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{"sheet":"OpéMatricielles","index":0,"n_rows":244,"n_cols":9,"rows_kept":244,"cut":false,"hidden":false,"merged":[[18,1,18,4],[19,1,19,4],[17,5,17,8],[18,5,18,8],[19,5,19,8],[0,0,0,8],[3,0,3,1],[132,0,132,3],[92,5,92,7],[1,3,1,5],[1,6,1,7],[36,0,37,0],[93,5,93,7],[20,1,20,8],[17,1,17,4],[62,0,62,3],[94,5,94,7],[95,5,95,7],[96,5,96,7],[240,0,240,5],[162,1,162,3]]}
["UTILISATION DES FORMULES MATRICIELLES DANS EXCEL"]
["conventions des couleurs",null,"donnée","formule non matricielle",null,null,"formule matricielle",null,"© Monteil 2001,2002"]
[]
["FORMULES DE BASE"]
["Renvoi d'une plage : différentes manières d'opérer"]
["plage-source","Art A","Art B1","Art B2"]
[]
["renvoi classique",{"$f":"B6","v":"Art A"},{"$f":"C6","v":"Art B1"},{"$f":"D6","v":"Art B2"},"formule sur 1 cellule, puis poignée de recopie"]
[null,null,null,null,"(on recopie TOUT : formule + format)"]
[]
["idem + Ctrl-Entrée",{"$f":"B6","v":"Art A"},{"$f":"C6","v":"Art B1"},{"$f":"D6","v":"Art B2"},"formule sur 1 cellule, recopiée dans la présélection"]
[null,null,null,null,"(seule est recopiée la formule, pas le format)"]
[]
["renvoi matriciel",{"$f":"B6:D6","v":"Art A"},"Art B1","Art B2","formule unique sur l'ensemble de la présélection"]
["(Maj-Ctrl-Entrée)"]
[]
["Rappel : raccourcis-clavier de déplacement rapide dans une plage ou une feuille"]
["Ctrl-Flèche","si on n'est pas en bout de plage : ",null,null,null,"va en bout de la plage courante"]
[null,"si on est en bout de plage : ",null,null,null,"va sur la prochaine plage"]
[null,"si on est hors d'une plage :",null,null,null,"va sur la prochaine plage"]
["Ctrl-Début, Ctrl-Fin","va au début ou à la fin de la feuille de calcul"]
["Si la touche MAJ est utilisée en plus, elle étend la sélection à partir de la position courante"]
[]
["Opérateurs et fonctions classiques utilisés matriciellement : parallélisme"]
["prix HT",1,10,100]
["quantités",15,5,3]
["TOTAL HT",{"$f":"PrixHT*Quantites","v":15},50,300,"produit de 2 plages cellule par cellule"]
["TOTAL TTC",{"$f":"TotauxHT*1.196","v":17.939999999999998},59.8,358.8,"produit d'une plage par une constante"]
["pour modifier :","le faire sur n'importe quelle cellule de la plage (puis Maj-Ctrl-Entrée)"]
[]
["Arrondi dizaine sup.",{"$f":"CEILING(TotauxTTC,10)","v":20},60,360,"application d'une fonction sur toute une plage"]
["Total HT > 200",{"$f":"TotauxHT>200","v":false},false,true,"condition"]
["Total TTC : -10% …",{"$f":"IF(TotauxHT>200,TotauxTTC*90%,TotauxTTC)","v":17.939999999999998},59.8,322.92,"application de la fonction SI"]
["… si Total HT > 200"]
[]
["3 repères","A","B","C"]
["2 intervalles",{"$f":"B36 & \"-\" & C36","v":"A-B"},{"$f":"C36 & \"-\" & D36","v":"B-C"},"formule non matricielle sur une cellule, puis recopie"]
[null,{"$f":" B36:C36 & \"-\" & C36:D36","v":"A-B"},"B-C","formule matricielle unique sur l'ensemble de la plage"]
[]
["Fonctions classiques opérant sur des plages (ex. : SOMME)"]
["Somme standard : non matricielle car résultat sur une seule cellule",null,null,null,null,null,{"$f":"SUM(TotauxTTC)","v":436.54}]
[]
["Somme sur une plage resultant d'un calcul matriciel",null,null,null,null,null,{"$f":"SUM(PrixHT*Quantites*1.196)","v":436.54}]
