2022-2023年四川省绵阳市某校初三（上）月考数学试卷

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6.$%${\ெan\alpha=-3)$,ᑣ${\dfrac{\cos\lefl(\alpha+\dfrac{\pi}{4}\right)){\sin\alpha+2\cos2022-2023
ḕ□᪥ᨴὃᦪᔁ\alpha|=!$()ஹ⌱⚪A.S{\dfrac{2\sqrt{2}){5}}$B.${-2\sqrt{2}}SC.${-\dfrac{\sqrt{2}}{5}}$D.${-\sqrt{2}}$1.ᐰ${U=Vefl\{l,2,3,4,5\right\}}$,ᔠ${M$${\complement_{U}M=\leM{L25gh}$,ᑣA.${2\inM)SB.${3\inM}$7.᳝B᳝BCD1EᵨGHḄIJBKJL?MJNOᡂḄ᳝BJLD.ᡧR᳝BCDSTᓫVWC.S{4

1ot\inM!$D.S{5\»ot\inM}$${\rmcm}$᝞Yᡠ[?ᑣ\CDḄᡧ☢☢^_.2,$%)⚪S{p\exisisx\in\bfR)$,${\sinx\lt1}$,)⚪${q:\forallx\in\bfR}$,${{\rme}A{|x|}\ge1)$,ᑣ+ᑡ)⚪-./)⚪Ḅ1()A.${p\wedgeq!$B.S{

2egp\wedgeq}SA.S{1600\rmcmA{2)}$C.S{p\wedge

3egq}$B.${3200\rmcmA(2H$D.${

4eg\left(p\veeq\right)}$C.${3350\rmcmA{2}!$D.${4800\rmcmA{2}!$3.${4)}$156ᙠ${\tcxlbfR}$Ḅᕜ9.${3}$Ḅ:ᦪ.<$=1”0,\,2)}$>?$({f(x)={\begin{matrix}{3xA{2}-x,0\lcqx\lcq1},\\(2-x.l\ltx\lt2},\end{matrix})\right.})$ᑣ${%8.${\triangleABC}$Ḅᑁa$জ}$,${B!$,${C}$Ḅcdᑖf.${aᵯS{b}$,${c}$h${aios\dfrac{5}{2})=(}$${)}$B+b\cosA=2c\cosC}$,fi${\sinA=\sinB$,jlj$
'triangleABC}$ḄRk1
A.lῪaRB.ldaRC.${Wfrac{l}{2}}$D.S{\dfrac{l}{4}}$C.lῪnaaRD.lῪaRᡈnaaR4.$%x\right)=\sinx+fA{\prime}\Ieft(OVright)\cosx}$,ᑣ4p${y=Ncfi(x\right)}$ᙠq${\left(0,f\lcfU0\ri2h1)\righi))$ᜐḄᑗptu.()9.${\omega\gtO}$,^®^k$(y=\cos\left(\oniegax+\dfrac{\piH3Bright)${\dfracvpi}(3}}$wᓫVxyz{:ᦪ${y=\sin\omegax}$ḄY|}ᔠ?ᑣS{\omega}$Ḅᨬ.()A.${x-y+l=0}SB.${x+y-l=0}$A.${klfrac{ll}{2}}$B.${\dfrac{7}{2}!$C.S{x-y-l=0}$D.S{x+y+l=0}$C.${\dfrac{5}{2}}$D.${\dfrac{3}{2}!$5.$%:ᦪ${Ncft(x\righi)}$ḄY|᝞Yᡠ[?ᑣ\:ᦪḄ᪆.()10.$%${a=\sin4,b=Mn2,c=2N0.3}}$,jIJ()A.${b\lta\lic}$B.${c\ltb\lta)$IC.${a\ltb\llc}$D.${a\ltc\ltb!$11.$%:ᦪx\right)=\sinx+\cosx+2\sinx\cosx+2)$,jlj()A.${fMeft(x\righl)}$Ḅᨬᜧ.${3}$,ᨬ.${1}$A.${f\left(x\right)=\dfrac(xA{2}}{eA{x}+eA{-x}}}$B.${fMeft(x\righl)}$Ḅᨬᜧ.