Mathématiques

Question

QUI PEUX M AIDER MON DM EST EN 2 PARTIES
QUI PEUX M AIDER MON DM EST EN 2 PARTIES

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  • Exercice 1
    E = 2/5 + (-3/4) x 5
    E = 2/5 + (-3x5/4)
    E = 2/5 + (-15/4)
    E = 2/5 - 15/4
    E = 2x4/5x4 - 15x5/4x5
    E = 8/20 - 75/20
    E = -67/20

    F = -(-1/5)² - 2/5
    F = -(-1)²/(5)² - 2/5
    F = -(1/25) - 2/5
    F = -1/25 - 2x5/5x5
    F = -1/25 - 10/25
    F = -11/25

    G = [4-(2-5)²]/(4+5)
    G = [4-(-3)²]/9
    G = (4-9)/9
    G = -5/9

    H = (3/2)² -(1/3) x(5/2)
    H = (3x3/2x2) - (1x5/3x2)
    H = 9/4 - 5/6
    H = 9x3/4x3 - 5x2/6x2
    H = 27/12 - 10/12
    h = 17/12

    Exercice 2
    Rappel des calculs de puissance de 10 (^ se lit puissance)
    10^0 = 1
    10^1 = 10
    10^a x 10^b = 10^(a+b)
    1/10^a = 10^-a

    a) C = (3,5x10^-11x2x10^8)/(0,2x10^-9)
    C = (3,5x2x10^(-11+8))/(2x10^-1x10^-9)
    C = (3,5x2x10^-3)/(2x10^(-1-9))
    C = (3,5x2x10^-3)/(2x10^-10)
    C = (3,5x10^-3x10^10x2)/2
    C = 3,5x10^(-3+10)
    C = 3,5 x 10^7

    S = (2x10^-5x1,2x10^2)/(3x10^-7)
    S = (2x1,2x10^(-5+2))x10^7/3
    S = 2,4 x 10^(-3+7)/3
    S = 0,8 x 10^4
    S = 8 x 10^-1 x10^4
    S = 8 x 10^(-1+4)
    S = 8 x 10^3

    b) C = 35000 x 10^3
    donc S < C

    c) C x S = 3,5 x 10^7 x 8 x 10^3
    C x S = 3,5 x 8 x 10^(7+3)
    C x S = 28 x 10^10
    C x S = 280 000 000 000

    C/S = (3,5 x 10^7)/(8 x 10^3)
    C/S = (3,5 x 10^7 x 10^-3)/8
    C/S = 0.4375 x 10^(7-3)
    C/S = 0.4375 x 10^4
    C/S = 4375

  • Exercice 1
    Ecrire les différentes étapes et donner le résultat sous forme de fraction simplifiée :

    E = 2/5 + (-3/4) x 5
    E = 2/5 - 3/4 x 5
    E = 2/5 - 3 x 5
                     4
    E = 2/5 - 12/4
    E = 2 x 4 / 5 x 4 - 15 x 5 / 4 x 5
    E = 8/20 - 75/20
    E = - 67/20

    F = - (-1/5)² - 2/5
    F = - (-1)² / (5)² - 2/5
    F = - (1/25) - 2/5
    F = -1/25 - 2 x 5 / 5 x 5
    F = -1/25 - 10/25
    F = -11/25

    G = 4 - (2 - 5)² / (4 + 5)
    G = 4 - (-3)² / 9
    G = (4 - 9) / 9
    G = -5/9

    H = (3/2)² - (1/3) x (5/2)
    H = (3 x 3 / 2 x 2) - (1 x 5)
                                 (3 x 2)
    H = 9/4 - 5/6
    H = 9 x 3 / 4 x 3 - 5 x 2 / 6 x 2
    H = 27/12 - 10/12
    H = 17/12

    Exercice 2
    Donner l'écriture scientifique de C et S

    a)
    C = (3,5 x 10⁻¹¹ x 2 x 10⁸) / (0,2 x 10⁻⁹)
    C = (3,5 x 2 x 10)⁻¹¹⁺⁸ / (2 x 10⁻¹ x 10⁻⁹)
    C = (3,5 x 2 x 10⁻³) / (2 x 10⁻¹⁻⁹)
    C = (3,5 x 2 x10⁻³) / (2 x 10⁻¹⁰)
    C = (3,5 x 10⁻³ x 10¹⁰ x 2) / 2
    C = 3,5 x 10⁻³⁺¹⁰
    C = 3,5 x 10⁷

    S = (2 x 10⁻⁵ x 1,2 x 10²) / (3 x 10⁻⁷)
    S = (2 x 1,2 x 10⁻⁵⁺²) x 10⁷ sur³
    S = 2,4 x 10⁻³⁺⁷ / 3
    S = 0,8 x 10⁴
    S = 8 x 10⁻¹ x 10⁴
    S = 8 x 10⁻¹⁺⁴
    S = 8 x 10³

    b) Comparer C et S :
    C > S

    c) Calculer le produit C x S et le quotient C/S
    C x S = 3,5 x 10⁷ x 8 x 10³
    C x S = 3,5 x 8 x 10⁷⁺³
    C x S = 28 x 10¹⁰, soit  280 000 000 000


    C/S = (3,5 x 10⁷) / (8 x 10³)
    C/S = (3,5 x 10⁷ x 10⁻³) / 8
    C/S = 0,4375 x 10⁷⁻³
    C/S = 0,4375 x 10⁴
    C/S = 4375

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