Ed engenharia unip - complementos de física

9 A
V(t) =15t2-750t+9000
V(3) = 15(3)² - 750(3) + 9000
V(3) = 15.9 – 2250 + 9000
V(3) = 135 -2250 + 9000
V(3) = 6885

10 E
V(t) =15t2-750t+9000
V’(t) = 15.2t – 750 + 0
V’(t) = 30t - 750
V’(3) = 30.(3) - 750
V’(3) = 90 - 750
V’(3) = -660 litros/hora

14 A
AO + OD + DP
Cancela PL e IH

15 A
AQ = AE + EG + GP + PQ
.’. AQ = AE + AC + 2/3 AB

23 B
Pois y'=u.u'
.'. y'=senx+(x+16).cosx

24 A f(x)=x³-8 f'(x)=3x²-0 f'(-2)=3(-2)²-0 f'(-2)=3.4-0
.'. f'(-2)=12

25 A
F(x)=e^x . sen(2x)
F’(x)=1e^x . 2cos2x
F’(0)=1 .2cos0
F’(0)=1 . 2 . 1
F’(0)=2

26 E
u.v = (2,-4).(0,-3)
u.v = 2.0+(-4.-3)
u.v = 0+12
.'. u.v = 12

27. C
u.v=2.u . 5.v= 2(2,-4).5(1,-2)
u.v=(4,-8).(5,-10)
u.v=(4.5-(-8.10))
u.v=20+80
.’. u.v=100

31 A
u.v=(1.2+(-2).1+(-1).0)
u.v=(2-2-0)
.'. u.v=0

33 B
u.v=(1.2+x.1+8.(-4))
u.v=2+x-32
u.v=x-30
.'. se são ortogonais, iguala a zero => x-30=0 x=30

36 C

Pois, na afirmativa I a derivada de f(x)=sen(2x + 4) = f'(x)=2cos(2x + 4)

37 D

Pois: I - F'(x)=3x³-¹+0=3x² (primitiva) II - F'(x)=4x^4-1 +0=4x³ (primitiva)
III - F'(x)=5x^5-1 -0=5x^4 (primitiva)

38 B
S=ʃ(14t-6t²)dt
S=14t²/2 - 6t³/3 + c
S=7t²-2t³+c
16=7(1)²-2(1)³+c
16=7-2+c
16=5+c c=16-5 => c=11
.'. S(t)=7t²-6t³+11

39 A ʃ(2x+cosx)dx = 2x²/2 + senx + c
.'. =x²+senx+c

40 C
Pois na alternativa III ʃxe^xdx =