ED 482X Respostas

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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