<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/c5122ea8-ec8f-4696-a609-a943a1623b8e/bg1.png"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0"><span class="fc2 sc0">M</span><span class="fc2 sc0">ét</span><span class="blank _0"></span><span class="fc2 sc0">o</span><span class="fc2 sc0">d</span><span class="fc2 sc0">os </span><span class="fc2 sc0">Quan</span><span class="blank _0"></span><span class="fc2 sc0">t</span><span class="blank _1"></span><span class="fc2 sc0">ita</span><span class="blank _0"></span><span class="fc2 sc0">t</span><span class="fc2 sc0">iv</span><span class="fc2 sc0">os</span></div><div class="t m0 x2 h3 y3 ff1 fs0 fc1 sc0 ls0 ws0"><span class="fc2 sc0">M</span><span class="fc2 sc0">ét</span><span class="blank _0"></span><span class="fc2 sc0">o</span><span class="fc2 sc0">d</span><span class="fc2 sc0">os </span><span class="fc2 sc0">Quan</span><span class="blank _0"></span><span class="fc2 sc0">t</span><span class="blank _1"></span><span class="fc2 sc0">ita</span><span class="blank _0"></span><span class="fc2 sc0">t</span><span class="fc2 sc0">iv</span><span class="fc2 sc0">os</span></div><div class="t m0 x1 h3 y4 ff1 fs0 fc0 sc0 ls0 ws0"><span class="fc2 sc0">M</span><span class="fc2 sc0">a</span><span class="blank _0"></span><span class="fc2 sc0">t</span><span class="blank _0"></span><span class="fc2 sc0">emá</span><span class="blank _2"></span><span class="fc2 sc0">t</span><span class="blank _1"></span><span class="fc2 sc0">ic</span><span class="fc2 sc0">os</span></div><div class="t m0 x2 h3 y5 ff1 fs0 fc1 sc0 ls0 ws0"><span class="fc2 sc0">M</span><span class="fc2 sc0">a</span><span class="blank _2"></span><span class="fc2 sc0">t</span><span class="fc2 sc0">emá</span><span class="blank _2"></span><span class="fc2 sc0">t</span><span class="blank _1"></span><span class="fc2 sc0">ic</span><span class="fc2 sc0">os</span></div><div class="t m0 x3 h4 y6 ff2 fs1 fc1 sc0 ls0 ws1">AU<span class="blank _0"></span>TORIA</div><div class="t m0 x3 h5 y7 ff3 fs2 fc1 sc0 ls0 ws0">Luciano Xa<span class="blank _0"></span>vier de Azev<span class="blank _0"></span>edo</div></div><a class="l" data-dest-detail="[1,"XYZ",56,799.92,null]"><div class="d m1" style="border-style:none;position:absolute;left:101.000008px;bottom:700.169980px;width:393.000022px;height:43.500000px;background-color:rgba(255,255,255,0.000001);"></div></a></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w3 h1" alt="" src="https://files.passeidireto.com/c5122ea8-ec8f-4696-a609-a943a1623b8e/bg2.png"><div class="c x0 y8 w3 h6"><div class="t m0 x4 h7 y9 ff4 fs2 fc3 sc0 ls0 ws0"><span class="fc2 sc0">B</span><span class="blank _3"> </span><span class="fc2 sc0">e</span><span class="blank _3"> </span><span class="fc2 sc0">m</span><span class="blank _3"> </span><span class="fc2 sc0"> </span><span class="blank _3"> </span><span class="fc2 sc0">v</span><span class="blank _3"> </span><span class="fc2 sc0">i</span><span class="blank _3"> </span><span class="fc2 sc0">n</span><span class="blank _3"> </span><span class="fc2 sc0">d</span><span class="blank _3"> </span><span class="fc2 sc0">o</span><span class="blank _3"> </span><span class="fc2 sc0">(</span><span class="blank _3"> </span><span class="fc2 sc0">a</span><span class="blank _3"> </span><span class="fc2 sc0">)</span><span class="blank _3"> </span><span class="fc2 sc0">!</span></div><div class="t m0 x5 h8 ya ff2 fs3 fc4 sc0 ls0 ws0">Seja muito bem-<span class="blank _0"></span>vindo(a)!</div><div class="t m0 x5 h8 yb ff2 fs3 fc4 sc0 ls0 ws0">P<span class="blank _0"></span>rezado(a) <span class="blank _4"> </span>aluno(a), <span class="blank _4"> </span>desenvolv<span class="blank _0"></span>er <span class="blank _4"> </span>habilidades <span class="blank _4"> </span>matemáticas <span class="blank _4"> </span>pode <span class="blank _4"> </span>abrir <span class="blank _4"> </span>novos</div><div class="t m0 x5 h8 yc ff2 fs3 fc4 sc0 ls0 ws0">horizont<span class="blank _0"></span>es, <span class="blank"> </span>pois <span class="blank"> </span>a <span class="blank"> </span>mat<span class="blank _0"></span>emática <span class="blank"> </span>é <span class="blank"> </span>importante <span class="blank"> </span>p<span class="blank _0"></span>ara <span class="blank"> </span>análise, <span class="blank"> </span>t<span class="blank _0"></span>omada <span class="blank"> </span>de <span class="blank"> </span>decisões <span class="blank"> </span>e</div><div class="t m0 x5 h8 yd ff2 fs3 fc4 sc0 ls0 ws0">projeç<span class="blank _0"></span>ões <span class="blank _5"> </span>em <span class="blank _5"> </span>uma <span class="blank _5"> </span>or<span class="blank _0"></span>ganização. <span class="blank _6"> </span>Então, <span class="blank _6"> </span>vemos <span class="blank _6"> </span>uma <span class="blank _6"> </span>crescent<span class="blank _0"></span>e <span class="blank _6"> </span>por <span class="blank _5"> </span>busca <span class="blank _6"> </span>de</div><div class="t m0 x5 h8 ye ff2 fs3 fc4 sc0 ls0 ws0">pro\ue67dssionais que t<span class="blank _0"></span>êm base para pr<span class="blank _0"></span>ocessos decisórios nas mais div<span class="blank _0"></span>ersas áre<span class="blank _0"></span>as.