[null,"une formule standard devient matricielle si un résultat intermédiaire l'est"]
[]
["Somme conditionnelle sur les articles B (nom débutant par \"Art B\")",null,null,null,null,null,{"$f":"SUM(IF(LEFT(Articles,5)=\"Art B\",TotauxTTC))","v":418.6}]
[null,"SOMME avec fonction SI utilisée matriciellement"]
[]
["Même chose avec une seconde condition (Total HT < 200)",null,null,null,null,null,{"$f":"SUM(IF(LEFT(Articles,5)=\"Art B\",IF(TotauxHT<200,TotauxTTC)))","v":59.8}]
[null,"SOMME avec 2 fonctions SI imbriquées et utilisées matriciellement"]
[]
["Constantes matricielles"]
[null,{"$f":"{1,2,3;4,5,6}*100000","v":100000},200000,300000,null,"NOTA","en version anglaise d'Excel,"]
[null,400000,500000,600000,null,null,"utiliser {1,2,3;4,5,6} ou {1\\2\\3;4\\5\\6} "]
[null,null,null,null,null,null,"en version française d'Excel,"]
[null,null,null,null,null,null,"utiliser {1.2.3;4.5.6}"]
["Exemple : équation du second degré a.x2 + b.x + c = 0"]
["Solutions : si Delta (= b2-4.a.c) est positif, on a deux racines [-b +- Racine(Delta)]/(2.a)"]
[null,"a","b","c",null,"Delta",null,"x1","x2"]
["équation x2 = x+1",1,-1,-1,null,{"$f":"coef_b^2-4*coef_a*coef_c","v":5},null,{"$f":"IF(Delta>=0,(-coef_b+{-1,1}*SQRT(Delta))/(2*coef_a),NA())","v":-0.6180339887498949},1.6180339887498949]
[null,null,null,null,null,null,null,"carré des racines"]
[null,null,null,null,null,null,null,{"$f":"H60:I60^2","v":0.38196601125010521},2.6180339887498949]
["FONCTIONS PUREMENT MATRICIELLES"]
["Fonction DECALER : extraction d'une ligne, colonne ou sous-tableau"]
[null,"soit un tableau T",1,2,3,null,{"$f":"OFFSET(T,,j-1,,1)","v":1}]
["nb lignes",{"$f":"ROWS(T)","v":4},4,5,6,null,4]
["nb colonnes",{"$f":"COLUMNS(T)","v":3},7,8,9,null,7]
[null,null,10,11,12,null,10]
[null,null,null,null,null,null,"j-ème colonne"]
["i-ème ligne",1,{"$f":"OFFSET(T,i-1,,1)","v":1},2,3,null,1]
[]
[null,"sous-tableau 2 x 2",{"$f":"OFFSET(T,i-1,j-1,2,2)","v":1},2]
[null,null,4,5]
[]
["Fonction TRANSPOSE : transposée d'un vecteur ou d'une matrice"]
["sur un vecteur V",1,2,3,"V'",{"$f":"TRANSPOSE(V)","v":1}]
[null,null,null,null,null,2]
[null,null,null,null,null,3]
[]
["sur une matrice M",1,2,3,"M'",{"$f":"TRANSPOSE(M)","v":1},4]
[null,4,5,6,null,2,5]
[null,null,null,null,null,3,6]
[]
["Fonction TABLE (menu \"Données / Table…\")"]
[null,"X","Log(X)",null,"Autre méthode"]
[null,10,{"$f":"LOG(B86)","v":1},null,"sans TABLE"]
[null,1,0,null,{"$f":"LOG(B87:B90)","v":0}]
[null,2,0.3010299956639812,null,0.3010299956639812]
[null,4,0.6020599913279624,null,0.6020599913279624]
[null,8,0.90308998699194354,null,0.90308998699194354]
[]
["Fonction FREQUENCE : fréquence d'occurrence de valeurs dans des classes"]
[null,"Valeurs","Bornes","Fréquences",null,"Classes (opérateur &)"]
[null,1,10,{"$f":"FREQUENCY(Valeurs,Bornes)","v":4},null,{"$f":"C94 & \" et moins\"","v":"10 et moins"}]
[null,2,20,1,null,{"$f":"\"de \" & C94 & \" exclu à \" & C95 & \" inclus\"","v":"de 10 exclu à 20 inclus"}]
[null,4,30,0,null,{"$f":"\"de \" & C95 & \" exclu à \" & C96 & \" inclus\"","v":"de 20 exclu à 30 inclus"}]
[null,8,null,2,null,{"$f":"\"plus de \" & C96","v":"plus de 30"}]
[null,16,null,"Attention : 1 classe de plus que de bornes !"]
