1.5 10^-9 9.8/(100 1.9 10^-19)

rr:=PowerExpand[%/. repSI/. repSIe]

({{repSI:={G->((6.67` n (m^2))/((10^11) (kg^2))),g->((9.8` m)/(s^2)),Mearth->6.` (10^24) kg,Msun->2.` (10^30) kg,Rearth->6400 km,AU->150.` (10^6) km,cm->0.01` m,mm->0.001` m,km->1000 m,mile->1609 m,hour->3600 s,min->60 s,deg->((π rad)/180),gram->0.001` kg,joule->n m,n->((kg m)/(s^2)),rad->1,in->2.54` cm,ft->12 in}}})({{repSI:={G->((6.67` n (m^2))/((10^11) (kg^2))),g->((9.8` m)/(s^2)),Mearth->6.` (10^24) kg,Msun->2.` (10^30) kg,Rearth->6400 km,AU->150.` (10^6) km,cm->0.01` m,mm->0.001` m,km->1000 m,mile->1609 m,hour->3600 s,min->60 s,deg->((π rad)/180),gram->0.001` kg,joule->n m,n->((kg m)/(s^2)),rad->1,in->2.54` cm,ft->12 in}}})

({{repSI:={G->((6.67` n (m^2))/((10^11) (kg^2))),g->((9.8` m)/(s^2)),Mearth->6.` (10^24) kg,Msun->2.` (10^30) kg,Rearth->6400 km,AU->150.` (10^6) km,cm->0.01` m,mm->0.001` m,km->1000 m,mile->1609 m,hour->3600 s,min->60 s,deg->((π rad)/180),gram->0.001` kg,joule->n m,n->((kg m)/(s^2)),rad->1,in->2.54` cm,ft->12 in}}})({{repSI:={G->((6.67` n (m^2))/((10^11) (kg^2))),g->((9.8` m)/(s^2)),Mearth->6.` (10^24) kg,Msun->2.` (10^30) kg,Rearth->6400 km,AU->150.` (10^6) km,cm->0.01` m,mm->0.001` m,km->1000 m,mile->1609 m,hour->3600 s,min->60 s,deg->((π rad)/180),gram->0.001` kg,joule->n m,n->((kg m)/(s^2)),rad->1,in->2.54` cm,ft->12 in}}})({{repSI:={G->((6.67` n (m^2))/((10^11) (kg^2))),g->((9.8` m)/(s^2)),Mearth->6.` (10^24) kg,Msun->2.` (10^30) kg,Rearth->6400 km,AU->150.` (10^6) km,cm->0.01` m,mm->0.001` m,km->1000 m,mile->1609 m,hour->3600 s,min->60 s,deg->((π rad)/180),gram->0.001` kg,joule->n m,n->((kg m)/(s^2)),rad->1,in->2.54` cm,ft->12 in}}})

repSIe:={me->9.1`*^-31 kg,mp->1.67`*^-27 kg,e->-1.6`*^-19 coul,ep0->((8.841941282883074`*^-12 (coul^2))/((m^2) n)),k->ke,mu0->((1.2566370614359173`*^-6 m tesla)/amp),muC->1.`*^-6 coul,nC->1.`*^-9 coul,mF->.001far,muF->1.`*^-6 far,nF->1.`*^-9 far,Mohm->1.`*^6 ohm,MOhm->1.`*^6 ohm,kOhm->1000.` ohm,kV->1000.` volt,MV->1.`*^6 volt,mT->0.001` tesla,mH->0.001` henry,far->(coul/volt),ohm->(volt/amp),volt->(joule/coul),amp->(coul/s),tesla->((n s)/(coul m)),henry->(((m^2) tesla)/amp)}

k nC/mm^2

rr

ke=9.*10^9 n m^2/coul^2

ke e^2/cm^2

rr

Solve[50m/s t==1/2 3m/s^2 (t-1s)^2,t]

%//N

Plot[{50t, 1/2 3 (t-1)^2}, {t,0,36}]

d t+c t^2+b t^3

D[%,t]

%/.{d->m/s^2,c->-4m/s^3,b->3m/s^4}

%/.t->2s

((30m/s)^2-(10m/s)^2)/(2 80m)

A={-3,2,0};B={1,2,0}

Cross[A,B]

Norm[3. A-6B]

A.B

ArcCos[1/Norm[B]/Norm[A]]180./Pi

200/g

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(100m/s)^2/(2g)

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250mile/hour^2

rr

%//N

/m

8.4^2/90

dis=t Sin[t]

vel=D[dis,t]

acc=D[vel,t]

Plot[{dis+5,vel,acc,dis+5.1,-vel-3}, {t,0,10},PlotStyle->{Black,Red,Blue,Black,{Red,Dashed}}]

Show[Plot[{dis+5,vel,acc,dis+5.1,-vel-3}, {t,0,10},PlotStyle->{Black,{ Red,Dashing[{.05,.02}]},Blue,Black,{Red,Dashed}}],Graphics[{Text[Style["x(t)",Medium], {2,8}],Text[Style["A",Medium], {5,6.2}],Text[Style["B",Medium], {7.5,6}],Text[Style["C",Medium], {5.5,-4.75}]}],Ticks->None,LabelStyle->Medium, AxesLabel->{"t"," "}]

250mile/hour

rr

%//N

Clear[a,b];a={1,2,3};b={4,-5,6}

Norm[a+b]

%//N

(*111exam2F23*)

Integrate[6n+3x^2 n/m^2,{x,0m,3m}]

Solve[1/2 3kg (v^2-4^2 m^2/s^2)==45 joule,v]

rr

%//N

108m/s Sqrt[2 85m/g]

rr

N[%]