${3}$,ᨬ.${-l)$B.${Alefl(x\right)=\dfrac{eA{x}+eA{-x)}{xA{3}}}$C.${Neft(x\right)}$Ḅᨬᜧ.${3+Gqrt{2}}$,ᨬ.${\dfrac{3}{4}}$C.${f\left(x\right)=\dfrac{xA{2}}{cA{x}-eA{-x}}}$D.${Nefi(x\righi))$Ḅᨬᜧ.${3+ᓃqrt{2}}$,ᨬ.${3\sqrt{2}}$D.${f\left(x\right)=\dfrac{eA{x}-eA{-x}}{xA{3}}}$12.$%:ᦪS{f\lefl
x\right=Vnx-xw2}-ax}$ᨵwq?ᑣᦪ${a}$Ḅ1

5A.${\Ieft(-\infty.-l\right)}$B.S{\left(-l,O\right)}$C.${\left(0,l\right)!$D.${\left(0,+\infty\right)!$ஹ⚪${1.1v{0}+^{\1112}-0.5v{-2}+\lg25+2\lg2=}$.${Aᵯ${B)$w${10\sqrt{2}}$,$}$${C)$$জ}$ᡠᡂḄa.${60A{\circ})$,$জ}$${C)$$}$ᡠᡂḄa.${75A{\circ}}$,ᑣ${B)$${C}$Ḅ.________.x\right)=xA{3)+a\sinx+b\tanx+1)$(${a}$,${b}$.¢ᦪ),1\right)=3)$,ᑣ${f\left(-1\right)=!$.$%:ᦪ$(v᝿¤(x\right)=\ln*M}${$¦\§1(x\right)=-xN2}+\dfrac{7}{3}x}$ḄY|ᙠ${\¨©1,3\right]}$ªᙠᐵ¬${x}Sc®Ḅq?ᑣ${m}$Ḅ1__________.ஹ¯⚪${\triangIeABC}$Ḅᑁa${A}$.${B}$,${C}$Ḅcdᑖf.${a}$,${b}$.${c}$,h${b\sinB'cosC=\cosB\left(\sqrt{3}a-b\sinC\right)!$$((1)}$°a${B)$${(2)}$${b=4)$,°$vtriangleABC}$ᕜxḄᨬᜧ.ூ⌱²${4<}$ᙶ᪗µ{¶ᦪtu௃ᙠnaᙶ᪗µ${¸஺º}$-.»ᙶ᪗¼q.᩽q?${x}S¾¿.᩽ÀÁ᩽ᙶ᪗µ?4p${C}$Ḅ¶ᦪtu.${Meft\{\begin{array}{1}{x=3\cos\theta},\\{y=2\sin\theta},\cnd{array)\right.}$${(Vheta}$.¶ᦪ)?np${1}$Ḅ᩽ᙶ᪗tu.${\!410“|11\3Ã2-2\±0\005\»^112+21=0}$.${(1))$$ᓃ=3}$,°${C}${${1}$ḄÅqᙶ᪗${(2)}$${C}$Ḅqᑮ${1}SḄᨬᜧ.${5«qrt{2}}$,°$Ç}$,ூ⌱²${4-5)$WÈl⌱É௃$%:ᦪx\right)=|2x-21+|2x+31)$x\right)+1x-1|Me10}$${ফ}$$Ë4(*\1^Ì)}$Ḅᨬ.${1}$,${a+3b=[}$,°$Í{2}+▬2}}$Ḅᨬ.3⚓ᐳ14⚓4⚓ᐳ14⚓

6ᑭᵨ`ᦪẆbcdZefᑗdhi¶ὃ¯ᫀ{⚪᪆ூ᪆௃⚪ᨚ᪆2022-2023
ḕ□᪥()ᨴὃᦪᔁூ௃ஹ⌱⚪S{f\lcf((x\right)=\sinx+fA{\primc)\lcft(0\right)\cosx,\therefbrcfA{\prime}\left(x\right)=\cosx-I.2kprime}\lcft(OXright)\sinx)$,:.${fA{\prime)\left(O\right)=1,f\left(O\righ()=1)$,ூᫀ௃ᦑcd${y}$${=NefUx\right)}$ᙠf${\left(0.f\lcft(O\right)\right)}$ᜐḄᑗdhi>ᙠxy+l=0}$,ᦑ⌱${A}$B5.ூὃ௃ூᫀ௃⊡ᐸDூ᪆௃ூὃ௃⚪ᨚ᪆DᦪḄmnூ௃ூ᪆௃ᐜᑏᔠ${M}$,ᯠ!⌲⚗$%ᓽ'.