[null,32]
[null,64,null,"La plage résultante des fréquences DOIT être en colonne !"]
[]
["Si on veut les fréquences directement sur une ligne horizontale :"]
[null,{"$f":"TRANSPOSE(FREQUENCY(Valeurs,Bornes))","v":4},1,0,2]
[]
[]
["Fonction DROITEREG : régression linéaire simple"]
["mesures :"]
["X observés",1,2,3,4,5]
["Y observés",11.1,12,12.9,14.5,14.5]
["calcul de a et b sans fonction matricielle : usage du solveur"]
[null,"but : minimiser la somme des carrés des résidus"]
[null,"a","b"]
["Y = a.X + b",1,10]
["Y estimés",{"$f":"a*Xobs+b","v":11},12,13,14,15]
["résidus Yestim-Yobs",{"$f":"Yestim-Yobs","v":-9.9999999999999645E-2},0,9.9999999999999645E-2,-0.5,0.5]
[null,null,null,null,"somme carrés",{"$f":"SUM(Residus^2)","v":0.5199999999999998}]
["calcul direct : fonction matricielle DROITEREG"]
[null,{"$f":"LINEST(Yobs,Xobs)","v":0.92999999999999994},10.210000000000001,null,"somme carrés",{"$f":"SUM((B118*Xobs+C118-Yobs)^2)","v":0.47099999999999997}]
["Fonction DROITEREG : régression linéaire multiple"]
["mesures :"]
["X1 observés",{"$f":"Xobs","v":1},2,3,4,5,"(on récupère les X précédents)"]
["X2 observés",0.2,0,-0.2,1,0]
["Y observés",{"$f":"Yobs","v":11.1},12,12.9,14.5,14.5,"(on récupère les Y précédents)"]
["calcul sans fonction matricielle : usage du solveur pour minimiser la somme des carrés des résidus"]
[null,"a2","a1","a0 (=b)"]
["Y2=a2.X2+a1.X1+a0",1,1,10]
["Y2 estimés",{"$f":"a_2*X2obs+a_1*X1obs+a_0","v":11.2},12,12.8,15,15]
["résidus Yestim2-Yobs",{"$f":"Y2estim-Yobs","v":9.9999999999999645E-2},0,-9.9999999999999645E-2,0.5,0.5]
[null,null,null,null,"somme des carrés",{"$f":"SUM(Residus2^2)","v":0.5199999999999998}]
["calcul direct : fonction matricielle DROITEREG"]
[null,{"$f":"LINEST(Yobs,X1etX2obs)","v":0.68957345971563933},0.88862559241706152,10.196208530805688,null,{"$f":"SUM((B131*X2obs+C131*Xobs+D131-Yobs)^2)","v":6.9668246445498197E-2}]
[]
["OPERATIONS DE CALCUL MATRICIEL"]
["Produit Scalaire "]
["Prix au Supermarché (ticket de caisse)",null,null,"Article","Qté","PU","Total"]
[null,null,null,"Vin",1,100,{"$f":"E136*F136","v":100},"produit 1"]
[null,null,null,"Fromage",2,10,{"$f":"E137*F137","v":20},"produit 2"]
[null,null,null,"Pain",5,1,{"$f":"E138*F138","v":5},"produit 3"]
["Somme des Produits",null,null,null,null,null,{"$f":"SUM(G136:G138)","v":125},"Somme"]
[]
["Calcul direct 1","fonction SOMMEPROD(V1;V2)",null,null,null,null,{"$f":"SUMPRODUCT(E136:E138,F136:F138)","v":125}]