</div><div class="t m0 x5 h8 yf ff2 fs3 fc4 sc0 ls0 ws0">É com <span class="blank _1"> </span>muit<span class="blank _0"></span>o prazer que <span class="blank _1"> </span>apresent<span class="blank _0"></span>o a <span class="blank _1"> </span>você, aluno(a), este material. Nele abordaremos</div><div class="t m0 x5 h8 y10 ff2 fs3 fc4 sc0 ls0 ws0">conceit<span class="blank _0"></span>os <span class="blank _7"> </span>relacionados <span class="blank _7"> </span>a <span class="blank _7"> </span>Mét<span class="blank _0"></span>odos <span class="blank _7"> </span>Quantitativos <span class="blank _7"> </span>Matemátic<span class="blank _0"></span>os. <span class="blank _7"> </span>Mas <span class="blank _7"> </span>o <span class="blank _7"> </span>que <span class="blank _7"> </span>são <span class="blank _7"> </span>tais</div><div class="t m0 x5 h8 y11 ff2 fs3 fc4 sc0 ls0 ws0">métodos<span class="blank _0"></span>? <span class="blank _8"> </span>São <span class="blank _8"> </span>ferramentas <span class="blank _8"> </span>que <span class="blank _8"> </span>dão <span class="blank _8"> </span>suporte <span class="blank _8"> </span>para <span class="blank _8"> </span>aplicaç<span class="blank _0"></span>ões <span class="blank _8"> </span>matemáticas <span class="blank _8"> </span>em</div><div class="t m0 x5 h8 y12 ff2 fs3 fc4 sc0 ls0 ws0">modelagem <span class="blank _9"> </span>em <span class="blank _9"> </span>diver<span class="blank _0"></span>sas <span class="blank _9"> </span>ciências, <span class="blank _9"> </span>como <span class="blank _7"> </span>economia, <span class="blank _9"> </span>f<span class="blank _a"> </span>ísica, <span class="blank _9"> </span>biologia, <span class="blank _7"> </span>dentre <span class="blank _9"> </span>outras.</div><div class="t m0 x5 h8 y13 ff2 fs3 fc4 sc0 ls0 ws0">Escre<span class="blank _0"></span>vi <span class="blank _3"> </span>est<span class="blank _0"></span>e <span class="blank _3"> </span>mat<span class="blank _0"></span>erial <span class="blank _3"> </span>com <span class="blank _1"> </span>o <span class="blank _3"> </span>objetiv<span class="blank _0"></span>o <span class="blank _3"> </span>de <span class="blank _3"> </span>aumentar <span class="blank _1"> </span>os <span class="blank _3"> </span>níveis <span class="blank _1"> </span>de <span class="blank _3"> </span>autoc<span class="blank _0"></span>on\ue67dança <span class="blank _3"> </span>e <span class="blank _1"> </span>criar</div><div class="t m0 x5 h8 y14 ff2 fs3 fc4 sc0 ls0 ws0">mecanismos para que v<span class="blank _0"></span>ocê possa inter<span class="blank _0"></span>agir com a matemática. \ue6d0</div><div class="t m0 x5 h8 y15 ff2 fs3 fc4 sc0 ls0 ws0">O <span class="blank _8"> </span>mat<span class="blank _0"></span>erial <span class="blank _b"> </span>está <span class="blank _b"> </span>distribuído <span class="blank _b"> </span>em <span class="blank _8"> </span>quatro <span class="blank _b"> </span>unidades, <span class="blank _b"> </span>em <span class="blank _b"> </span>que <span class="blank _8"> </span>buscamos <span class="blank _b"> </span>conceitos</div><div class="t m0 x5 h8 y16 ff2 fs3 fc4 sc0 ls0 ws0">elementares <span class="blank _1"> </span>dentro <span class="blank _1"> </span>da <span class="blank _3"> </span>matemática. <span class="blank _1"> </span>Acreditamos <span class="blank _1"> </span>que <span class="blank _3"> </span>voc<span class="blank _0"></span>ê, <span class="blank _3"> </span>depois <span class="blank _1"> </span>deste <span class="blank _1"> </span>curso, <span class="blank _1"> </span>terá</div><div class="t m0 x5 h8 y17 ff2 fs3 fc4 sc0 ls0 ws0">capacidade de abordar temas como teoria dos conjunt<span class="blank _0"></span>os e <span class="blank _1"> </span>funções em seu dia <span class="blank _1"> </span>a dia.</div><div class="t m0 x5 h8 y18 ff2 fs3 fc4 sc0 ls0 ws0">Na <span class="blank _c"> </span>Unidade <span class="blank _c"> </span>I <span class="blank _c"> </span>trataremos <span class="blank _8"> </span>de <span class="blank _c"> </span>matemática <span class="blank _c"> </span>básica <span class="blank _c"> </span>e <span class="blank _c"> </span>conjunt<span class="blank _0"></span>os <span class="blank _c"> </span>numéricos. <span class="blank _c"> </span>E<span class="blank _0"></span>ssa</div><div class="t m0 x5 h8 y19 ff2 fs3 fc4 sc0 ls0 ws0">unidade <span class="blank _a"> </span>irá <span class="blank _d"> </span>trazer <span class="blank _a"> </span>uma <span class="blank _a"> </span>abordagem <span class="blank _d"> </span>de <span class="blank _a"> </span>conceitos <span class="blank _3"> </span>elem<span class="blank _1"> </span>entar<span class="blank _0"></span>es <span class="blank _d"> </span>que, <span class="blank _a"> </span>como <span class="blank _d"> </span>o <span class="blank _a"> </span>próprio</div><div class="t m0 x5 h8 y1a ff2 fs3 fc4 sc0 ls0 ws0">nome <span class="blank _7"> </span>diz, <span class="blank _e"> </span>é <span class="blank _e"> </span>base <span