ᵫ${U=\left\{1,2,3,4,5\right\)}$fi${\complement_{U)M=\left\{1,⚪ᨚ᪆2\right\!}$^${M=\left\{3,4,5\right\}}$,ᦑ⌱${B}$.ூ௃2.${f\left(x\right))$ḄQRo>${Meh(-\infty.O\right)\cup\left(0.+\infty\right))$,ᦑ᣸◀${A}$ூᫀ௃rs${B}$,t$]Neft(x\righi)=\dfrac{u{x}+eA{-x}}{xA{3}},NefK-x\righi)=\dfrac{eN-x}+eA{x}}{\left(-Ax\right)A{3}}=-\dfrac{eA{-x}+eA{x}}{xA{3})=-f\left(x\right))$,ᦑ${£\16w(x\right)=\dfrac{eA{x}+eA(-ூὃ௃X}}*A{3}}}$P᜻Dᦪஹ᣸◀${B}$.+ᔠ,⚪ᐸ-Ꮇᑨ0rs${C}$,tx\right)=\dfrac{xA{2}}{eA{x}-eA{-x}},f\left(-x\right)=\dfrac{\left(-xVright)A{2}}{eA{-12ὶ45"ᡈ"஻9"":"x}}=-\dfrac{xA{2}}{eA{x}-eA{-x}}=-ftleft(x\right)}$,ᦑ${f\left(x\right)=\dfirac{xk{2}}{eA{x}-6A{-x[)}$P᜻Dᦪ?᣸◀${C}$.ூ᪆௃yᳮ=${Neft(x\right)=\dfrac{e"x)-eN-x}}(xA{3}}}$PᏔDᦪ?ᦑ⌱${D}$⚪ᨚ᪆6.ூ௃ூᫀ௃ᵫ;<'=,⚪S{p}$>-,⚪.,⚪${q}$>-,⚪?BᡠA${p\wedgeq}$>-,⚪.ூὃ௃ᦑ⌱${\rmA}$.y|}|Dᦪ~Ḅᐵ3.|Ḅூᫀ௃ூ᪆௃D⚪ᨚ᪆ூὃ௃ᑖCDᦪḄGᵨூ௃DᦪḄIJᵫ${\dfrac{V:osMeft(\alpha+\dfrac{\pi}{4}\right)){\sin\alpha+2\cos\alpha|=\dfrac{\dfrac{\sqrt{2}}{2}(\cos\alpha-\sin\alpha)}{\sin\alpha+2\cos\alpha}=\dfrac{\dfrac{\sqrt{2}}{2}\left(1-\tan\alpha\right)}{\tan'alphaூ᪆௃+2)=\dfrac{\dfrac{\sqrt{2}}{2}\times4){-1)=-2\sqrt{2}}$ᑭᵨDᦪḄᕜMAᑖCDᦪᓄOIᓽ'.ᦑ⌱${B}$.ூ௃7.$(f(x))$PQRᙠ${V^X{Y$ZḄᕜM>${3}$ḄDᦪ.ூᫀ௃ᑣ${(\(1^_{5}{2})=f(klfrac(l}{2})=3\times(\dfrac{1}{2})A(2}-\dfrac{1}{2}=\dfrac{1}{4}}$.Dᦑ⌱${\rmD}$.ூὃ௃4.ᡧ☢ூᫀ௃ூ᪆௃A⚪ᨚ᪆ூὃ௃

7ூ¯௃ᵫ${\omcga\giO}$%W<${k=l}$>ᨬ?ᦑ${\omega_{\rm\min)=\dfrac{7}{2}}$,⌱$}$.:᝞Y?${\angleAOB=\alpha,OB=r)$,ᵫÒxÓÔÕ${Meft\{\begin{array){1}{80=\alphar),\\ᡈὅ?E^${y=\cos\lcf((\omcgax+\dfrac{\piH3}\right)}S^D${\omegax+\dfrac{\pi}{3}=23ú$>${º=1)$,ᵫ{160=\alpha\left(r+40\right)},\end{array)\right.)$Õ${'alpha=2,r=40)$,${y=\sin\omcgax}$%<${\omcgax=\dfrac{\pi){2}}$>${º=1}$,ᑣ\CDḄᡧ☢☢^_.S{S_{ᡧRCOD}-SÖᡧRAOB}=\dfrac{l}{2}\times160\times\left(40+40\right)-ᦑᵫ⚪øÕ${\dfrac{5\pi}{3\omega}-\dfrac{\pi}{3}=\dfrac{\pi}{2\omega}}$,Õ${\omega=Wfrac{7}{2}}$.