Gabarito-ED- 2° Sem. Engenharia-UNIP

1-Resp. B

Agricultura atual 20-10-10 100Kg

Terra Nossa       10-10-20 300Kg

100+300=400

20+30=50 (50/400)x100=12,5%

10+30=40 (40/400)x100=10%

10+60=70 (70/400)x100=17,5%

2-Resp. A

a=(y2-y1)/(x2-x1) 0=-2.35+b

a=(60-0)/(5-35) b-70=0

a=60/-30 b=70

a=-2 y=-2x+70

2x=-y+70

x=-0,5y+35

3-Resp. D

h=-4,9t²+49 Taxa de variação

Altura do prédio=49cm dh/dt=h'(t)=-9,8t

0=-4,9t²+49

4,9t²=49

t²=10

t=3,16s

tempo de queda é de aproximadamente 3,2s

4-Resp. E

IB(t)=t²-24t+143

 xv=-b/2a yv=-b²-4ac/4a

xv=-(-24/2) yv=-(576-572/4)

xv=12 yv=-4/4

yv=-1

 tmin=12

IBmin=-1

5-Resp. E

Segmento AB AB=(1-(-2),-4-3)

A=(-2,3) AB=(3,-7)

B=(1,-4)

6-Resp. B

cos0º=1 v3=1,732 u.v.θ

45º=0,707 6.9.-0,866

90º=0 -46,764=-27v3

150º=-0,866

180º=-1

7-Resp. B

u+v u=2i+3j-k

 v=-i+2j

 u+v=i+5j-k

 u.v u.v=2.-1i3.2j-1.0k

 u.v=-2i+6j

8-Resp. C

u=5i+2j-k v=-4i+2j+k

 u.v=5.-4i2.2j-1.1k

 u.v=-20i+4j-k

 u.v=-20+4-1

 u.v=-17

9-Resp. A

V(t)=15t²-750t+9000

 V(3)=15(3)²-750(3)+9000

 V(3)=135-2250+9000

 V(3)=6885

10-Resp .E

ΔV/Δt=V'=2.15t-750

 V'=30t-750

 V'=30.3-750

 V'=90-750

 V'=660L/h

11-Resp. D

v(t)=-4,5t²+18t

 v'=-9t+18 v(t)=-4,5.(2)²+18.2

 9t-18=0 v(t)=-18+36

 9t=18 v(t)=18m/s

 t=2s

12-Resp. A

u|=√(-3)²+4²+0² -0,6/-3=0,8/4

 |u|=√9+16+0 -0,6.4=-3.0,8

 |u|=√25 -2,4=-2,4

 |u|=5

1=√(-0,6)²+0,8² 9/-3=-12/4

 1=√0,36+0,64 4.9=-12.-3

 1=√1 36=36

 1=1

 |u|=√9²+12²

 |u|=√81+144

 |u|=√225

 |u|=15

13-Resp. A

w=α.u+β.v

 (-17,12)=α.(-2,0)+β.(3,-4)

 (-17,12)=-2α+3β;-4β+0

  -4β=12 -2α+3β=-17

 -β=3 -2α+3.-3=-17

 β=-3 -2α=-17+9

 -2α=-8

 α=4

14-Resp. A

AO+DE+PL+FQ+IH

 AO+OD+DM+ML+LP

 AP

15-Resp. E

AQ=AC+CG+GQ

 AQ=AC+AE+2/3GH

 AQ=AE+AC+2/3AB

16-Resp. D

u=(1,-2) 2u=(2,-4)

 v=(-4,0) 4v=(-16,0)

 2u-4v=(2-(-16),-4-0)

 2u-4v=(18,-4)

 u=(1,-2) |u+V|=√(-3)²+(-2)²

 v=(-3,0) |u+v|=√9+4

 u+v=(-3,-2) |u+v|=√13

 1/4=-2/0

 8≠0

17-Resp. B

x+12/6=3/9

 9(x+12)=3.6

 9x+108=18

 9x=-108+18

 9x=-90

 x=-10

18-Resp. D

|s|=√3²+(-6)²

 |s|=√9+36

 |s|=√45

 |s|=3√5

19-Resp. B

AB=(x2-x1,y2-y1) A(-1,3) B(0,-4)

 AB=(0-(-1),-4-3)

 AB=(1,-7)

 1/4=-7/28

 1.28=-4.-7

 28=28

20-Resp. B

AB=(x2-x1,y2-y1) A=(-1,0) B=(-2,1)

 AB=(-2-(-1),1-0)