class="blank _e"> </span>para <span class="blank _e"> </span>vários <span class="blank _e"> </span>assuntos <span class="blank _e"> </span>dentro <span class="blank _e"> </span>das <span class="blank _e"> </span>outras <span class="blank _e"> </span>unidades. <span class="blank _7"> </span>Na <span class="blank _e"> </span>Unidade <span class="blank _e"> </span>II</div><div class="t m0 x5 h8 y1b ff2 fs3 fc4 sc0 ls0 ws0">abordar<span class="blank _0"></span>emos <span class="blank _6"> </span>relações <span class="blank _6"> </span>e <span class="blank _5"> </span>funções, <span class="blank _6"> </span>que <span class="blank _6"> </span>são <span class="blank _5"> </span>ferramentas <span class="blank _6"> </span>com <span class="blank _6"> </span>grande <span class="blank _6"> </span>uso <span class="blank _6"> </span>em</div><div class="t m0 x5 h8 y1c ff2 fs3 fc4 sc0 ls0 ws0">modelagem <span class="blank _f"> </span>matemática. <span class="blank _d"> </span>Na <span class="blank _f"> </span>Unidade <span class="blank _d"> </span>III <span class="blank _f"> </span>continuaremos <span class="blank _d"> </span>tratando <span class="blank _f"> </span>de <span class="blank _f"> </span>funções, <span class="blank _d"> </span>mas</div><div class="t m0 x5 h8 y1d ff2 fs3 fc4 sc0 ls0 ws0">um <span class="blank _9"> </span>caso <span class="blank"> </span>particular, <span class="blank _9"> </span>uma <span class="blank"> </span>f<span class="blank _0"></span>amília <span class="blank _9"> </span>de <span class="blank"> </span>funções <span class="blank _9"> </span>chamadas <span class="blank _9"> </span>funções <span class="blank _9"> </span>polinomiais, <span class="blank"> </span>esta</div><div class="t m0 x5 h8 y1e ff2 fs3 fc4 sc0 ls0 ws0">com <span class="blank _7"> </span>uma <span class="blank"> </span>gama <span class="blank _7"> </span>de <span class="blank _9"> </span>aplicações <span class="blank _9"> </span>gigantesca. <span class="blank _7"> </span>Por <span class="blank _9"> </span>\ue67dm, <span class="blank _9"> </span>na <span class="blank _9"> </span>Unidade <span class="blank"> </span>I<span class="blank _0"></span>V<span class="blank _0"></span>, <span class="blank _9"> </span>as <span class="blank _9"> </span>chamadas</div><div class="t m0 x5 h8 y1f ff2 fs3 fc4 sc0 ls0 ws0">funções <span class="blank _10"> </span>modulares <span class="blank _10"> </span>e <span class="blank _10"> </span>exponenciais, <span class="blank _10"> </span>essa <span class="blank _10"> </span>última <span class="blank _10"> </span>usada <span class="blank _11"> </span>em <span class="blank _10"> </span>vários <span class="blank _10"> </span>conc<span class="blank _0"></span>eitos</div><div class="t m0 x5 h8 y20 ff2 fs3 fc4 sc0 ls0 ws2">econômicos.</div><div class="t m0 x5 h8 y21 ff2 fs3 fc4 sc0 ls0 ws0">Espero <span class="blank _9"> </span>que <span class="blank"> </span>v<span class="blank _0"></span>ocê <span class="blank _9"> </span>aprov<span class="blank _0"></span>eite <span class="blank _9"> </span>ao <span class="blank"> </span>máximo <span class="blank _9"> </span>este <span class="blank"> </span>mat<span class="blank _2"></span>erial <span class="blank"> </span>que <span class="blank"> </span>f<span class="blank _0"></span>oi <span class="blank"> </span>c<span class="blank _0"></span>onfeccionado <span class="blank _9"> </span>com</div><div class="t m0 x5 h8 y22 ff2 fs3 fc4 sc0 ls0 ws0">muito carinho <span class="blank _1"> </span>e dedicação. <span class="blank _1"> </span>C<span class="blank _0"></span>onvido você para, <span class="blank _1"> </span>junto conosco<span class="blank _0"></span>, <span class="blank _1"> </span>perc<span class="blank _0"></span>orrer esta <span class="blank _1"> </span>jornada</div><div class="t m0 x5 h8 y23 ff2 fs3 fc4 sc0 ls0 ws0">de <span class="blank _3"> </span>conhecimento <span class="blank _3"> </span>e <span class="blank _3"> </span>multiplicar <span class="blank _3"> </span>os <span class="blank _3"> </span>conhecimentos <span class="blank _3"> </span>sobre <span class="blank _3"> </span>tant<span class="blank _0"></span>os <span class="blank _3"> </span>assuntos <span class="blank _3"> </span>abordados</div><div class="t m0 x5 h8 y24 ff2 fs3 fc4 sc0 ls0 ws0">em <span class="blank _4"> </span>nosso <span class="blank _4"> </span>material. <span class="blank _4"> </span>Esperamos <span class="blank _11"> </span>contribuir <span class="blank _4"> </span>para <span class="blank _4"> </span>seu <span class="blank _4"> </span>cresciment<span class="blank _0"></span>o <span class="blank _4"> </span>pessoal <span class="blank _4"> </span>e</div><div class="t m0 x5 h8 y25 ff2 fs3 fc4 sc0 ls0 ws2">pro\ue67dssional.</div><div class="t m0 x5 h9 y26 ff3 fs3 fc4 sc0 ls0 ws0">Muito obrigado e bom estudo!