\dfrac{1}{2}\times80\times4800\left(\rmcmA{2}\right)}S.10.ூ¯ᫀ௃Cூὃf௃ᢣᦪஹcᦪḄüᔠìýூ᪆௃Ü⚪ᨚÞ᪆ᦑ⌱${\rmD}$.ூ¯௃8.þ.${c=2A{0.3}\gt2A{O}=1,\quadb=\ln2\in\left(0,l\right))$,ூ¯ᫀ௃ᡠ»${\pi\lt4Mt\dfrac{3জi}{2}}$,ᡠ»${a=\sin4m0}$,ᦑ${a\ltb\ltc}$Bᦑ⌱:${C)$ூὃf௃11.¾Ø5ᳮூ¯ᫀ௃aRḄRkᑨÛCூ᪆௃ூὃf௃Ü⚪ᨚÞ᪆a:ᦪḄᨬூ¯௃ூ᪆௃᪷àᩩâWS{a\cosB+b\cosA=2c\cosC)$,Ü⚪ᨚÞ᪆ᑭᵨ¾Ø5ᳮÔÕS{\sinA\cosB+\sinB\cosA=2\sinC\cosC}$ூ¯௃᦮ᳮÕ${\sinA+B\right)=\sinC=2\sinOcosC}$${J$${0\ltCMt\pi!$,jὮvsinOne0}$þ.:ᦪ${v1÷(x\right)=\sinx+\cosx+2\sinx\cosx+2}$ᓄçÕ:${\cosC=\dfrac{lH2}}$,ᦑ$èé6^{\N}{3}}$${\sinx+\cosx=\sqrt{2}\sin\left(x+\dfrac{\pi}{4}\right)=1.t\in\lcf([-\sqrt{2},\sqrt{2}\right]}$ᙠ${\triangleABC}$-,ᵫ¬${\sinA=\sinB}$,ᡠ»${A=B}$(ÈÔê${ë+8=\D)$)ᑣ${2\sinx\cosx=tA{2}-l}Sᦑ$জ=8=<=ìí{\}{3}}$.ᡠ»${\lriangleABC}$.ldaR.ᡠ»${y=S{2}+t+l=\left(t+\dfrac{1}{2}\right)A{2}+\dfrac{3}{4}.(\in\left[-\sqrt{2},\sqrt{2}\right])$ᦑ⌱:${B}$,<${t=Mfrac{l}{2}}$>?${f\Ieft(t\right)_{\rm\min)=\dfrac{3}{4}}$ÿ${t=\sqrt{2}}$
${f\left(t\right)9._{\max}=3+\sqrt{2})$ூ¯ᫀ௃ᦑ⌱:${C}$B12.ூὃf௃ூᫀ௃:ᦪy=Asin(wx+4))ḄY|îᣚAூ᪆௃ூὃf௃Ü⚪ᨚÞ᪆ᑭᵨᦪẆᦪᨵᐵḄ⚪ூ¯௃ூ᪆௃ð:ᦪ${y=\cos\left(\omegax+\dfrac{\pi}{3}\right)}$ḄY|ᔣòóô${\<11'ö(:vpi}{3}}$wᓫVxy?Õ⚪ᨚ᪆${y=\cos\left|\omega\left(x+\dfrac{\pi}{3}\right)+\dfrac{\pi}{3}\right]}$^)|l]^.ூ௃÷${º=\85Meft[\omega(x+\dfrac{\pi}{3})+\dfrac{\pi}{3}\rightJ=\cos(\omegax+\dfrac{\omegaᦪ${f\left(x\right)=\lnx-xN2}-ax}$Ḅ!${\left(0,+\infty\right)!$\pi}{3}+\dfrac{\pi}{3})=\sin\left[^dfrac{\pi}{2}+(\omegax+\dfrac{\omega\pi}{3}+\dfrac{\pi){3})\right]=\sin"x\right)=\lnx-xA{2}-ax=0)$,ᑣ${\lnx-xA{2}=ax)$(\omegax+\dfrac{\omega\pi}{3}+\dfrac{5\pi}{6})}$,ᓽᦪ${g\left(x\right)=\lnx-xA{2}}$'(${y=ax)$ᨵ)*+ᦑᵫ⚪ø%${«in\omegax=)$$(\sin\omegax+\dfrac{\omega\pi}{3}+\dfrac{5\pi}{6}\right))$,ᡠ»,:${gA{\prime)\left(x\right)=\dfrac{1}{x}-2x=\dfrac{l-2xA{2}}{x}}S.,$,${gA{\prime}\left(x\right)\gt0)$,${\omegax+\dfrac{\omega\pi){3}+\dfrac{5\pi}{6}=2k\pi+\omegax\left(k\inZXright)}$,ÕS{\omega=6k-ᑣ${()\ltx\lt\dfrac{\sqrt{2}}{2)}$\dfrac{5}{2}\pi\quad\left(k\inZ\right))$,$../*381«))$ᙠ${2n(0,\34(:{62}}{2}38111)}$7ᓫ9⌴;,ᙠ=>ᵨ?