[null,"ou formule matricielle SOMME(V1*V2)",null,null,null,null,{"$f":"SUM(E136:E138*F136:F138)","v":125}]
[null,"contrainte : plages toutes 2 verticales (ou toutes 2 horizontales)"]
[]
["Calcul direct 2","fonction PRODUITMAT(V1;V2)"]
[null,"contrainte : 1ère plage horizontale, 2ème plage verticale (et non l'inverse)"]
[null,null,null,null,"PU"]
[null,"Vin",null,null,100,null,null,"Produit Scalaire"]
[null,null,"From",null,10,null,null,"="]
[null,null,null,"Pain",1,null,null," Somme Pondérée"]
["Quantités",1,2,5,{"$f":"MMULT(B151:D151,E148:E150)","v":125},"Prix total"]
[]
["Produit Matriciel (généralisation du produit scalaire) : fonction PRODUITMAT (matricielle)"]
["Plusieurs clients (1 client/ligne) et plusieurs dates (1 date/colonne)"]
[null,null,null,null,"Date 1","Date 2"]
[null,"Vin",null,null,100,100]
[null,null,"From",null,10,15]
[null,null,null,"Pain",1,2]
["Client 1",1,2,5,{"$f":"MMULT(Clients,Dates)","v":125},140,"Prix totaux"]
["Client 2",0,3,2,32,49]
["Client 3",1,0,4,104,108]
["Client 4",2,2,1,221,232]
[null,"=> Quantités = Pondération"]
[]
["dimension des plages matricielles : Clients(m,n) x Dates(n,p) => PrixTotaux(m,p)"]
["contrainte : nombre de colonnes (n) de la matrice 1 = nombre de lignes de la matrice 2"]
[]
["Notes d'élèves dans plusieurs matières coefficientées"]
[null,null,null,null,"Coefs","=> Coefficients = Pondération"]
[null,"Math",null,null,3,null,"Total Coefs"]
[null,null,"Sport",null,1,null,{"$f":"SUM(CoefsMatieres)","v":6}]
[null,null,null,"Chinois",2,null,"Moyennes"]
["Elève A",14,12,13,{"$f":"MMULT(Eleves,CoefsMatieres)","v":80},"Totaux",{"$f":"E173:E176/G171","v":13.333333333333334}]
["Elève B",11,17,15,80,null,13.333333333333334]
["Elève C",16,11,12,83,null,13.833333333333334]
["Elève D",10,15,14,73,null,12.166666666666666]
[]
["Attention : le produit matriciel n'est pas commutatif !"]
[null,null,null,null,"PU"]
[null,null,null,null,100]
[null,null,null,null,10]
[null,null,null,null,1]
["Quantités",1,2,5,{"$f":"MMULT(B183:D183,E180:E182)","v":125},"Prix total"]
[]
[null,null,"Quantités"]
[null,null,1,2,5]
["PU",100,{"$f":"MMULT(B187:B189,C186:E186)","v":100},200,500]
[null,10,10,20,50]
[null,1,1,2,5]
[]
["Attention : ne pas confondre produit classique et produit matriciel !"]
["La confusion n'est possible que sur des matrices carrées (sinon : incompatibilité des dimensions !)"]