 AB=(-1,1)

 |AB|=√(-1)²+1² AB/|AB|=(-1/√2,1/√2)

 |AB|=√1+1 AB/|AB|=(-1.√2/√2.√2,1.√2/√2.√2)

 |AB|=√2 AB/|AB|=(-√2/2,√2/2)

 |AB|

21-Resp. C

V(t)=6t³+1,5t

 V(t)=6.2³+1,5.2

 V(t)=6.8+3

 V(t)=48+3

 V(t)=51

22-Resp. B

V(t)=6.t³+1,5t

 V'=3.6t²+1,5

 V'=18t²+1,5

 V'=18.2²+1,5

 V'=18.4+1,5

 V'=72+1,5

 V'=73,5L/min

23-Resp. B

y=(x+16).senx

 y'=u'.v+u.v'

 y'=1.senx+(x+16).cosx

 y'=senx+(x+16).cosx

24-Resp. A

f(x)=x³-8 xo=-2

 y'=3x² a=f'(-2)

 f'(-2)=3.(-2)²

 f'(-2)=3.4

 f'(-2)=12

25-Resp. A

 f(x)=ex.sen(2x) u=2x

 f'(x)=(ex.senu+ex.cosu).u' u=2

 f'(x)=((ex.(senu+cosu)).u'

 f'(x)=((ex´(sen2x+cos2x)).2

 f'(0)=((e0.(sen2.0+cos2.0)).2

f'(0)=((1.(0+1)).2

 f'(0)=1.2

 f'(0)=2

26-Resp. E

u=(2,-4) u.v=(2.0+4.-3)

 v=(0,-3) u.v=(0+12)

 u.v=12

27-Resp. C

u=(2,-4) 2.u=(2.2,2.-4) 2u(4,-8)

 v=(1,-2) 5.v=(5.1,5.-2) 5v(5,-10)

 2u.5v=(4.5+(-8.-10))

 2u.5v=(20+80)

 2u.5v=100

28-Resp. A

u=(2,-4,2) A=|u˄v|

  v=(1,-4,0)

 |ij k i j| ijk

 |u˄v|=|1-40 1 -4| -80-4

 |2-42 2 -4| -(0-28)

 (-8,-2,4)

 A=|(-8,-2,4)|=√(-8)²+(-2)²+4²=√84

 A=2˄√21

29-Resp. E

|u|=2 A=b.h

 |v|=3 A=|u|.|v|.senθ/2

 θ=30º A=2.3.0,5/2

 A=1,5uA

30-Resp. B

u=(1,-2,-1)

 v=(2,1,0)

 w.u=0 (a,b,c).(1,-2,-1)=a-2b-c=0

 w.v=0 (a,b,c).(2,1,0)=2a+b =0

 a-2b-c=0 w=√2²+(-4)²+10²=2√30

 2a+b =0 w=√4+16+100=2√30

 a²+b²+c²=2√30 w=√120=2√30

31-Resp. A

u=(1,-2,-1)

 v=(2,1,0)

 u.v=(1.2+(-2.1)+(-1.0))

 u.v=(2-2+0)

 u.v=0

32-Resp. C

|u|=3 (u+v).(u+2v)

 |v|=4 u²+2.v.u+u.v+2.v²

 3²+2.0+0+2.4²

 9+0+0+32

 41

33-Resp. B

u=(1,x,8)

 v=(2,1,-4)

 u.v=0

 (1.2+x.1+(8.-4)=0

 (2+x-32)=0

 x-30=0

 x=30

34-Resp. A

u=(0,-3,-1) i j k

 v=(2,4,0) 0 -2 0

 4 0 6

 | i j k i j | u˄v=(4,-2,6)

 u˄v=|0 -3 -1 0 -3|

 | 2 4 0 2 4|

35-Resp. D

f(x)=e(cosx)

 u=cosx u'=-senx

 f'(x)=e(u).u'

 f'(x)=-senx.e(cosx)

 f(x)=ln(x²+4) u'=2x

 u=x²+4

 f(x)=ln(u)

 f(x)=1/u.u'

 f'(x)=1/x²+4.2x

 f'(x)=2x/x²+4

 f(x)=√3x+6 u'=3

 f(x)=(3x+6)1/2 f(x)=3/2.1/u1/2

 u=3x+6 f(x)=3/2√3x+6

 f'(x)=(u)1/2

 f'(x)=1/2.u-1/2.u'

 f'(x)=3/2.u-1/2

36-Resp. C

 f(x)=sen(2x+4) u'=2

  u=2x+4

 f(x)=sen(u)

 f'(x)=cos(u).u'

 f'(x)=2cos(2x+4)

 f(x)=cos(3x+6) u'=3

 u=3x+6

 f(x)=cos(u)

 f'(x)=-sen(u).u'

 f'(x)=-sen(3x+6).3

 f'(x)=-3sen(3x+6)

 f(x)=(x²+4x)³

 u=x²+4x u'=2x+4

 f(x)=(u)³

 f'(x)=3u².2x+4

 f'(x)=3(x²+4x).2x+4

 f'(x)=(x²+4x)².(6x+12)

37-Resp. D

F(x)=x³+4 (x³+4)'=f(x)

 f(x)=3x²

 F(x)=x^4+2 (x^4+2)'=f(x)

 f(x)=4x³

 F(x)=x^5-2 (x^5-2)'=f(x)

 f(x)=5x^4

38-Resp. B

v=ds/dt=>ds=v.dt

 s=ʃv.dt

 16=-2.1³+7.1²+c s=ʃ(14t-6t²).dt

 16=-2+7+c s=14t²/2-6t³/3+c

 16=5+c s=7t²-2t³+c

 c=11 s=7t²-2t³+11

39-Resp. A

ʃ(2x+cosx)dx = senx+2x²/2+c

 X²+senx+c

40-Resp. C

ʃ(senx+4)dx ʃ(1/x+12)dx f(x)=ex

 -cosx+C+4x ln|x|+c+12x (ex)'=f(x)

 -cosx+4x+C ln|x|+12x+c