</div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/c5122ea8-ec8f-4696-a609-a943a1623b8e/bg3.png"><div class="c x0 y1 w2 h2"><div class="t m0 x0 h3 y3 ff5 fs0 fc1 sc0 ls0 ws0"><span class="fc2 sc0">Unidad</span><span class="fc2 sc0">e </span><span class="fc2 sc0">1</span></div><div class="t m0 x2 h3 y27 ff5 fs0 fc1 sc0 ls0 ws0"><span class="fc2 sc0">M</span><span class="fc2 sc0">a</span><span class="blank _2"></span><span class="fc2 sc0">t</span><span class="fc2 sc0">emá</span><span class="blank _2"></span><span class="fc2 sc0">t</span><span class="blank _1"></span><span class="fc2 sc0">ic</span><span class="fc2 sc0">a </span><span class="fc2 sc0">Básic</span><span class="fc2 sc0">a </span><span class="fc2 sc0">e</span></div><div class="t m0 x2 h3 y28 ff5 fs0 fc1 sc0 ls0 ws0"><span class="fc2 sc0">Conjun</span><span class="blank _2"></span><span class="fc2 sc0">t</span><span class="fc2 sc0">os </span><span class="fc2 sc0">Num</span><span class="blank _0"></span><span class="fc2 sc0">ér</span><span class="fc2 sc0">ic</span><span class="fc2 sc0">os</span></div><div class="t m0 x3 ha y6 ff6 fs1 fc1 sc0 ls0 ws1">AU<span class="blank _0"></span>TORIA</div><div class="t m0 x3 h5 y7 ff7 fs2 fc1 sc0 ls0 ws0">Luciano Xa<span class="blank _0"></span>vier de Azev<span class="blank _0"></span>edo</div></div><a class="l" data-dest-detail="[3,"XYZ",56,799.92,null]"><div class="d m1" style="border-style:none;position:absolute;left:101.000008px;bottom:700.169980px;width:393.000022px;height:43.500000px;background-color:rgba(255,255,255,0.000001);"></div></a></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w3 h1" alt="" src="https://files.passeidireto.com/c5122ea8-ec8f-4696-a609-a943a1623b8e/bg4.png"><div class="c x0 y8 w3 h6"><div class="t m0 x5 hb y29 ff8 fs4 fc3 sc0 ls0 ws0"><span class="fc2 sc0">In</span><span class="blank _0"></span><span class="fc2 sc0">tr</span><span class="blank _0"></span><span class="fc2 sc0">o</span><span class="fc2 sc0">dução</span></div><div class="t m0 x5 hc y2a ff6 fs3 fc4 sc0 ls0 ws0">Caro(a) aluno(a), seja bem-<span class="blank _0"></span>vindo à primeira unidade de nosso mat<span class="blank _0"></span>erial.</div><div class="t m0 x5 hc y2b ff6 fs3 fc4 sc0 ls0 ws0">A <span class="blank _7"> </span>Matemática <span class="blank _7"> </span>é <span class="blank _7"> </span>uma <span class="blank _9"> </span>ciência <span class="blank _7"> </span>essencial <span class="blank _9"> </span>à <span class="blank _7"> </span>vida <span class="blank _9"> </span>do <span class="blank _7"> </span>ser <span class="blank _9"> </span>humano. <span class="blank _7"> </span>Napoleão <span class="blank _7"> </span>disse: <span class="blank _7"> </span>\u201co</div><div class="t m0 x5 hc y2c ff6 fs3 fc4 sc0 ls0 ws0">progr<span class="blank _0"></span>esso <span class="blank _12"> </span>de <span class="blank _12"> </span>um <span class="blank _12"> </span>po<span class="blank _0"></span>vo <span class="blank _12"> </span>depende, <span class="blank _12"> </span>e<span class="blank _0"></span>x<span class="blank _0"></span>clusivament<span class="blank _0"></span>e, <span class="blank _12"> </span>do <span class="blank _12"> </span>desenv<span class="blank _0"></span>olvimento <span class="blank _13"> </span>da</div><div class="t m0 x5 hc y2d ff6 fs3 fc4 sc0 ls0 ws0">matemática<span class="blank _0"></span>\u201d. <span class="blank _7"> </span>A <span class="blank _7"> </span>Matemática <span class="blank _e"> </span>é <span class="blank _9"> </span>a <span class="blank _7"> </span>base <span class="blank _7"> </span>para <span class="blank _7"> </span>todas <span class="blank _7"> </span>as <span class="blank _7"> </span>ciências <span class="blank _7"> </span>e <span class="blank _9"> </span>artes, <span class="blank _7"> </span>por <span class="blank _7"> </span>envolv<span class="blank _0"></span>er</div><div class="t m0 x5 hc y2e ff6 fs3 fc4 sc0 ls0 ws0">conceit<span class="blank _0"></span>os necessários e fundamentais dentr<span class="blank _0"></span>o da matemática.</div><div class="t m0 x5 hc y2f ff6 fs3 fc4 sc0 ls0 ws0">Os <span class="blank _e"> </span>conteúdos <span class="blank _e"> </span>apresentados <span class="blank _e"> </span>na <span class="blank _7"> </span>primeira <span class="blank _e"> </span>parte <span class="blank _e"> </span>desta <span class="blank _7"> </span>unidade <span class="blank _7"> </span>serão <span class="blank _e"> </span>chamados <span class="blank _7"> </span>de</div><div class="t m0 x5 hc y30 ff6 fs3 fc4 sc0 ls0 ws0">Matemática <span class="blank _9"> </span>Básica, <span class="blank _9"> </span>que <span class="blank"> </span>não <span class="blank _9"> </span>é <span class="blank"> </span>r<span class="blank _0"></span>estrita <span class="blank _9"> </span>apenas <span class="blank"> </span>às <span class="blank _9"> </span>operações <span class="blank _9"> </span>de <span class="blank"> </span>soma, <span class="blank _9"> </span>subtração,</div><div class="t m0 x5 hc y31 ff6 fs3 fc4 sc0 ls0 ws0">multiplicação <span class="blank _1"> </span>e <span class="blank _1"> </span>divisão, <span class="blank _1"> </span>como <span class="blank _1"> </span>muita <span class="blank _1"> </span>gent<span class="blank _0"></span>e <span class="blank _1"> </span>pensa, <span class="blank _1"> </span>tem muito <span class="blank _1"> </span>mais. <span class="blank _1"> </span>Em <span class="blank _1"> </span>um <span class="blank _1"> </span>segundo</div><div class="t m0 x5 hc y32 ff6 fs3 fc4 sc0 ls0 ws0">momento<span class="blank _0"></span>, <span class="blank _a"> </span>apresentaremos <span class="blank _3"> </span>os <span class="blank _a"> </span>Conjunt<span class="blank _0"></span>os <span class="blank _a"> </span>Numéricos, <span class="blank _a"> </span>que <span class="blank _a"> </span>são <span class="blank _a"> </span>as <span class="blank _a"> </span>classi\ue67dcações <span class="blank _a"> </span>para</div><div class="t m0 x5 hc y33 ff6 fs3 fc4 sc0 ls0 ws0">os números conf<span class="blank _0"></span>orme sua natureza.