[null,"Matrice A",null,"Matrice B",null,"Produit classique A.B"]
[null,1,2,5,6,{"$f":"MatriceA*MatriceB","v":5},12]
[null,3,4,7,8,21,32]
[]
[null,null,null,{"$f":"MatriceB","v":5},6,"B"]
[null,"A",null,7,8]
[null,{"$f":"MatriceA","v":1},2,{"$f":"MMULT(B199:C200,D197:E198)","v":19},22,"Produit matriciel A x B"]
[null,3,4,43,50]
[]
[null,null,null,{"$f":"MatriceA","v":1},2,"A"]
[null,"B",null,3,4]
[null,{"$f":"MatriceB","v":5},6,{"$f":"MMULT(B204:C205,D202:E203)","v":23},34,"Produit matriciel B x A"]
[null,7,8,31,46]
[]
["Résolution d'un système d'équations linéaires : fonction INVERSEMAT (matricielle)"]
["Exemple","X1","+ X2","+ X3","= 1"]
[null,"X1","- X2","+ X3","= 2"]
[null,"X1","+ X2","- X3","= 3"]
[]
["Ecriture matricielle",null,null,"X","X1 ?"]
["Coefs x X = K",null,null,null,"X2 ?"]
[null,null,null,null,"X3 ?"]
["Coefs",1,1,1,1,"K"]
[null,1,-1,1,2]
[null,1,1,-1,3]
[]
["Résolution : prémultiplier par 1/Coefs",null,null,"K",{"$f":"K","v":1}]
["X =(1/Coefs) x K",null,null,null,2]
["1/Coefs = matrice-inverse de Coefs",null,null,null,3]
["1/Coefs",{"$f":"MINVERSE(Coefs)","v":0},0.5,0.5,{"$f":"MMULT(invCoefs,K)","v":2.5},"X"]
["ou Inv(Coefs)",0.5,-0.5,0,-0.5]
["ou Coefs-1",0.5,0,-0.5,-1]
[]
["Vérification",null,"Coefs x X - K",{"$f":"MMULT(Coefs,X)-K","v":0},"doit être égal au vecteur nul"]
[null,null,null,0,"(aux erreurs d'arrondi près)"]
[null,null,null,0]
[]
["Résolution directe sans utiliser les étapes intermédiaires (avec présentation horizontale) :"]
["X",{"$f":"TRANSPOSE(MMULT(MINVERSE(Coefs),K))","v":2.5},-0.5,-1]
[]
["Déterminant d'une matrice carrée : fonction DETERMAT (non matricielle)"]
["MC1",1,2,null,null,"déterminant"]
[null,3,4,null,null,{"$f":"MDETERM(_MC1)","v":-2}]
[]
["MC2",1,2,3,null,"déterminant"]
[null,3,1,2,null,{"$f":"MDETERM(_MC2)","v":18}]
[null,2,3,1]
[]
["LIMITE DES FORMULES MATRICIELLES D'EXCEL"]
["On ne peut pas insérer ou supprimer des lignes ou colonnes fractionnant une matrice utilisée dans une formule"]
["Solution : supprimer la formule matricielle, insérer ou supprimer les lignes ou colonnes, remettre la formule"]
["NOTA : il est clair que le nommage des matrices facilite grandement les choses !"]