@^^{Bqrt{2}}{2},7⚓ᐳ14⚓8⚓ᐳ14⚓

8+\infty\righl)}$7ᓫ9⌴Cூᫀ௃i$$(g\left(x\right)=\lnx-x42})$${E=2*GḄᑗᙶ᪗!x_{0},\lnx_{0}-xA{2}_{0}Vight))$,ᑗ${-1}$K᳛${k=\dfrac{1}{x_{0}}-2x_{0}}$ூὃ௃ᑣᨵ${Mcfi\{\bcgin{array}{1!{a=\dfrac{1}{x_{0}}-2x_{0}}\\{\lnx_{0}-xA{2}_{0}=ax_{0}}\end{array)ᦪ᜻ᏔឋḄឋv\right)$,MN${a}$O:${xA{2}_{0}+\lnxJ0}-l=0)$ᦪḄwxPᯠ${y=xA{2}+Mnx-1)$ᙠᙠ0ஹ+\infiy\righi)}$7ᓫ9⌴;S${x=l}$
${y=0)$ூ᪆௃ᑣ${T{0}=1U=1}$⚪ᨚ᪆Vᦪ${g\left(x\right)=\InWXY{2}}$'(${y=ax}$ᨵ)*+ᑣ$Zm-1)$ᦑ⌱${A}$.ூ௃S^j${x\in\left(Adfrac{\pi}{2}+k\pi.\dfrac{\pi}{2}+k\pi\right)\left(k\inZVight)}$,ᐵya\z^${g\Ieft(xXright)=f\left(x\right)-1=xA{3}+a\sinx+b\tanx)$S{g\left(-x\right)=-\left(xA{3}+a\sinx+bManx\righ()=-g\left(x\right)}$ᑣ${1|(x\right)}$}᜻ᦪ,~!${g\lefi(l\right)=f\left(l\right)-1=2)$,ᡠ${g\left(-l\right)=f\left(-IXright)-l=-2}$,ᡠ${f\left(/\righl)=-l}$ᦑᫀ!:${-1!$.ூᫀ௃$\ln3-2,\ln\dfrac{3}{2}+\dfrac{5}{4}\right])$ூὃ௃ᑭᵨᦪẆᦪᨵᐵḄ⚪ூ᪆௃᪷p⚪nᙌᓄ!ᦪ$(f(x)=Vnx-m}$$\x\right)=W0-4M(:{7”3}$Ḅᙠ$([1,3]}$7ᙠᐳᓄ!$[01=\1”ᓝᐭ{2}+@(7}{3ஹ}$ᙠ${[1,3]}S7ᨵ.M^${h\left(x\right)=\lnx-ஹ⚪x^{2}+\dfrac{xA{2}){3}\left(x\in\left[l,3\right]\right)}$,ᵨᦪẆᦪᓫ9ឋO$3)}$ᙠ1,ூᫀ௃3\rightJ}$7ḄxO${m}$Ḅx.${1)$ூ௃ூὃ௃cᵫ⚪nOᦪ${>ឃ581]஺=\1”}$$ᕜ1(W\¢1«)=*Y{2}-£ᵫ{7}{3}$ḄᙠI,\ᦪ]ᐸ_`3\right]}$7ᙠᐳூ᪆௃ᓽ${Mnx-m-xA{2}+klfrac{7}{3}x=O}$ᙠ1,3\righ1]}$7ᨵ⚪ᨚ᪆ᓽ${¤=ᵫ^>{2}+\(1({7}{3¥}$ᙠ${\᝶§1,33¨1]}$7ᨵஹூ௃"${h(x)=\lnx-xN2}+\dfrac{7}{3}x}$,${x\in[1,3])$,ab${=l+2>4+2\left(\lg5+Mg2\right)=-1+2=1)$KIJ${hA{\|)rime}\left(x\right)=\dfrac{1}{x}-2x+\dfrac{7}{3}=-\dfrac(\left(3x+l\right)\left(2x-3\right)!{3x)}$.ᦑᫀ!cᡠ${x\in\left[I,3\right]}$
