Wolfram|Alpha Activity - Topic, College Algebra Activities - Sample

CHTKKT KVQJ@TH]O@G ∔ ^@@J@LOS]

]yqk $^``j`los}$ og}` \`jethbzHjqfh skhtcf kglogk' [sk }fk tks{j}s }` hgs|kt }fk e`jj`|ogl x{ks}o`gs' 8' \fh} chtkkts htk lt`{qkm |o}f ~``j`los}0

4' F`| c{ttkg} |hs }fos mh}h lh}fktkm0

3' \fh} os }fk c{ttkg} bkmohg |hlk qkt ykht0

=' \fh} os }fk c{ttkg} bkhg |hlk qkt ykht0

;' \`jethbzHjqfh {sks }fk bkmohg |hlk qkt ykht }` }thci }fk |hlk fos}`ty' \fy m` y`{ }fogi }fk bkmohg |hlk |hs {skm th}fkt }fhg }fk bkhg |hlk0

5' \fh} os }fk ykhtjy cfhglk og bkmohg |hlk0

<' Jk}  v  tkqtkskg} }fk g{bdkt `e ykhts he}kt 411?' Hss{bogl }fh} }fk ykhtjy cfhglk `e bkmohg |hlk os c`gs}hg}' \fh} kx{h}o`g chg dk {skm }` eogm }fk |hlk `e h ~``j`los}0

6' [sk }fk kx{h}o`g e`tbkm og #< }` mk}ktbogk }fk bkmohg |hlk `e h ~``j`los} og 418;'

?' Og |fh} ykht |ojj }fk bkmohg |hlk `e h ~``j`los} s{tqhss -?;*1110

81' Skjkc} }fk $Sf`| kbqj`ybkg} fos}`ty$ jogi {gmkt }fk $Bkmohg \hlk fos}`ty$ skc}o`g' Chg y`{ bhik hgy c`gcj{so`gs c`gcktgogl }fk e{}{tk `e h chtkkt hs h ~``j`los}0

S{llks}o`gs> Skjkc} hg`}fkt chtkkt hgm tkskhtcf o} {sogl \`jethbzHjqfh' M`ks o} hqqkht }fh} }fk bkmohg |hlk os

ogctkhsogl h} h c`gs}hg} th}k0 ]ty }` mk}ktbogk hg hqqt`vobh}k kx{h}o`g e`t }fk tkjh}o`gsfoq dk}|kkg ykhts he}kt }fk c{ttkg} ykht hgm bkmohg |hlk' \fh} m`ks }fk kbqj`ybkg} fos}`ty sf`|0 Chg y`{ {sk hg kx{h}o`g }` sf`| }fk tkjh}o`gsfoq dk}|kkg g{bdkt `e qkts`gs kbqj`ykm og }fh} chtkkt hgm }obk he}kt }fk c{ttkg} ykht0

? C`jjklk Hjlkdth Hc}ouo}oks ]fk kg}otk sk} `e hc}ouo}oks os huhojhdjk dy c`g}hc}ogl y`{t Qkhts`g tkqtkskg}h}ouk'

Kx{h}o`gs hgm Ogkx{hjo}oks

[sogl \H

LJ@DHJ \HTBOGL

Skhtcf \`jethbzHjqfh e`t $|kh}fkt'$ 8' ]`mhy,s Mh}k>

J`ch}o`g>

4' Eojj og }fk e`jj`|ogl oge`tbh}o`g et`b }fk }hdjk e`{gm {gmkt $Fos}`tochj

]kbqkth}{tks e`t ]`mhy,s Mh}k'$ ]ty }` lk} h} jkhs} 81 ykhts `e mh}h' _`{ bhy fhuk }` cfhglk }fk j`ch}o`g }` h jhtlkt }`|g' Louk h sch}}kt qj`} `e }fk mh}h dkj`|'

_kht

v

Bhvob{b ]kbqkth}{tk & E/ y ±

8??? 4111 4118 4114 4113 411= 411; 4115

3' Eogm }fk jogkht eo} `e }fk jogk }` }fk mh}h' ]yqk $eo}$ hgm kg}kt c``tmogh}ks e`t }fk q`og}s loukg og }fk }hdjk>

 y  2

411< 4116 411?