</div><div class="t m0 x5 hc y34 ff6 fs3 fc4 sc0 ls0 ws0">O <span class="blank _3"> </span>que <span class="blank _1"> </span>faremos <span class="blank _1"> </span>nesta <span class="blank _3"> </span>unidade <span class="blank _3"> </span>é <span class="blank _3"> </span>focar <span class="blank _1"> </span>em <span class="blank _3"> </span>cont<span class="blank _0"></span>eúdos <span class="blank _1"> </span>especí\ue67dcos <span class="blank _3"> </span>de <span class="blank _3"> </span>álgebra <span class="blank _1"> </span>que <span class="blank _3"> </span>são</div><div class="t m0 x5 hc y35 ff6 fs3 fc4 sc0 ls0 ws0">essenciais <span class="blank _7"> </span>para <span class="blank _7"> </span>o <span class="blank _7"> </span>bom <span class="blank _7"> </span>desenv<span class="blank _0"></span>olvimento <span class="blank _7"> </span>dos <span class="blank _7"> </span>métodos <span class="blank _e"> </span>quantitativos <span class="blank _7"> </span>matemátic<span class="blank _0"></span>os.</div><div class="t m0 x5 hc y36 ff6 fs3 fc4 sc0 ls0 ws0">Tr<span class="blank _0"></span>ataremos das expressões numéricas que são ferramentas importantes pelo fat<span class="blank _0"></span>o de</div><div class="t m0 x5 hc y37 ff6 fs3 fc4 sc0 ls0 ws0">indicarem <span class="blank _d"> </span>organização <span class="blank _f"> </span>de <span class="blank _e"> </span>operações. <span class="blank _d"> </span>Depois <span class="blank _e"> </span>voc<span class="blank _0"></span>ê <span class="blank _f"> </span>irá <span class="blank _f"> </span>trabalhar <span class="blank _f"> </span>com <span class="blank _f"> </span>regra <span class="blank _d"> </span>de <span class="blank _f"> </span>três,</div><div class="t m0 x5 hc y38 ff6 fs3 fc4 sc0 ls0 ws0">famosa <span class="blank _3"> </span>conhecida <span class="blank _3"> </span>desde <span class="blank _3"> </span>o <span class="blank _3"> </span>ensino <span class="blank _3"> </span>fundamental. <span class="blank _a"> </span>Ela <span class="blank _3"> </span>tem <span class="blank _3"> </span>o <span class="blank _3"> </span>intuit<span class="blank _0"></span>o <span class="blank _3"> </span>de <span class="blank _3"> </span>trabalhar <span class="blank _3"> </span>com</div><div class="t m0 x5 hc y39 ff6 fs3 fc4 sc0 ls0 ws0">grandezas dir<span class="blank _0"></span>etas e inver<span class="blank _0"></span>sas.</div><div class="t m0 x5 hc y3a ff6 fs3 fc4 sc0 ls0 ws0">Ainda <span class="blank"> </span>nesta <span class="blank"> </span>unidade <span class="blank"> </span>falar<span class="blank _0"></span>emos <span class="blank"> </span>sobre <span class="blank"> </span>um <span class="blank _9"> </span>conceito <span class="blank _9"> </span>que <span class="blank"> </span>está <span class="blank"> </span>present<span class="blank _0"></span>e, <span class="blank"> </span>de <span class="blank"> </span>for<span class="blank _0"></span>ma</div><div class="t m0 x5 hc y3b ff6 fs3 fc4 sc0 ls0 ws0">f<span class="blank _3"> </span>requente, <span class="blank _7"> </span>em <span class="blank _7"> </span>nosso <span class="blank _9"> </span>dia <span class="blank _9"> </span>a <span class="blank _7"> </span>dia: <span class="blank _9"> </span>as <span class="blank _9"> </span>porc<span class="blank _0"></span>entagens. <span class="blank _9"> </span>V<span class="blank _2"></span>ocê <span class="blank _7"> </span>irá <span class="blank _7"> </span>aprender <span class="blank _9"> </span>como <span class="blank _7"> </span>fazer <span class="blank _7"> </span>o</div><div class="t m0 x5 hc y3c ff6 fs3 fc4 sc0 ls0 ws0">cálculo <span class="blank _e"> </span>deste <span class="blank _f"> </span>conceito<span class="blank _0"></span>. <span class="blank _e"> </span>Outro <span class="blank _f"> </span>assunto <span class="blank _e"> </span>importante <span class="blank _e"> </span>abordado <span class="blank _f"> </span>n<span class="blank _1"> </span>esta <span class="blank _f"> </span>unidade <span class="blank _7"> </span>são <span class="blank _e"> </span>as</div><div class="t m0 x5 hc y3d ff6 fs3 fc4 sc0 ls0 ws0">equações, <span class="blank _7"> </span>no <span class="blank _9"> </span>momento, <span class="blank _7"> </span>do <span class="blank _9"> </span>primeiro <span class="blank _7"> </span>e <span class="blank _9"> </span>segundo <span class="blank _7"> </span>grau. <span class="blank _9"> </span>Iremos <span class="blank _7"> </span>abordar <span class="blank _9"> </span>resoluç<span class="blank _0"></span>ões</div><div class="t m0 x5 hc y3e ff6 fs3 fc4 sc0 ls0 ws0">para <span class="blank _3"> </span>essas <span class="blank _3"> </span>equações <span class="blank _3"> </span>e <span class="blank _3"> </span>também <span class="blank _3"> </span>iremos <span class="blank _3"> </span>analisar <span class="blank _3"> </span>alguns <span class="blank _3"> </span>problemas <span class="blank _3"> </span>refer<span class="blank _0"></span>entes <span class="blank _3"> </span>a <span class="blank _3"> </span>elas.