,${hA{\prime}\left(x\right)|$,${h\left(*\1^)}$©$ª}$Ḅ«ᓄ¬᝞¯⊤ூᫀ௃${10\sqrt{3}}$${x}$${1}$${\left(l,\dfrac{3}{2)$(\dfrac{3}{$(\left(\dfrac{${3ூὃ௃\right)!$2}}$3}{2},}$3\right))$-cefḄg▭iᵨjkᳮ$(hA{\prime)\left(x\${+}$$(0)$${-}$right))$ூ᪆௃$(h\left(x\right)!$${\dfrac{4){${

9earrow)$᩽ᜧx${\searrow}$${M⚪ᨚ᪆3}}$n3-ூ௃2!$ᵫ⚪nO${A=60Y{\circ},B=75A{\circ},C=180A{\circ}-60A{\circ}-75A{\circ}=45A{\circ}}$ᵫ7⊤§±${h\left(l\right)=\dfrac{4}{3}}$,S{h\left(3\right)=\ln3-2\lt\dfrac{4}{3})$,᪷pjkᳮOS{BC=\dfrac{AB}{\sinC}\cdot\sinA=\dfrac110\sqrt{2}}{\dfrac(\sqrt{2}}{2}}\times²${h\left(\dhc{3}{2}\right)=\ln\dfrac{3}{2|+\dfrac{5}{4}}$,\dfrac{\sqrt{3}}{2}=10\sqrt{3})$(qr)

10ᡠ${x\inMefl[l,3\righெ]}$
,${h(x)\in\lcf([\ln3-2,\lnklfrac{3}{2}+klfrac{5}{4}\righ(])$,${d=\dfrac{|2\sin\theta-6\cos\theta+a-1|){\sqr({5}}=\dfrac{|2\sqrt{IO}\sin(\theta-\varphi)+\alpha-Iᦑ${m}$Ḅx}${Mefi[\In32Mnkifrac{3}{2}+\dfrac{5}{4}\righU}$.I}{\sqrl{5}}ஹ\tan\varphi=3}$·ஹ⚪$»ᙢ©1}$
${d}$Ḅᨬᜧx!${\dfrac{2\sqrt{10}+a-l}{\sqrt{5}}}$,ூᫀ௃ᵫ⚪ÐO${"(Òফsqrt{10}+a”}{\sqrH5}}=5\sqn{2}}$cপᵫ${ᡊ53B\cosC=\cosB\left(\sqri{3}a-b\sinC\right))$,^${b\left(\sinB\cosC+\cosB\sinC\right)ᡠ${a=l+3\sqrt{10}}$$Z31}$
${d}$Ḅᨬᜧx!$ndfrac{2\sqrt{10}-a+l}{\sqrt{5}}}$,=\sqrt{3}a\cosB)Sᡠ${b\sin\left(B+C\right)=\sqrt{3}a\cosB)$,ᓽ${b\sinA=\sqrt{3}a\cosB)$ᵫ⚪ÐO${\dfrac{2\sqrt{10}a+l}{\sqrt{5}}=5\sqrt{2}}$²ᵫjkᳮᨵ$>sinBVcdot\sinA=\sqrt{3inAVcdot\cosB)$ᡠ${a=l-3\sqn{IO}}$²${\sinA\gtO)$,ᡠ${\tanB=\sqrt{3}!$ூὃ௃²${0\hB\lt\pi}$ÔᦪÈÉḄÕᓄᡠ${B=\dfrac{\pi}{3}}$'(Ḅ᩽ᙶ᪗'eᙶ᪗ḄÕᓄ(2)~!${b=4}$${4osB=\dfrac{aA{2}+cA{2}-M{2}}{2ac}=\dfrac{l}{2}}$,gp${\left(a+c\right)A{2}-ᑮ'(ḄÍÎb16=3ac)$ூ᪆௃Wa+c\right)A{2}-16=3ac\le\dfrac{3}{4}\left(a+c\right)A{2})$,Sº$»=஺}$
¼½ᡂ¿⚪ᨚ᪆ᡠ${a+cMe8}$,ᡠ${a+b+c\le12}$ᡠ${\triangleY13(}$ᕜÀḄᨬᜧx!${12.}$ூ௃ூὃ௃:(1)Ç(${C}$ḄÈÉ!${Öᓄa!{2}}{9}+\dfrac{yA{2}}{4}=l[$$[a=3)$
