Ed calculo geometria analitica

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Ed calc. De geometria analítica
1) Agricultura atual Terr a Nossa 20- 10-10 10-10- 20 100Kg 300Kg 10 0+300=400 
20+30=50 (50/400)x10 0=12,5% 10+30 =40 (40/400)x100=10% 10+60=70 
(70/400)x100=17,5% 12,5-10-17, 5 
 
2) 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) h=-4,9t²+49 T axa de variaç ão Altura do prédio=4 9cm dh/dt=h'(t)= -9,8t 0 =-4,9t²+49 
4,9t²=49 t²=10 t=3,16s tempo de queda é de a proximadam ente 3,2s 
 
 
4)IB(t)=t²-24t+143 x v=-b/2a yv=-b²-4ac/4a xv=- (-24/2) yv=-( 576-572/4) xv=12 yv=-4/4 
yv=-1 tmin=12 I Bmin=-1 
Resposta:E
 
 
5)Segmento AB A B=(1-(-2),- 4-3) A=(-2,3) AB=(3,- 7) B=(1,-4) 
6)cos0º=1 v3=1,732 u .v.θ 45º=0,707 6.9. -0,866 90º=0 -46,764=-27v 3 150º=-0,866 180º=-1 
 
7)u+v u=2i+3j- k v=-i+2j u+v=i+5j- k u.v u.v=2.-1 i3.2j-1.0k u.v=-2i+6j Resposta:B 
 
8)u=5i+2j-k v=-4i+2j+k u.v=5.-4i2 .2j-1.1k u.v=-20 i+4j-k u.v=-20+4-1 u.v=-17 
 Resposta:C 
 
9)V(t)=15t²-750t+ 9000 V(3)=15(3)²- 750(3)+9000 V(3)= 135-2250+9 000 V(3)=6885 
 Resposta:A
10)ΔV/Δt=V'=2.15t- 750 V'=30t-75 0 V'=30.3-750 V'= 90-750 V'=660 L/h 
 Resposta:E
11)v(t)=-4,5t²+18t v' =-9t+18 v(t)=- 4,5.(2)²+18.2 9t- 18=0 v(t)=-1 8+36 9t=18 v(t)=18 m/s t=2s 
Resposta:D
 
12)|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 
 Resposta:A
 
13)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 Resposta:A
 
 
14)AO+DE+PL+FQ+IH AO+OD+DM+ML+L P AP 
Resposta:A
15)AQ=AC+CG+GQ AQ=AC+AE+2/3GH AQ =AE+AC+2/3AB 
Resposta:E
16) 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
Resposta:D
 
17) x+12/6=3/9 9(x+12)= 3.6 9x+108=18 9x= -108 +18 9x=-90 x =-10
Resposta:B 
 18) |s|=√3²+(-6)² |s|=√9+36 |s|=√45 |s |=3√5 
 Resposta:D
19) 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 
Resposta:B
 
20)AB=(x2-x1, y2-y1) A=(-1,0) B =(-2,1) AB=(-2-( -1),1-0) AB=(-1,1) |AB |=√(-1)²+1² A B/|AB|=(-1/√2,1/√2) |AB|=√1+1 A B/|AB|=(-1.√2/√2.√2 ,1.√2/√2.√2) |AB|=√2 AB/|AB|=(-√ 2/2,√2/2) |AB| 
Resposta:B 
 
21)V(t)=6t³+1,5t V(t)=6.2³ +1,5.2 V( t)=6.8+3 V(t)=48+3 V(t)=51 
 Resposta:C
 
22)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 
 Resposta:B
23)y=(x+16).senx y'=u'.v+u.v' y'=1.senx+(x+16).cosx y'=senx+(x+16).cosx 
 Resposta:B
 
24)f(x)=x³ -8 xo=-2 y'=3x² a=f'( -2) f'(-2)=3.(-2)² f'(-2)=3.4 f'( -2)=12 
 Resposta:A
 
25) 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´(s en2x+cos2x)).2 f'(0)=((e0.(sen2.0+cos 2.0)).2 f'(0)=((1.(0+1)).2 f '(0)=1.2 f '(0)=2 
 Resposta:A
 
26)u=(2,-4) u.v =(2.0+4.-3) v=(0,-3) u. v=(0+12) u.v=12 
 Resposta:E
27) u=(2,-4) 2.u=(2 .2,2.-4) 2u(4,- 8) v=(1,-2) 5.v=(5.1,5. -2) 5v(5,-10) 2 u.5v=(4.5+(- 8.-10)) 
2u.5v=(20+80) 2u.5v=1 00 
Resposta:C
 
28) 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 
 Resposta:A
 
29) |u|=2 A=b.h |v|=3 A=|u|.|v|.senθ/2 θ=3 0º A=2.3.0,5/2 A=1,5u A 
 Resposta:E
 
30) 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+1 00=2√30 a²+b²+c²=2√30 w=√120=2√30 
w=2√30=2√30 2a+b =0 a-2b- c=0 2.2-4=0 2-(-2.-4) -10=0 w=(2,-4,10) 0 =0 2+8-10=0 |w|=2√30 
0=0 
 Resposta:B
 
31) u=(1,-2,-1) v=(2,1,0) u.v=(1.2+( -2.1)+(-1.0)) u.v=(2-2+0) u.v=0 
 Resposta:A
32) |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 Resposta:C 
33) 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 
Resposta:B 
 
34) 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| 
 Resposta:A
35) f(x)=e(cosx ) u=cosx u'=-s enx 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/x ²+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 
 Resposta:D
 
36) 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(x ²+4x).2x+4 f'(x)=(x²+4x)².(6x+12) 
 Resposta:C
 
37) 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 Resposta:D
 
 
38) v=ds/dt=>ds=v.dt s= ʃv.dt 16=-2.1³ +7.1²+c s=ʃ(14t-6 t²).dt 16=-2+ 7+c s=14t²/2-6t ³/3+c 16=5+c 
s=7t²-2t³+c c=11 s =7t²-2t³+11 
Resposta:B
 
 
39) ʃ(2x+cosx)dx = s enx+2x²/2+c X²+senx+c 
Resposta:A
 
 
40) 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
Resposta:C