</div><div class="t m0 x5 hc y3f ff6 fs3 fc4 sc0 ls0 ws0">Por <span class="blank"> </span>\ue67dm, <span class="blank _14"> </span>entrar<span class="blank _0"></span>emos <span class="blank _14"> </span>na <span class="blank _14"> </span>t<span class="blank _0"></span>eoria <span class="blank"> </span>dos <span class="blank _14"> </span>conjunt<span class="blank _0"></span>os. <span class="blank _14"> </span>F<span class="blank _0"></span>aremos <span class="blank _14"> </span>um <span class="blank"> </span>\u201c<span class="blank _1"> </span>passeio\u201d <span class="blank _14"> </span>sobr<span class="blank _0"></span>e <span class="blank _14"> </span>esse</div><div class="t m0 x5 hc y40 ff6 fs3 fc4 sc0 ls0 ws0">assunto <span class="blank _e"> </span>que <span class="blank _7"> </span>é <span class="blank _7"> </span>a <span class="blank _7"> </span>base <span class="blank _7"> </span>de <span class="blank _9"> </span>vár<span class="blank _0"></span>ios <span class="blank _7"> </span>conceit<span class="blank _0"></span>os <span class="blank _7"> </span>dentro <span class="blank _7"> </span>da <span class="blank _7"> </span>matemática. <span class="blank _e"> </span>Iremos <span class="blank _7"> </span>abordar</div><div class="t m0 x5 hc y41 ff6 fs3 fc4 sc0 ls0 ws0">tipos <span class="blank _d"> </span>de <span class="blank _a"> </span>conjuntos <span class="blank _a"> </span>e <span class="blank _d"> </span>as <span class="blank _d"> </span>classi\ue67dcações <span class="blank _a"> </span>para <span class="blank _d"> </span>os <span class="blank _a"> </span>núm<span class="blank _1"> </span>er<span class="blank _0"></span>os, <span class="blank _d"> </span>naturais, <span class="blank _a"> </span>inteiros, <span class="blank _a"> </span>racionais,</div><div class="t m0 x5 hc y42 ff6 fs3 fc4 sc0 ls0 ws0">irracionais e r<span class="blank _0"></span>eais, que são chamados de c<span class="blank _0"></span>onjuntos numéric<span class="blank _0"></span>os.</div><div class="t m0 x5 hc y43 ff6 fs3 fc4 sc0 ls0 ws0">Apro<span class="blank _0"></span>veit<span class="blank _0"></span>e ao máximo seus estudos. V<span class="blank _2"></span>amos lá então!</div><div class="t m0 x5 hc y44 ff6 fs3 fc4 sc0 ls0 ws0">Bons estudos!</div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/c5122ea8-ec8f-4696-a609-a943a1623b8e/bg5.png"><div class="c x0 y1 w2 h2"><div class="t m0 x2 h3 y3 ff9 fs0 fc1 sc0 ls0 ws0"><span class="fc2 sc0">Expr</span><span class="blank _0"></span><span class="fc2 sc0">e</span><span class="fc2 sc0">ssõ</span><span class="fc2 sc0">e</span><span class="fc2 sc0">s </span><span class="fc2 sc0">N</span><span class="fc2 sc0">um</span><span class="fc2 sc0">ér</span><span class="blank _1"></span><span class="fc2 sc0">ic</span><span class="fc2 sc0">as</span></div><div class="t m0 x3 ha y6 ffa fs1 fc1 sc0 ls0 ws1">AU<span class="blank _0"></span>TORIA</div><div class="t m0 x3 h5 y7 ffb fs2 fc1 sc0 ls0 ws0">Luciano Xa<span class="blank _0"></span>vier de Azev<span class="blank _0"></span>edo</div></div><a class="l" data-dest-detail="[5,"XYZ",56,799.92,null]"><div class="d m1" style="border-style:none;position:absolute;left:101.000008px;bottom:700.169980px;width:393.000022px;height:43.500000px;background-color:rgba(255,255,255,0.000001);"></div></a></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w3 h1" alt="" src="https://files.passeidireto.com/c5122ea8-ec8f-4696-a609-a943a1623b8e/bg6.png"><div class="c x0 y1 w2 h2"><div class="t m0 x5 hd y45 ffa fs5 fc4 sc0 ls0 ws0">V<span class="blank _2"></span>ocê <span class="blank _e"> </span>deve <span class="blank _f"> </span>ter <span class="blank _e"> </span>ouvido <span class="blank _7"> </span>falar <span class="blank _e"> </span>muito <span class="blank _f"> </span>em <span class="blank _7"> </span>Expr<span class="blank _0"></span>essões <span class="blank _e"> </span>Numéricas, <span class="blank _7"> </span>mas <span class="blank _e"> </span>o <span class="blank _e"> </span>que <span class="blank _7"> </span>é <span class="blank _e"> </span>isso<span class="blank _0"></span>? <span class="blank _e"> </span>A</div><div class="t m0 x5 hd y46 ffa fs5 fc4 sc0 ls0 ws0">resposta é <span class="blank _1"> </span>simples, <span class="blank _1"> </span>são <span class="blank _1"> </span>sequências <span class="blank _1"> </span>de <span class="blank _1"> </span>operações que <span class="blank _1"> </span>são <span class="blank _1"> </span>ordenadas, ou <span class="blank _1"> </span>seja, <span class="blank _1"> </span>devem</div><div