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Exercicios resolvidos  001
Exercicios resolvidos  001
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Exercicios resolvidos 001

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  • 1. PROVA FINAL DE MATEMÁTICA BÁSICA Tec. Sistemas de Informação - Prof. Milton – 16/fev/2007  2 x + y = 641)  log (x) + log (y) = log ( 8 ) Solução: x + y = 6 Resposta: x = 2 e y = 4 x.y = 8 ou x=4ey=2  2 2 x+ y = 4  12)  x − y 2 =   2 Solução: 2x + y = 2 Resposta: x = e y = 1 1 x-y=- 2 5 13) ≥ 2x − 1 x−2 Solução: | 5x-10 | ≥ | 2x-1 | Resposta: 11 1 (-∞, ] U [ 3, + ∞ ) – { } 7 24) Solução: Resposta: 3 x 4 3 tg 30° = = x= m 3 4 3 1 1 1 15) + + + 1 + sen x 1 + cos x 1 + sec x 1 + csc 2 x 2 2 2 Solução: 1 1 Resposta: 2 sec x = e csc x = cos x sen x 2x − 36) –2 ≤ <7 6 Solução: –12 ≤ 2x – 3 < 42 Resposta: − 9 45 [ , ) 2 27) Determinar a reta que passa pela interseção das circunferências x² + y² – 2x – 2y + 1 = 0 e x² + y² – 8x – 2y + 13 = 0 e pelo v’rtive da parábola y = (x-3)². Solução: x² + y² – 2x – 2y + 1 = 0 Resposta: x+y=3 – x² – y² + 8x + 2y – 13 = 0 6x –12 = 0 x=2 y = 1 P(2,1) Parábola: vértive = V(3,0)
  • 2. 8) Solução: Resposta: c + 300 = 3000 # X = 4100 c + 300 + b + 400 = 8000 # Y= 5300 300 + b + 400 + a = 9000 c = 2700 b = 4600 c = 3700 # ( X U Y ) = 9000 # ( Y U Z ) = 8000 # Z = 30009) 2 cos θ - 3 = 0 Solução: 2 cos θ = 3 Resposta: θ = 30° 3 cos θ = 2 3 cos 30° = 2 a 2 + b2 + c210) a + b + c = 3, abc = 1 e ab + bc + ca = 4. Calcule 2abc Solução: (a + b + c)² = 3² Resposta: 1 a² + b² + c² + 2ab + 2bc + 2ca = 9 2 a² + b² + c² + 2(ab + bc + ca) = 9 a² + b² + c² + 2(4) = 9 a² + b² + c² = 1 a 2 + b2 + c2 1 = 2abc 2×1

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