=' Louk }fk sj`qk `e }fk kx{h}o`g> ;' \fh} m`ks }fk }fk sj`qk ogmoch}k ogmoch}k og }ktbs `e ykht hgm bhvob{b }kbqkth}{tk0 }kbqkth}{tk0 5' M`ks y`{t tks{j} ogmoch}k }fh} }fktk bhy dk h lj`dhj |htbogl qt`djkb0 Dtokejy kvqjhog y`{t hgs|kt' <' Skjkc} hg`}fkt mh}k e`t }fk shbk co}y' Lh}fkt }fk shbk }yqk `e fos}`tochj mh}h hgm eogm }fk jogkht eo} `e }fk

jogk }` }fk mh}h' mh}h' Jogkht Kx{h}o`g Kx{h}o`g>

 y  2

_kht

6' Htk y`{t tks{j}s &e`t #= hgm

8???

#< sobojht0 Louk h sf`t}

4111

kvqjhgh}o`g `g }fk sobojhto}oks hgm moeektkgcks `e }fk kx{h}o`gs'

4118

v

Bhvob{b ]kbqkth}{tk & E/ y ±

4114 4113 411= 411; 4115 411< 4116

S{llks}o`gs> Kvqhgm }fos qt`nkc} s` }fh} y`{ c`jjkc} mh}h `ukt }fk kg}otk

411?

ckg}{ty' ]ty hukthlk }kbqkth}{tks `t bogob{b }kbqkth}{tks ogs}khm `e {sogl bhvob{b }kbqkth}{tks' Cf``sk j`ch}o`gs og `}fkt qht}s `e }fk |`tjm }` skk oe }fktk os q`ssodjk lj`dhj |htbogl'

8; C`jjklk Hjlkdth Hc}ouo}oks ]fk kg}otk sk} `e hc}ouo}oks os huhojhdjk dy c`g}hc}ogl y`{t Qkhts`g tkqtkskg}h}ouk'

E{gc}o`gs hgm Lthqfs

[sogl \H

CHTKKT KVQJ@TH]O@G ∔ ^@@J@LOS]

]yqk $^``j`los}$ og}` \`jethbzHjqfh skhtcf kglogk' [sk }fk tks{j}s }` hgs|kt }fk e`jj`|ogl x{ks}o`gs' 8' \fh} chtkkts htk lt`{qkm |o}f ~``j`los}0

4' F`| c{ttkg} |hs }fos mh}h lh}fktkm0

\ojmjoek Do`j`los}

411?

3' \fh} os }fk c{ttkg} bkmohg |hlk qkt ykht0 -;;*811

=' \fh} os }fk c{ttkg} bkhg |hlk qkt ykht0

-;6*=61

;' \`jethbzHjqfh {sks }fk bkmohg |hlk qkt ykht }` }thci }fk |hlk fos}`ty' \fy m` y`{ }fogi }fk bkmohg |hlk |hs {skm th}fkt }fhg }fk bkhg |hlk0 ]fk bkmohg |hlk os jkss qt`gk }` dk heekc}km dy }fk folf |hlks qhom }` s{qktuos`ts'

5' \fh} os }fk ykhtjy cfhglk og bkmohg |hlk0 -8611

<' Jk}  v  tkqtkskg} }fk g{bdkt `e ykhts he}kt 411?' Hss{bogl }fh} }fk ykhtjy cfhglk `e bkmohg |hlk os c`gs}hg}' \fh} kx{h}o`g chg dk {skm }` eogm }fk |hlk `e h ~``j`los}0 y 2 ;;*811 )8611v

6' [sk }fk kx{h}o`g e`tbkm og #< }` mk}ktbogk }fk bkmohg |hlk `e h ~``j`los} og 418;' -5;*?11

?' Og |fh} ykht |ojj }fk bkmohg |hlk `e h ~``j`los} s{tqhss -?;*1110 4134

81' Skjkc} }fk $Sf`| kbqj`ybkg} fos}`ty$ jogi {gmkt }fk $Bkmohg \hlk fos}`ty$ skc}o`g' Chg y`{ bhik hgy c`gcj{so`gs c`gcktgogl }fk e{}{tk `e h chtkkt hs h ~``j`los}0 Hgs|kts uhty' Et`b 4118 ∔ 4113* }fk g{bdkt `e  ~``j`los} |hs c`gs}hg}' Et`b 4114 }` 4115* }fk g{bdkt ltk| h} h tkjh}oukjy c`gs}hg} th}k' ]fk g{bdkt `e n`ds ekjj sjolf}jy og 411<'

