Exercícios de Matemática Aplicada

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Lista 1 - To´picos de matema´tica aplicada (Cap´ıtulo de revisa˜o) (2013)
Professora Claudia
1. Calcular o valor nume´rico das expresso˜es:
a) 20− (−45)
(−3)2 + (−2)(−1)
5 (Resp: 27)
b) 14 + (−2)4 − (−2)3 + 07 + 320 + 8.22 (Resp: 58)
c) −(−2)3 + (−1)0 −
√
25− 32 − 5
3
25
(Resp: 0)
d)
−(−2)2 − 3
√
27
(−3 + 5)0 − 2 (Resp: 7)
e)
(
1
4
)2
.
4
5
+
2
5(
2
3
)3 (Resp: 75)
f)
(
1− 1
2
)
3
4
+
1
5(
1− 4
5
)2 (Resp: 173 )
g) 2−1 + 6.
(
2
3
)−2
−
(
−1
3
)−1
(Resp: 17)
2. Resolva as seguintes equac¸o˜es.
a) 2x− 3 = 17 (Resp: 7)
b) 4x + 7 = x− 8 (Resp: −5)
c) 3− 7(1− 2x) = 5− (x− 9) (Resp: 6
5
)
d)
2x− 3
6
− x− 1
8
=
3x− 5
12
(Resp: 1)
e)
x
4
− 2x− 1
3
=
x + 1
6
(Resp: 2
7
)
f) x− x− 2
3
= 2− 2− x
4
(Resp: 2)
3. Determine as seguintes equac¸o˜es.
a) x2 − 3x + 2 = 0 (Resp: S = {2, 1})
b) −x2 + 7x− 10 = 0 (Resp: S = {2, 5})
c) 5x2 − x + 7 = 0 (Resp: ∆ < 0 enta˜o S = { })
d) x2 − 25 = 0 (Resp: S = {−5, 5})
e) 5x2 − 10x = 0 (Resp: S = {2, 0})
f) 5 + x2 = 9 (Resp: S = {2,−2})
g) 7x2 − 3x = 4x + x2 (Resp: S = {0, 7
6
})
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