{"sheet":"Frequence","index":1,"n_rows":126,"n_cols":13,"rows_kept":126,"cut":false,"hidden":false,"merged":[[0,1,0,13],[1,3,1,4]]}
[null,"Génération de nombres aléatoires"]
[null,"Bornes","Intervalles","Fréquences",null,null,null,null,"Nombre total de valeurs :",{"$f":"SUM(D4:D23)","v":1000},null,"Moyenne :",{"$f":"AVERAGE(Donnees)","v":51.97455027273179}]
[null,0]
[null,5,{"$f":"\"[\"&B3&\"-\"&B4&\"]\"","v":"[0-5]"},{"$f":"FREQUENCY(Donnees,Bornes)","v":42},{"$f":"Frequences/NbValeurs","v":4.2000000000000003E-2}]
[null,10,{"$f":"\"]\"&B4&\"-\"&B5&\"]\"","v":"]5-10]"},38,3.7999999999999999E-2]
[null,15,"]10-15]",55,5.5E-2]
[null,20,"]15-20]",48,4.8000000000000001E-2]
[null,25,"]20-25]",48,4.8000000000000001E-2]
[null,30,"]25-30]",54,5.3999999999999999E-2]
[null,35,"]30-35]",41,4.1000000000000002E-2]
[null,40,"]35-40]",39,3.9E-2]
[null,45,"]40-45]",59,5.8999999999999997E-2]
[null,50,"]45-50]",52,5.1999999999999998E-2]
[null,55,"]50-55]",53,5.2999999999999999E-2]
[null,60,"]55-60]",48,4.8000000000000001E-2]
[null,65,"]60-65]",41,4.1000000000000002E-2]
[null,70,"]65-70]",53,5.2999999999999999E-2]
[null,75,"]70-75]",58,5.8000000000000003E-2]
[null,80,"]75-80]",49,4.9000000000000002E-2]
[null,85,"]80-85]",54,5.3999999999999999E-2]
[null,90,"]85-90]",52,5.1999999999999998E-2]
[null,95,"]90-95]",53,5.2999999999999999E-2]
[null,100,"]95-100]",63,6.3E-2]
[]
[null,"Taper F9 pour générer de nouvelles valeurs"]
[]
[null,{"$f":"100*RAND()","v":92.587169927427752},21.671404783153779,13.051105409142194,37.869146570407963,36.050611641071342,40.764834484905563,48.497588066443228,93.751831407479457,29.406610660973321,86.657941787113415]
[null,50.317954612038342,88.774535213716263,90.646997864565847,72.968366463701116,19.992231932402603,87.788889983558988,28.232035087250829,58.624308257466339,25.750760783048431,23.812835611662809]
[null,98.303000494344744,56.793659795260723,9.4498635330413698,82.661162636469669,28.791961084024877,88.498790394709232,16.24105151379408,85.194756271536903,59.059860001320097,72.770686329834362]
[null,3.3100112995951392,15.882537797090656,98.394883165146624,76.92219584031713,66.109171916724947,71.866786960684877,54.151207914194487,46.966064490140212,2.700412173894029,28.578086793089263]
[null,66.30024004277989,84.472004046370301,60.093623995490496,49.192676601483775,53.975288222118088,81.232120587350835,4.8536941145281176,89.946432406238813,42.113988475818317,31.446389014869947]
[null,89.16824887054095,3.3564079039793304,50.848007266988262,28.153977556485366,30.619144068109183,56.55113336915425,18.380463185922157,1.1481922902038866,78.956095147666446,70.606859573922776]
[null,96.341879522270531,18.306308170024366,46.703464069135606,46.530665601618935,86.125059372927595,21.151680065104937,12.720989853149689,17.082816100292032,32.684546786489996,75.028728164710927]
[null,15.065198272838265,97.667240010463757,28.496097196449078,52.528873300549904,69.643502980091711,82.018337295967257,11.188479674053397,52.470022746185037,93.937194030858493,78.789376158676035]
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[null,59.660135840908104,3.1345168405391144,18.213666772012282,71.518511138071887,73.807652971535504,13.120182159223049,75.542564570664396,64.603845502763619,39.602795081012346,94.213763947428774]
[null,97.16982691677633,91.16334645053918,66.419754703984239,88.903526043380836,55.430552597443217,55.696340803584135,92.96928383133239,97.569714870699286,96.570255268604129,13.907622558356969]