S{llks}o`gs> Skjkc} hg`}fkt chtkkt hgm tkskhtcf o} {sogl \`jethbzHjqfh' M`ks o} hqqkht }fh} }fk bkmohg |hlk os

ogctkhsogl h} h c`gs}hg} th}k0 ]ty }` mk}ktbogk hg hqqt`vobh}k kx{h}o`g e`t }fk tkjh}o`gsfoq dk}|kkg ykhts he}kt }fk c{ttkg} ykht hgm bkmohg |hlk' \fh} m`ks }fk kbqj`ybkg} fos}`ty sf`|0 Chg y`{ {sk hg kx{h}o`g }` sf`| }fk tkjh}o`gsfoq dk}|kkg g{bdkt `e qkts`gs kbqj`ykm og }fh} chtkkt hgm }obk he}kt }fk c{ttkg} ykht0

;8 C`jjklk Hjlkdth Hc}ouo}oks ]fk kg}otk sk} `e hc}ouo}oks os huhojhdjk dy c`g}hc}ogl y`{t Qkhts`g tkqtkskg}h}ouk'

Kx{h}o`gs hgm Ogkx{hjo}oks

[sogl \H

LJ@DHJ \HTBOGL

Skhtcf \`jethbzHjqfh e`t $|kh}fkt'$ 8' ]`mhy,s Mh}k>

5/4=/411?

Hgs|kts |ojj uhty mkqkgmogl `g j`ch}o`g'

J`ch}o`g>

Dhy}`|g* ]V

4' Eojj og }fk e`jj`|ogl oge`tbh}o`g et`b }fk }hdjk e`{gm {gmkt $Fos}`tochj

]kbqkth}{tks e`t ]`mhy,s Mh}k'$ ]ty }` lk} h} jkhs} 81 ykhts `e mh}h' _`{ bhy fhuk }` cfhglk }fk j`ch}o`g }` h jhtlkt }`|g' Louk h sch}}kt qj`} `e }fk mh}h dkj`|' 3' Eogm }fk jogkht eo} `e }fk jogk }` }fk mh}h' ]yqk $eo}$ hgm kg}kt c``tmogh}ks e`t }fk q`og}s loukg og }fk }hdjk>  y  2 1'=35v ) 6?'<8

=' Louk }fk sj`qk `e }fk kx{h}o`g> 1'=35 ;' \fh} m`ks }fk sj`qk ogmoch}k og }ktbs `e ykht hgm bhvob{b }kbqkth}{tk0 H sj`qk `e 1'=35 ogmoch}ks }fh} }fk }kbqkth}{tk os

8???

1

Bhvob{b ]kbqkth}{tk & E/ y 6?'5

4111

8

?;

4118

4

6?'5

4114

3

6?'5

4113

=

?8'=

411=

;

64'=

411;

5

811'=

4115

<

?3'4

411<

6

?8'=

4116

?

65

411?

81

814

_kht

v

±

ogctkhsogl dy 1'=35 mkltkks khcf ykht'

5' M`ks y`{t tks{j} ogmoch}k }fh} }fktk bhy dk h lj`dhj |htbogl qt`djkb0 Dtokejy kvqjhog y`{t hgs|kt' Sogck }fk

<'

sj`qk os q`so}ouk* h chsk bhy dk bhmk }fh} }fk }kbqkth}{tk os ogctkhsogl' Sogck |k htk j`` iogl h} h 81∔ykht }obk qkto`m* hgm `gjy `gk j`ch}o`g* }fk chsk bhy dk bhmk }fh} }fktk os g`} kg`{lf tkskhtcf }` bhik hg oge`tbkm mkcoso`g' Bhvob{b _kht v ]kbqkth}{tk & E/ Skjkc} hg`}fkt mh}k e`t }fk shbk co}y' Lh}fkt }fk shbk }yqk `e fos}`tochj y ±

mh}h hgm eogm }fk jogkht eo} `e }fk jogk }` }fk mh}h' Jogkht Kx{h}o`g>  y  2

8???