${1)$ḄÈÉ!$(y-2x+2=0}$jkᳮ)eÂÃḄjkbᵫ${\left\{\begin{array}{1}{y-2x+2=0}\\{\dfrac{xA{2}){9)+\dfrac{yA{2}}{4)=1},\end{array)\right.)SOS{\left\{\begin{array}{l}{x=0)\\{y=-2}\end{array)\right.}$ᡈ\begin{array}{l}{x=\dfrac{9}{5}}\\Äkᳮ{y=\dfrac{8}{5}}\end{array}\right.}$ூ᪆௃ᡠ${C)$${1}$Ḅ+ᙶ᪗!${Mefi(0,-2\righl),\left(\dfrac(9}{5},\dfrac{8}{5}\right)!$⚪ᨚ᪆(2)${l}$ḄÈÉ!${y-2x+a-l=0)$ூ௃ᦑ${C}$7Ḅ3\cos\theta,2\sin\theta\right)}$ᑮ${1}$ḄÍÎcপᵫ${b\sinB\cosC=\cosBMcfl(\sqrt{3}a-b\sinC\^ight)}$,O${b\lefl(\sinB'cosC+\cosB\sinC\righ஺${d=\dfrac{|2\sin\theta-6\cos\theta+a-1|){\sqrt{5}}=\dfrac{|2\sqrt{10}\sin(\theta-\varphi)+\alpha-1I}{\sqrt{5}},\tan\varphi=3}$=\sqrt{3}a\cosB)Sᡠ${b\sin\left(B+C\right)=\sqrt{3}a\cosB}S,BP${b\sinA=\sqrt{3}a\cosB)$$×361}$
,${d}$Ḅᨬᜧx!${\dfrac{2\sqrt{10}+a-l}{\sqrt{5}}}$,²ᵫjkᳮᨵ${“B\cdot\sinA=\sqrt{3}\sinAMol\cosB!$ᵫ⚪ÐO${0@{211{l()}+a-l){\sqrt{5}}=5\sqrt{2}}$²${\sinA\gt0)$,ᡠ${ManB=\sqrt{3})$ᡠ${a=l+3\sqrt{10}}$²${OMtB\lt\pi}$l}$
${d}$Ḅᨬᜧx!${\dfrac{2\sqrt{10}-a+lH\sqrt{5}}}$,ᡠ${B=\dfrac{\pi}{3}}$ᵫ⚪ÐO${\dfrac{2\sqrt{10}a+l}{\sqrt{5}}=5\sqrt{2}}$Aᡠ${a=l-3\sqrt{10}}$(2)~!${b=4}$${4osB=\dfrac{aA{2}+cN2}-bA{2}}{2ac}=\dfrac{l}{2}}$,gp${\left(a+c\right){2}-ூᫀ௃I6=3ac)$ᡠ${Meft(a+c\right)A{2}-16=3ac\le\dfrac{3}{4}\left(a+c\right)A{2}}$,Sº$Æ=஺}$
¼½ᡂ¿,x\right)+1x-11Me10}$,§O${3|xl|+|2x+3|\le10)$ᡠ${a+c\le8}$,ᡠ${a+b+cVe12}$$ØÙÚ(:{3}{2}}$
,MW${3-3x-\Ieft(2x-3\right)=-5x\)e10!$,O${x\ge-2}$,
${2\lex\leᡠ${\lriangleY8€?}$ᕜÀḄᨬᜧx!${12.}$\dfrac{3}{2}}$${^^^{3}{2}\1«\111}$
ᑣᨵ${3-3x+2x+3=6xMc10}$,O${x\gc4}$,
${M£Û{3}{2}\11W\11ூᫀ௃1}$cপÇ(${C}$ḄÈÉ!${\dfrac{xA{2}}{9}+\dfrac{yA{2}}{4}=1}$${x\gel}$
ᑣᨵ${3x3+2x+3=5x\lc10}$,O${x\le2}$,
${IVex\le2}$$Ê=3}$