class="t m0 x5 hd y47 ffa fs5 fc4 sc0 ls0 ws0">ser <span class="blank _a"> </span>realizadas <span class="blank _a"> </span>respeitando <span class="blank _d"> </span>deter<span class="blank _0"></span>minada <span class="blank _d"> </span>ordem. <span class="blank _a"> </span>Para <span class="blank _a"> </span>indicar <span class="blank _d"> </span>essa <span class="blank _d"> </span>ordem, <span class="blank _a"> </span>é <span class="blank _d"> </span>comum</div><div class="t m0 x5 hd y48 ffa fs5 fc4 sc0 ls0 ws0">usarmos <span class="blank _b"> </span>símbolos <span class="blank _8"> </span>de <span class="blank _8"> </span>separação <span class="blank _8"> </span>de <span class="blank _b"> </span>operações. <span class="blank _8"> </span>Esses <span class="blank _b"> </span>símbolos <span class="blank _8"> </span>são <span class="blank _8"> </span>parênt<span class="blank _0"></span>eses,</div><div class="t m0 x5 hd y49 ffa fs5 fc4 sc0 ls0 ws0">colchet<span class="blank _0"></span>es <span class="blank _9"> </span>e <span class="blank"> </span>cha<span class="blank _0"></span>ves. <span class="blank _9"> </span>Par<span class="blank _0"></span>a <span class="blank"> </span>r<span class="blank _0"></span>esolver <span class="blank _9"> </span>uma <span class="blank _9"> </span>expressão <span class="blank _9"> </span>numérica <span class="blank _9"> </span>devemos <span class="blank _9"> </span>seguir <span class="blank _9"> </span>uma</div><div class="t m0 x5 hd y4a ffa fs5 fc4 sc0 ls0 ws0">ordem <span class="blank _a"> </span>de <span class="blank _d"> </span>resolução<span class="blank _0"></span>, <span class="blank _d"> </span>tant<span class="blank _0"></span>o <span class="blank _d"> </span>em <span class="blank _a"> </span>relação <span class="blank _d"> </span>aos <span class="blank _d"> </span>símbolos <span class="blank _a"> </span>de <span class="blank _d"> </span>separação <span class="blank _a"> </span>quanto <span class="blank _a"> </span>à <span class="blank _d"> </span>ordem</div><div class="t m0 x5 hd y4b ffa fs5 fc4 sc0 ls0 ws0">das operações. A or<span class="blank _0"></span>dem é essa:</div><div class="t m0 x5 hd y4c ffa fs5 fc4 sc0 ls0 ws0">Quanto os símbolos sep<span class="blank _0"></span>aradores:</div><div class="t m0 x6 hd y4d ffa fs5 fc4 sc0 ls0 ws0">1<span class="blank _0"></span>. <span class="blank _1"> </span>Eliminar os parênteses.</div><div class="t m0 x7 hd y4e ffa fs5 fc4 sc0 ls0 ws0">2<span class="blank _2"></span>. <span class="blank _3"> </span>Eliminar os colchet<span class="blank _0"></span>es.</div><div class="t m0 x7 hd y4f ffa fs5 fc4 sc0 ls0 ws0">3<span class="blank _0"></span>. <span class="blank _1"> </span>Eliminar as chaves.</div><div class="t m0 x5 hd y50 ffa fs5 fc4 sc0 ls0 ws0">Quanto às oper<span class="blank _0"></span>ações:</div><div class="t m0 x6 hd y51 ffa fs5 fc4 sc0 ls0 ws0">1<span class="blank _0"></span>. <span class="blank _1"> </span>Efetuar potenciação e radiciação.</div><div class="t m0 x7 hd y52 ffa fs5 fc4 sc0 ls0 ws0">2<span class="blank _2"></span>. <span class="blank _3"> </span>Efetuar multiplicação e divisão.</div><div class="t m0 x7 hd y53 ffa fs5 fc4 sc0 ls0 ws0">3<span class="blank _0"></span>. <span class="blank _1"> </span>Efetuar adição e subtração.</div><div class="t m0 x5 hd y54 ffa fs5 fc4 sc0 ls0 ws0">Ao <span class="blank _e"> </span>se <span class="blank _7"> </span>resolv<span class="blank _0"></span>er <span class="blank _e"> </span>a <span class="blank _7"> </span>expressão<span class="blank _0"></span>, <span class="blank _e"> </span>se <span class="blank _7"> </span>você <span class="blank _f"> </span>notar <span class="blank _7"> </span>mais <span class="blank _7"> </span>de <span class="blank _e"> </span>uma <span class="blank _7"> </span>operação <span class="blank _e"> </span>com <span class="blank _e"> </span>prioridade,</div><div class="t m0 x5 hd y55 ffa fs5 fc4 sc0 ls0 ws0">então se dev<span class="blank _0"></span>e começar com aquela que aparec<span class="blank _0"></span>e primeiro<span class="blank _0"></span>.</div><div class="t m0 x5 he y56 ffb fs5 fc4 sc0 ls0 ws0">Ex<span class="blank _0"></span>emplo resolvido:</div><div class="t m0 x5 hd y57 ffa fs5 fc4 sc0 ls0 ws0">Deter<span class="blank _0"></span>mine o valor da e<span class="blank _0"></span>xpressão E = 396 : {2.[ 26 \u2013 5.(2 + 3)2]} .</div><div class="t m0 x5 he y58 ffb fs5 fc4 sc0 ls0 ws3">Resolução:</div><div class="t m0 x5 hd y59 ffa fs5 fc4 sc0 ls0 ws0">Note <span class="blank _d"> </span>que, <span class="blank _e"> </span>pela <span class="blank _f"> </span>ordem <span class="blank _f"> </span>de <span class="blank _e"> </span>prioridade, <span class="blank _f"> </span>devemos <span class="blank _f"> </span>resolv<span class="blank _0"></span>er <span class="blank _f"> </span>a <span class="blank _e"> </span>soma <span class="blank _f"> </span>dentro <span class="blank _f"> </span>parênteses.</div><div class="t m0 x5 hd y5a ffa fs5 fc4 sc0 ls0 ws0">Desta forma t<span class="blank _0"></span>emos</div><div class="t m0 x5 hd y5b ffa fs5 fc4 sc0 ls0 ws0">E = 396 : {2.