Sqrt[(108m/s)^2+2g 85m]

rr

rr

1.6kg g

1.54 g kg

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64 kN 25/(25+3.3)

Sqrt[(10.2m/s)^2+2g 30m]

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4.25 kg (g-1.7 m/s^2)

rr

Norm[{15,20}]n/(17.7m/s^2)

rr

Sin[44deg]-.6*Cos[44deg]

g*%

rr

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g(-2.5Sin[45deg]+3.5Cos[30deg])

rr

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%/(2.5+3.5)

Sqrt[g 20m]

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(2Pi/3.14/s)^2 3.5m 30kg

30g

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Sqrt[.65 g 30m]

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120kg g .6

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80kg (g-(180m/s)^2/1.35/km)

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Clear[a,b];

{2,-3,5}.({3,-1,2}-{0,1,2})n*m

(120volt)^2/(1.26 10^-6 ohm m 9.3m)Pi (.92mm/2)^2

rr

1.67amp/(Pi(1.02mm)^2/4)

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20n/coul 3muC 10m

rr

rr

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Solve[1/2 me v^2==-e 9.9kV,v]

rr

3.9 10^6 volt/m ep0

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4cm cm 22 n/coul Cos[70deg]

rr

rr

5muC 3muC k /.3 /m

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9/6.5  49 49/2 10^-6

18+2.4 9

25 6.5 10^9

52 5/8

%//N

52 3./8

1.3 10^-6 muC/m^3 Pi (.03m)^2 .04m/ep0

rr

{6,-3}.{-1,-2}

Sqrt[2g 5m 2/6.]

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Sqrt[2g 5m 2/9.]

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Sqrt[50^2+2 9.8 70]

40000km/(8km/s)

6400*(24 3600/5000)^(2/3)

%//N

8. 1/Sqrt[1+910/6400]

6. Sqrt[13]

Sqrt[2 .1^2 g kg^2 12m]

rr

.5 3200n/m (4.8cm)^2-.5 2.9kg (1.6m/s)^2

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1/2 (5.7m/s)^2-3m g Sin[11deg]-.36 g 3m Cos[11deg]

rr

rr

Clear[L,t,mu,v];Solve[g L Sin[t]-1/2 v^2==-mu g Cos[t]L,L]

L/.%[[1]]

%/.{v->5.7m/s,t->11deg,mu->.36}

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192n/64-1500g/4900 kg

rr

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800n Sin[deg(180-30-45)]-.5*80kg g Sin[30deg]-120kg g Sin[30deg]

rr

rr

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%/.{kg->1,m->1,s->1}

117 15-50 35

Clear[rhoR, V, rho];Solve[{ rhoR V g==61.9n,rhoR V g-rhoW V g==37.6n, rhoR V g-rho V g==19.4n },{rhoR,V,rho}]

%%/.rhoW->1000kg/m^3

1/2 3kg (.7m/s)^2-kg g m+.925 2kg g m

rr

Solve[1/2 (mA+mB)v^2-mB g h==-mu mA g h,mu]

mu/.%[[1]]

%/.{mA->2kg,mB->kg,h->m,v->.7m/s}

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1/2 3kg (.7m/s)^2-kg g m+.4625 2kg g m

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28muC/(10cm)^2 k

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Sqrt[2(-e)/me 3750volt]

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k (7.36 10^-7coul)^2/(15cm)^2

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mu0 3amp/(2Pi 7.5cm)

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Pi(.025m)^2 3  .38tesla/s/(.39ohm)

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mu0 Pi (2cm)^2 (100/m)^2  80cm 0.2 amp/s

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%/volt
rr

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1/20+2/10

4k 10nC/m/(10cm)

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Integrate[1/(y^2+1)^(3/2),{y,0,z}, Assumptions->z>0]

%/.z->L/(2d)//Simplify

2k lam/d*L/Sqrt[L^2+4d^2]

Clear[A,B,a,b,c]; A={3,-5,0};B={5,4,0};

Norm[3A+2B]//N

A.B

180./Pi ArcCos[-5/Norm[A]/Norm[B]]

Cross[A,B]

k e^2/(.53 10^(-10)m)^2/me

rr

kq (1/(x-a)^2-1/(x+a)^2)//Simplify

%-4a kq x/(x^2-a^2)^2

%//Simplify

k (6nC)^2/(2cm)^2 1.41

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k 4muC(9muC/(6cm)^2+3muC/(12cm)^2)

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k 24muC 2cm/cm^3

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.003gram g/250 /nC

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2k 4nC 4cm Sqrt[3]/(8cm)^3

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4k muC 1.41cm/cm^3

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2k 10nC/m/10/cm

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(*121e3S24*)

q=-2.e;mm=4mp;v=4 10^6m/s{1,0,1};B=6tesla{1,1,0}

q  Cross[v,B]/mm

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Clear[e,q,mm,v,B];

3.75/2

% 4

mu0 2 amp 3.amp 6/(2Pi)(1/2-1/6)

rr

mu0 36amp/8 /cm(1/30-1/40)

rr

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%/(10^-6 tesla)

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mu0/(16cm) 3/8

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%/(10^-6 tesla)

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mu0 16amp/(2Pi 8cm)3/8

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% 10^6/tesla

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mu0 7.4amp 200/cm/tesla

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50m/s 3m 16tesla/1200/ohm

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2 10^-28 kg 1.4 10^6 m/s/(e 5cm)/tesla

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Cross[{1,0,1},{1,1,0}]

mu0 1.88amp 7.5 amp/(.25cm)

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mu0 (6amp^2)6cm/cm((1/2-1/6))/2/Pi

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