Resposta ed de Top de matematica

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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