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1) Agricultura atual Terra Nossa 20-10-10 10-10-20 100Kg 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% 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 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)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)Segmento AB AB=(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=-27v3 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.-1i3.2j-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=-20i+4j-k u.v=-20+4-1 u.v=-17 9)V(t)=15t²-750t+9000 V(3)=15(3)²-750(3)+9000 V(3)=135-2250+9000 V(3)=6885 10)ΔV/Δt=V'=2.15t-750 V'=30t-750 V'=30.3-750 V'=90-750 V'=660L/h 11)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)|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)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)AO+DE+PL+FQ+IH AO+OD+DM+ML+LP AP 15)AQ=AC+CG+GQ AQ=AC+AE+2/3GH AQ=AE+AC+2/3AB 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 17) x+12/6=3/9 9(x+12)=3.6 9x+108=18 9x=-108+18 9x=-90 x=-10 18) |s|=√3²+(-6)² |s|=√9+36 |s|=√45 |s|=3√5 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 20)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)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)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)y=(x+16).senx y'=u'.v+u.v' y'=1.senx+(x+16).cosx y'=senx+(x+16).cosx 24)f(x)=x³-8 xo=-2 y'=3x² a=f'(-2) f'(-2)=3.(-2)² f'(-2)=3.4 f'(-2)=12 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´(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)u=(2,-4) u.v=(2.0+4.-3) v=(0,-3) u.v=(0+12) u.v=12 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) 2u.5v=(4.5+(-8.-10)) 2u.5v=(20+80) 2u.5v=100 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 29)|u|=2 A=b.h |v|=3 A=|u|.|v|.senθ/2 θ=30º A=2.3.0,5/2 A=1,5uA 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+100=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 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 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 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 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| 35)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) 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)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)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)ʃ(2x+cosx)dx = senx+2x²/2+c X²+senx+c 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
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