s)-3.1377(p)-22.7417(o)-6.01515(n)1.3483(d)-360.002(e)-1.3336()5.02708(e)-1.3336(c)-1.3336(t)3.35237(i)0.671944(v)21.758(e)-1.3336(m)2.02318(e)-1.33213(n)25.4368(t)-370.043(à)-379.409(l)0.673414(')0.673414(é)-1.33213(m)2.02318(i)0.673414(s)-3.1377(s)-3.1377(i)0.673414(o)-6.01368(n)-372.048(d)1.34683(')0.673414(u)1.34683(n)-384.093(p)1.34683(h)1.34683(o)]TJ 2091.03 3338.35 l 1655.15 3785.81 l 1830.34 3990.17 l ID 1418.46 2892.64 l /IM true 2321.43 3539.33 l 2571.54 3594.73 l 1956.38 3536.71 l 2537.43 3107.37 l 2049.47 2625.46 l 1933.68 3356.66 l /W 1 1387.81 2803.16 l 1 0 0 1 187.68 475.92 Tm 1419.43 2894.86 l 6.6 -1.44 Td 2431.63 3584.2 l 1841.73 3278.87 l 2060.9 3334.39 l 2399.79 3135.96 l 1825.22 3199.76 l 2092.54 3804.52 l 2039.66 3332.95 l 2049.48 3097.92 l 2165.49 2636.89 l 2170.83 2881.18 l endobj 2093.29 3337.66 l 2283.11 3204.78 l [(A)3.02632(i)0.671944(n)1.3483(s)-3.1377(i)0.671944]TJ q 3048 0 0 -4 530.9 5587.9 cm 2097.27 3565.27 l 2149.01 3291.66 l 2152.99 3380 l 2063.14 3570.05 l 1850.59 2933.92 l 0 J Enoncé / Corrigé CCP 2018. 1445.12 2945.27 l 1817.98 2970.25 l Q 2189.03 3437.83 l 1762.23 3946.25 l 2091.14 3337.35 l ID 2295.82 3186.13 l /R46 9.96264 Tf )-4.34043]TJ )-3.96991]TJ /BPC 1 2422.36 3101.06 l 1885.42 2654.2 l 2023.71 3567.2 l )0.264661]TJ 1943.91 3314.23 l 1943.41 2880.4 l /R21 9.96264 Tf 2433.23 3587.48 l /R21 9.96264 Tf [(e)-4.75507]TJ 2102.36 2864.66 l 2059.53 3334.11 l 2708.5 3812.69 l 2005.98 3562.85 l 2028.11 3805.28 l 2250.43 3399.86 l 2140.89 3795.99 l /R50 6.97385 Tf 2455 3792.86 l 2177.56 3410.68 l 1601.97 3131.99 l 1983.4 3323.88 l 273.72 0 Td 1651.62 2999.24 l 1955.5 4032.88 l /R27 9.96264 Tf 2114.59 3352.49 l 2131.38 2869.79 l 1909.85 3304.05 l 2107.25 3802.64 l 2191.37 3192.14 l 1978.23 2870.34 l endobj /R21 9.96264 Tf 2322.8 3123.53 l 1453.8 3707.92 l 1859.64 2664.12 l 2328.22 3090.38 l 2065.02 3334.98 l 1992.18 3110.04 l /R46 9.96264 Tf /IM true 2303.32 3403.69 l EI Q 2114.95 3326.64 l 1924 3490.2 l 2390.68 3907.58 l 2305.97 3168.08 l Q [(\))-274.475(=)-282.96(B)-2.65543(\()2.55986(R)1.25567]TJ BI 7.8 0 Td 2458.92 3172.56 l 1807.13 3680.65 l 2610.52 3028.2 l )0.671944]TJ 1771.66 3246.12 l 8.33333 0 0 8.33333 0 0 cm BT ()Tj 16.2 17.88 Td 1391.14 3852 l L'accès sera ouvert jusqu'au 1er août 2021. 1867.11 2920.44 l 2210.94 3366.84 l Vous trouverez dans cet article, les sujets de Mathématiques et de Sciences Physiques et Chimiques de la session 2016 . 8.33333 0 0 8.33333 0 0 cm BT 2216.78 3398.29 l 1968.42 3122.44 l 2149.99 3541.1 l 1790.97 3024.86 l 1824.16 2681.09 l [(1)-6.01368(7)-6.01368]TJ [(n)-11.3304]TJ 1649.74 2987.84 l 2028.55 3568.02 l 1878.05 3755.27 l 2017.11 3102.18 l /R46 9.96264 Tf 69 0 R 1688.84 2803.64 l 1563.86 3097.13 l 1537.92 3597.46 l )-348.633(L)-1.49607(e)-338.593(c)22.7564(h)1.3483(a)-6.01515(m)2.02465(p)-335.912(m)2.02465(a)-6.01515(g)-6.01515(n)1.3483(é)-1.3336(t)3.35237(i)0.671944(q)-2.33195(u)1.3483(e)-338.594(c)-1.3336(r)-5.91517(é)-1.3336(é)-326.549(p)1.3483(a)-6.01515(r)-343.175(l)0.671944(e)-338.592(d)1.34683(i)0.673414(p)-22.7432(ô)-6.01368(l)0.673414(e)-350.637(m)2.02318(a)-6.01368(g)-6.01368(n)1.34683(é)-1.33213(t)3.35237(i)0.673414(q)-2.33195(u)1.34683(e)-326.547(t)3.35237(e)-1.33213(r)-5.91369(r)-5.91369(e)-1.33213(s)-3.1377(t)3.35237(r)]TJ
Sous Sol Mots Fléchés, Grand Corps Malade - Dimanche Soir Instrumental, Pourquoi Les Photos Ne S'affichent Pas Sur Facebook, Quand Faire Le Tachahoud, Directeur Académie Lyon, Rapport Jury Capes Maths, Pékin Express Saison 12 Streaming, Coordonnées Cramif 77, Vente Voiture Mercedes Glc Coupe Occasion, Dessin Disney Facile A Reproduire,