${1}$ḄÈÉ!${y-2x+2=0}$ᵫ${\left\{\bcgin(array}{1}{y-2x+2=0}\\{\dfrac{xA{2}}{9)+\dfrac{yA{2}}{4}=l},\end{array}\right.}$OÜ7ᡠÝÞ¼b${f\left(xXrighl)+|x-l|\le10}$Ḅß!x|-2\Icx\le2\right\!}$${\left\{\begin{array}{1}{X=0}\\{y=-2}\end{array}\1^1)1.}$ᡈ${Meft\{\bcgin{array}(l}{x=\dfrac{9}{5}}\\cᵫà\x·eÞ¼b§O${Neft(xVright)=|2x-2|+|2x+3|\ge|\left(2x-2\right)2x+3\right)|=5}$Sº${Veft(2x-2\right)\IeR(2x+3\right)\leO}$
,ᓽ${-\dfrac{3}{2}\lexVe1}$
,¼½ᡂ¿ᦑ{y=\dfrac{8}{5}}\cnd{array)\righi.}$ᡠ${C}$${1}$Ḅ+ᙶ᪗!${Mefi(0,-2\righi),\left(\dfrac{9}{5}.\dfrac{8}{5}\right)!$${t=5}$ᡠ${a+3b=5}$(2)${1}$ḄÈÉ!${y-2x+a-l=0}$ᵫáâÞ¼b§O${Mett(lA{2}+3A{2}\right)\left(aA{2}+bA{2}\right)\ge\left(a+3b\right)A{2}=25}$,ᓽᦑ${C}$7Ḅ3os\theta,2\sin\theta\right)}$ᑮ${1ḄÍÎS{aA{2}+bA{2}\ge\dfrac{5}{2}}$11⚓ᐳ14⚓12⚓ᐳ14⚓

11Sº$(\left\{\bcgin{array}{l}{a=\dfrac{b}{3}}\\{a+3b=5)\cnd{array)\right.)$
ᓽ${\left\{\bcgin{array}{1}{a=\dfrac{I}{2}}\\{b=kifrac{3}{2}}\end{array}\right.!$
¼½ᡂ¿ᦑ$ÆY{2}+ã{2}}$Ḅᨬäx!${\dfrac{5}{2}}$ூὃ௃åæfbḄáâÞ¼bà\xÞ¼bḄçèéூ᪆௃⚪ᨚ᪆ூ௃(l)6${AIeft(x\right)+|x-1|Me10)$,§O${3|x-l|+|2x+3|Me10)$${x\le-\dfrac{3}(2}}$
ᑣᨵ${3-3x-Mefi(2x-3\right)=-5x\le10}$,O${x\ge-2}$,
${-2MexMe-\dfrac{3}{2}}$${-ê6^{3}{2}\1”\111}$
,ᑣᨵ${3.3x+2x+3=6-x\Ie10}$,O${x\ge«4}$,
${Mfirac{3“2}\ltx\lt1}$${x\gel)$
ᑣᨵ${3x-3+2x+3=5x\le10)$,O${x\le2}$,
${l\lex\le2}$Ü7ᡠÝÞ¼b$(Neëx\right)+|x-l|\le10)$Ḅß!${\left\{x|-2\lex\le2\right\}}Scᵫà\x·eÞ¼b§O${Nefl(x\right)=12x-2|+|2x+3|\ge|\lcft(2x-2\right)-\lcft(2x+3\righ()|=5)SSºW\leR(2x2\right)\Ie"(2x+3\righi)\kO}$
,ᓽ${Mfrac{3}{2}\lex\Ie1}$
,¼½ᡂ¿ᦑ${i=5}$ᡠ${a+3b=5}$ᵫáâÞ¼b§O${\left(lA(2)+3A{2}\right)\left(aA{2}+bA{2}\right)\ge\left(a+3b\right)A{2}=25)$,ᓽ$(aA{2}+bA{2}\gc\dfrac{5}{2}!$Sº$(\left\{\bcgin{array}{l}{a=\dfrac{b}{3}}\\{a+3b=5}\cnd{array)\right.)$
ᓽ${\left\{\bcgin{array}{1}{a=\dfrac{I}{2}}\\{b=kifrac{3}{2}}\end{array}\right.!$
¼½ᡂ¿ᦑ$ìY{2}+ã{2}}$Ḅᨬäx!${\dfrac{5}{2}}$