Matematyka
Ncole1997
2017-06-26 10:52:09
Proszę o pomoc ;) chociaż jedno zadanie Będę wdzieczna dziękuję
Odpowiedź
bebek9220
2017-06-26 11:44:37

zad 1 a₃ = a₁ + 2r = 9 a₇ = a₁ + 6r = 17 a₁ + 2r = 9 a₁ + 6r = 17 odejmujemy równania a₁ - a₁ + 2r - 6r = 9 - 17 - 4r = - 8 4r = 8 r = 8/4 = 2 a₁ + 2r = 9 a₁ + 2 * 2 = 9 a₁ + 4 = 9 a₁ = 9 - 4 = 5 odp : a₁ = 5 , r = 2 zad 2 a₁ = 1 a₂ = 1/2 a₃ = 1/4 q = a₃/a₂ = a₂/a₁ = 1/2 : 1 = 1/2 Sn = a₁(1 - qⁿ)/(1 - q) = [1 - (1/2)ⁿ]/(1 - 1/2) = [1 - (1/2)ⁿ]/(1/2) = 2[(1 - (1/2)ⁿ] =  = 2 - 2 * (1/2)ⁿ = 2 - 1ⁿ = 2 - 1 = 1 zad 3 4ˣ⁺⁴ =16ˣ⁻² 4ˣ⁺⁴ = (4²)ˣ⁻² 4ˣ⁺⁴ = 4²ˣ⁻⁴ x + 4 = 2x - 4 x - 2x = - 4 - 4 - x = - 8 x = 8 zad 4 f(x) = (2/3)³ˣ⁻⁵ g(x) = (4/9)⁵ˣ⁺¹ f(x) > g(x) (2/3)³ˣ⁻⁵ > (4/9)⁵ˣ⁺¹ (2/3)³ˣ⁻⁵ > (2/3)²⁽⁵ˣ⁺¹⁾ (2/3)³ˣ⁻⁵ > (2/3)¹⁰ˣ⁺² 3x - 5 < 10x + 2 3x - 10x < 2 + 5 - 7x < 7 7x > - 7 x > - 7/7 x > - 1 x ∈ (- 1 , + ∞) zad 5 y = log₃(2x - 5) - 2  założenie 2x - 5 > 0 ⇔ 2x > 5 ⇔ x > 5/2 ⇔ x > 2,5 Df: x ∈ (2,5 , + ∞) log₃(2x - 5) - 2 = 0 log₃(2x - 5) - log₃9 = 0 log₃(2x - 5)/9 = 0 3⁰ = (2x - 5)/9 1 = (2x - 5)/9 9 =2x - 5 2x = 9 + 5 = 14 x = 14/2 = 7

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