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PREPARATORIO DE SEGUNDO EXAMEN PARCIAL
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2 p mat100ab
1.
MAT100A Demostrarque lospuntosA(5;8) B(5;3)
y C(6;-2) formanparte de untriángulorectángulo. SeanlospuntosR(1;4) S(0;8) y T(8;-5) que formanparte de una circunferencia,determinarsu centro. Determinarunpuntode intersecciónentre las curvas: L1: 𝑒𝑥 7 − 4 9𝜋 𝑦 = 2 15 L2: 5 2 𝑦 − 6 9 (𝑥 − 3𝜋 7 ) = 2𝑒 Hallarel conjuntosolución 𝒙 ≥ −𝟏𝟖 ∧ −𝟓𝒙 > −𝟒 ∧ 𝟒 ≤ 𝟓𝒙 < 𝟒𝟓 Hallarel conjuntosolución 𝟕 < 𝒙 ∨ [0 ≥ 𝑥 ∧ ({𝟐, 𝟒} ∨ 𝟓 < 𝒙 < 𝟗 − {𝟔})] 𝑥 ≤ 0 − {−8} ∨ 𝑥 ≥ 2 → ]7;2] ∪ [4; +∞[ {6} ∪ [4;+∞[
2.
]7;2] ∩ [4;
+∞[ {6} ∩ [4;+∞[ MAT100B Definirel tipode triánguloque formanpuntosA(-5;9) B(6;3) yC(-3;-2). Determinarel centrode lacircunferencia;si lospuntosR(-1;4) S(0;8/3) y T(8/5;-5) que forman parte de dichacircunferencia. Determinarunpuntode intersecciónentre lascurvas: L1: 𝑥 7 − 4 9𝜋 𝑦 = 2 15 L2: 5 2 𝑦 − 6 9 (𝑥 − 𝜋 7 ) = 2𝑒 Hallarel conjuntosolución −𝟑𝒙 > −𝟒 ∧ 𝒙 ≥ −𝟐𝟓 ∧ 𝟑 ≤ 𝟒𝒙 < 𝟒𝟖 Hallarel conjuntosolución 𝟔 < 𝒙 ∨ [0 ≥ 𝑥 ∧ ({𝟐,−𝟒} ∨ 𝟓 < 𝒙 < 𝟏𝟎 − {𝟔, 𝟕})] ]6;10] ∪ [5;+∞[ {6,7} ∩ [6;+∞[
3.
]6;7] ∪ [10;+∞[ {6,10}
∩ [2;+∞[
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