[null,66.993855751535591,95.087193642254377,30.79559333748977,24.454710250571775,5.9631324532823822,1.5230106911253594,58.846593279952096,18.796127377119475,82.767661422155015,41.968713770202214]
[null,72.060511801734222,88.451006102773448,9.0686309628127297,58.678255815104428,69.0978667193272,98.020701371832871,79.278663755204221,11.820605147718233,24.32075792065659,33.802104591928583]
[null,16.102971547322198,10.242889525442479,40.385675342055002,0.74532271134221117,66.594998995601927,91.583322030697516,73.695532599104624,60.07036429334579,42.058960119420263,57.297883068887565]
[null,68.634889233777386,15.726180948122249,22.509572540064649,35.252780280737525,7.3659692020850205,4.5836230372288567,29.478286886060999,74.311481802350372,80.004366548066315,74.121475984975106]
[null,89.022779248314734,99.814859704292431,99.901512267705399,61.802005440081707,2.0718190304145789,96.613148331968574,47.76654406372721,95.991112245825647,5.8322949760128644,80.677808736959136]
[null,40.382458768776694,86.402629632766534,2.6686467165523697,18.306014708957118,14.912666628106862,51.287524722060553,25.136375473548199,98.356786140478675,70.837988088687723,71.199419171026079]
[null,53.915689596699337,22.70321628446802,94.052675180721806,95.515682295743403,45.747422381005734,35.378975162085183,72.746332106776478,25.161084173653514,91.096711347042657,57.930115438407626]
[null,84.553491091584306,21.449222095048871,47.680933225891152,54.305792312022163,60.509803504317318,57.196631159169584,87.861833352566393,60.346137329915081,92.147422882995215,15.844414284629627]

{"sheet":"ResolutionSysteme","index":2,"n_rows":94,"n_cols":15,"rows_kept":94,"cut":false,"hidden":false,"merged":[[0,0,0,13],[20,7,20,8]]}
["ETUDE DE LA TRAJECTOIRE D'UNE BALLE"]
["Objectif"]
[null,"faire passer une courbe parabolique par 3 points donnés (t1,z1), (t2,z2) et (t3,z3)"]
["Résolution mathématique"]
[null,"La courbe z(t) = a.t2 + b.t + c passe par les 3 points :"]
[null,null,"z1 = a.t12 + b.t1 + c"]
[null,null,"z2 = a.t22 + b.t2 + c"]
[null,null,"z3 = a.t32 + b.t3 + c"]
[null,"Les inconnues étant a, b et c, on a un système linéaire de 3 équations à 3 inconnues :"]
[null,null,"Z = M.X avec "]
[null,null,null,null,"z1",null,null,"t12","t1",1,null,"a"]
[null,null,null,"Z = ","z2",null,"M = ","t22","t2",1,"X = ","b"]
[null,null,null,null,"z3",null,null,"t32","t3",1,null,"c"]
[null,"Solution : X = Inv(M).Z"]
["Trajectoire d'une balle"]
[null,null,null,"T","Z",null,null,null,"M",null,null,"X",null,"vérification : Z-M.X"]
[null,null,"P1=(",10,6,")",null,{"$f":"T^2","v":100},{"$f":"T","v":10},{"$f":"1","v":1},null,{"$f":"MMULT(MINVERSE(M),Z)","v":-1.999999999999999E-2},null,{"$f":"Z-MMULT(M,X)","v":8.8817841970012523E-16}]
[null,null,"P2=(",20,8,")",null,400,20,1,null,0.7999999999999996,null,1.7763568394002505E-15]
[null,null,"P3=(",30,6,")",null,900,30,1,null,1.7763568394002505E-15,null,-1.7763568394002505E-15]
[]
[null,null,"Instant t",21.666666661156686,{"$f":"INDEX(X,1)*tqcq^2+INDEX(X,2)*tqcq+INDEX(X,3)","v":7.9444444448117757},"Altitude z",null,"z=0 en t = ",null,{"$f":"(-coef_b-SQRT(coef_b^2-4*coef_a*coef_c))/(2*coef_a)","v":40},null,"zmax = ",{"$f":"coef_a*t_zmax^2+coef_b*t_zmax+coef_c","v":7.9999999999999982},"en t =",{"$f":"-coef_b/2/coef_a","v":20}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Tabulation de la trajectoire parablique"]