1

<8'5

4111

8

61'5

4118

4

<;'4

4114

3

64'=

6' Htk y`{t tks{j}s &e`t #= hgm

4113

=

61'5

#< sobojht0 Louk h sf`t}

411=

;

?8'=

kvqjhgh}o`g `g }fk sobojhto}oks hgm moeektkgcks `e }fk kx{h}o`gs' ]fk sj`qk os kukg s}kkqkt' D`}f sf`| hg ogctkhsk og

411;

5

6<'6

4115

<

6?'5

411<

6

?8'=

4116

?

61'5

411?

81

8'1
}kbqkth}{tk'

S{llks}o`gs> Kvqhgm }fos qt`nkc} s` }fh} y`{ c`jjkc} mh}h `ukt }fk kg}otk

ckg}{ty' ]ty hukthlk }kbqkth}{tks `t bogob{b }kbqkth}{tks ogs}khm `e {sogl bhvob{b }kbqkth}{tks' Cf``sk j`ch}o`gs og `}fkt qht}s `e }fk |`tjm }` skk oe }fktk os q`ssodjk lj`dhj |htbogl'

;< C`jjklk Hjlkdth Hc}ouo}oks ]fk kg}otk sk} `e hc}ouo}oks os huhojhdjk dy c`g}hc}ogl y`{t Qkhts`g tkqtkskg}h}ouk'

E{gc}o`gs hgm Lthqfs

[sogl \H

C`jjklk Hjlkdth Hc}ouo}oks [sogl }fk \`jethbHjqfh]B

]HDJK @E C@G]KG]S OG]T@M[C]O@G

;

8' KX[H]O@GS HGM OGKX[HJO]OKS

5

QKTS@GHJ OGC@BK HGM QKTS@GHJ SHUOGLS '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''< JOEK KVQKC]HGC_ HGM JO]KTHC_ TH]KS ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''6 CHTKKT KVQJ@TH]O@G ∔ ^@@J@LOS]''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''? [SOGL JOLF] ]@ BKHS[TK HS]T@G@BOCHJ MOS]HGCKS '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''' 81

4' E[GC]O@GS HGM LTHQFS

84

DJ@@M HJC@F@J QKTCKG]HLK ''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''' 83 DHSKDHJJ QO]CFOGL'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''' 8= LJ@DHJ \HTBOGL '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''' 8; SH]KJJO]K ]THCIOGL ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''' 85

3' Q@J_G@BOHJ HGM TH]O@GHJ E[GC]O@GS

86

JOEK KVQKC]HGC_ @E H ['S' BHJK ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''' 8? ['S' C@GS[BKT SQKGMOGL''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''' 41 C@JM MKCKBDKT ]KBQKTH][TKS ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''' 48 D@M_ BHSS OGMKV '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''''' 44

]fk kg}otk sk} `e hc}ouo}oks os huhojhdjk dy c`g}hc}ogl y`{t Qkhts`g tkqtkskg}h}ouk'

=' KVQ@GKG]OHJ HGM J@LHTO]FBOC E[GC]O@GS

4=

S]@CI QTOCKS '''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 4; GH]O@GHJ MKD] '''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 45 \@TJM Q@Q[JH]O@G''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''''' 4< TK]OTKBKG] CHJC[JH]@T ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' 46

;' S_S]KBS @E KX[H]O@GS HGM OGKX[HJO]OKS

31

G[]TO]O@[S SGHCIS ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''' 38 C@BQHTOGL QH_ ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''' 34 C@BQ[]KT LTHQFOCS ''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''' 33 [SOGL BH]TOCKS ]@ EOGM H Q@J_G@BOHJ E[GC]O@G @E DKS] EO] '''''''''''''''''''''''''''''''''''''''''''''''''''' 3=

5' HGHJ_]OC LK@BK]T_

35

F[TTOCHGK ]THCIOGL ''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''''''' 3< J@THG ''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''' 36 KHT]FX[HIKS ''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 3? B@[G]HOG ][GGKJ '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''''' =1

<' SKX[KGCKS* SKTOKS* HGM QT@DHDOJO]_

=4

I@CF SG@\EJHIK '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''''' =3 QH_OGL @EE H CTKMO] CHTM ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' == ]FK LTKH] Q_THBOM '''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''' =; L@JMKG TH]O@ ''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' =5

]fk kg}otk sk} `e hc}ouo}oks os huhojhdjk dy c`g}hc}ogl y`{t Qkhts`g tkqtkskg}h}ouk'