["tmin","tmax","tpas",null,"t","z"]
[0,{"$f":"CEILING(MAX(T)+1,10)","v":40},{"$f":"(tmax-tmin)/50","v":0.8},null,null,{"$f":"z_de_tqcq","v":7.9444444448117757}]
[null,null,null,null,{"$f":"tmin","v":0},1.7763568394002505E-15]
[null,null,null,null,{"$f":"E39+tpas","v":0.8},0.62720000000000142]
[null,null,null,null,1.6,1.2288000000000012]
[null,null,null,null,2.4000000000000004,1.8048000000000011]
[null,null,null,null,3.2,2.3552000000000004]
[null,null,null,null,4,2.8800000000000003]
[null,null,null,null,4.8,3.3792]
[null,null,null,null,5.6,3.8527999999999998]
[null,null,null,null,6.3999999999999995,4.3007999999999997]
[null,null,null,null,7.1999999999999993,4.7231999999999985]
[null,null,null,null,7.9999999999999991,5.1199999999999983]
[null,null,null,null,8.7999999999999989,5.4911999999999983]
[null,null,null,null,9.6,5.8367999999999984]
[null,null,null,null,10.4,6.1567999999999987]
[null,null,null,null,11.200000000000001,6.4511999999999983]
[null,null,null,null,12.000000000000002,6.719999999999998]
[null,null,null,null,12.800000000000002,6.9631999999999987]
[null,null,null,null,13.600000000000003,7.1807999999999996]
[null,null,null,null,14.400000000000004,7.3727999999999998]
[null,null,null,null,15.200000000000005,7.5392000000000001]
[null,null,null,null,16.000000000000004,7.6799999999999988]
[null,null,null,null,16.800000000000004,7.7951999999999977]
[null,null,null,null,17.600000000000005,7.8847999999999985]
[null,null,null,null,18.400000000000006,7.9487999999999976]
[null,null,null,null,19.200000000000006,7.9871999999999979]
[null,null,null,null,20.000000000000007,7.9999999999999982]
[null,null,null,null,20.800000000000008,7.9871999999999961]
[null,null,null,null,21.600000000000009,7.9487999999999968]
[null,null,null,null,22.400000000000009,7.8847999999999967]
[null,null,null,null,23.20000000000001,7.7951999999999959]
[null,null,null,null,24.000000000000011,7.6799999999999979]
[null,null,null,null,24.800000000000011,7.5391999999999975]
[null,null,null,null,25.600000000000012,7.3727999999999962]
[null,null,null,null,{"$f":"E71+tpas","v":26.400000000000013},7.1807999999999961]
[null,null,null,null,27.200000000000014,6.9631999999999969]
[null,null,null,null,28.000000000000014,6.7199999999999918]
[null,null,null,null,28.800000000000015,6.4511999999999912]
[null,null,null,null,29.600000000000016,6.1567999999999916]
[null,null,null,null,30.400000000000016,5.8367999999999913]
[null,null,null,null,31.200000000000017,5.4911999999999903]
[null,null,null,null,32.000000000000014,5.1199999999999921]
[null,null,null,null,32.800000000000011,4.7231999999999896]
[null,null,null,null,33.600000000000009,4.3007999999999935]
[null,null,null,null,34.400000000000006,3.8528000000000002]
[null,null,null,null,35.200000000000003,3.3791999999999991]
[null,null,null,null,36,2.8800000000000008]
[null,null,null,null,36.799999999999997,2.3552000000000017]
[null,null,null,null,37.599999999999994,1.8048000000000055]
[null,null,null,null,38.399999999999991,1.2288000000000086]
[null,null,null,null,39.199999999999989,0.62720000000000731]
[null,null,null,null,39.999999999999986,1.2434497875801753E-14]
["Ajustement linéaire"]
["a","b","r2",null,"t","z"]
[{"$f":"LINEST(Z,T)","v":0},6.666666666666667,{"$f":"RSQ(Z,T)","v":0},null,null,{"$f":"A92*tqcq+B92","v":6.666666666666667}]
[null,null,null,null,{"$f":"tmin","v":0},6.666666666666667]
[null,null,null,null,{"$f":"tmax","v":40},6.666666666666667]