[ 26 \u2013 5.(5)2]}.</div><div class="t m0 x5 hd y5c ffa fs5 fc4 sc0 ls0 ws0">C<span class="blank _0"></span>omo <span class="blank _3"> </span>só <span class="blank _1"> </span>temos <span class="blank _1"> </span>um <span class="blank _3"> </span>element<span class="blank _0"></span>o <span class="blank _1"> </span>dentro <span class="blank _3"> </span>dos <span class="blank _1"> </span>parênt<span class="blank _0"></span>eses <span class="blank _1"> </span>podemos <span class="blank _3"> </span>eliminá-lo <span class="blank _1"> </span>fazendo <span class="blank _1"> </span>a</div><div class="t m0 x5 hd y5d ffa fs5 fc4 sc0 ls0 ws2">potência:</div><div class="t m0 x5 hd y5e ffa fs5 fc4 sc0 ls0 ws0">E = 396 : {2.[ 26 \u2013 5.25]} .</div><div class="t m0 x5 hd y5f ffa fs5 fc4 sc0 ls0 ws0">Agora, <span class="blank _3"> </span>iremos <span class="blank _3"> </span>trabalhar <span class="blank _3"> </span>os <span class="blank _a"> </span>colchet<span class="blank _0"></span>es, <span class="blank _a"> </span>dentro <span class="blank _3"> </span>temos <span class="blank _3"> </span>uma <span class="blank _a"> </span>operação <span class="blank _3"> </span>prioritária, <span class="blank _3"> </span>que <span class="blank _a"> </span>é</div><div class="t m0 x5 hd y60 ffa fs5 fc4 sc0 ls0 ws0">multiplicação, em seguida far<span class="blank _0"></span>emos a subtração. Então</div><div class="t m0 x5 hd y61 ffa fs5 fc4 sc0 ls0 ws0">E = 396 : {2.[26 \u2013 125]} . </div><div class="t m0 x5 hd y62 ffa fs5 fc4 sc0 ls0 ws0">E = 396 : {2.[\u2013 99]} .</div><div class="t m0 x5 hd y63 ffa fs5 fc4 sc0 ls0 ws0">Ficamos <span class="blank _a"> </span>com <span class="blank _d"> </span>apenas <span class="blank _d"> </span>um <span class="blank _d"> </span>elemento <span class="blank _d"> </span>dentro <span class="blank _a"> </span>dos <span class="blank _d"> </span>colchet<span class="blank _0"></span>es. <span class="blank _d"> </span>Agora <span class="blank _d"> </span>podemos <span class="blank _d"> </span>calcular</div><div class="t m0 x5 hd y64 ffa fs5 fc4 sc0 ls0 ws0">usando o produt<span class="blank _0"></span>o por dois.</div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y65 w3 hf" alt="" src="https://files.passeidireto.com/c5122ea8-ec8f-4696-a609-a943a1623b8e/bg7.png"><div class="c x0 y66 w2 h10"><div class="t m0 x5 hd y67 ffa fs5 fc4 sc0 ls0 ws0">E = 396 : {\u2013198} .</div><div class="t m0 x5 hd y68 ffa fs5 fc4 sc0 ls0 ws0">C<span class="blank _0"></span>omo <span class="blank _f"> </span>agora <span class="blank _f"> </span>temos <span class="blank _d"> </span>apenas <span class="blank _f"> </span>um <span class="blank _f"> </span>elem<span class="blank _1"> </span>ent<span class="blank _0"></span>o <span class="blank _f"> </span>dentro <span class="blank _d"> </span>das <span class="blank _f"> </span>chaves <span class="blank _d"> </span>podemos <span class="blank _f"> </span>eliminá-las,</div><div class="t m0 x5 hd y69 ffa fs5 fc4 sc0 ls0 ws0">assim E = \u2013 2.</div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/c5122ea8-ec8f-4696-a609-a943a1623b8e/bg8.png"><div class="c x0 y1 w2 h2"><div class="t m0 x2 h3 y3 ffc fs0 fc1 sc0 ls0 ws0"><span class="fc2 sc0">Re</span><span class="fc2 sc0">gr</span><span class="blank _0"></span><span class="fc2 sc0">a </span><span class="fc2 sc0">d</span><span class="fc2 sc0">e </span><span class="fc2 sc0">T</span><span class="blank _2"></span><span class="fc2 sc0">r</span><span class="blank _2"></span><span class="fc2 sc0">ê</span><span class="fc2 sc0">s</span></div><div class="t m0 x3 h11 y6 ffd fs1 fc1 sc0 ls0 ws1">AU<span class="blank _0"></span>TORIA</div><div class="t m0 x3 h5 y7 ffe fs2 fc1 sc0 ls0 ws0">Luciano Xa<span class="blank _0"></span>vier de Azev<span class="blank _0"></span>edo</div></div><a class="l" data-dest-detail="[8,"XYZ",56,799.92,null]"><div class="d m1" style="border-style:none;position:absolute;left:101.000008px;bottom:700.169980px;width:393.000022px;height:43.500000px;background-color:rgba(255,255,255,0.000001);"></div></a></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w3 h1" alt="" src="https://files.passeidireto.com/c5122ea8-ec8f-4696-a609-a943a1623b8e/bg9.png"><div class="c x0 y1 w2 h2"><div class="t m0 x5 h12 y45 ffd fs5 fc4 sc0 ls0 ws0">Regra <span class="blank _d"> </span>de <span class="blank _e"> </span>três <span class="blank _d"> </span>é <span class="blank _f"> </span>um <span class="blank _e"> </span>assunto <span class="blank _d"> </span>que <span class="blank _f"> </span>você <span class="blank _d"> </span>já <span class="blank _e"> </span>dev<span class="blank _0"></span>e <span class="blank _f"> </span>ter <span class="blank _f"> </span>ouvido <span class="blank _f"> </span>falar <span class="blank _d"> </span>muito. <span class="blank _d"> </span>Mas <span class="blank _f"> </span>o <span class="blank _e"> </span>que <span class="blank _f"> </span>é</div><div class="t m0 x5 h12 y46 ffd fs5 fc4 sc0 ls0 ws0">isso<span class="blank _2"></span>? <span class="blank"> </span>São <span class="blank _7"> </span>problemas <span class="blank _9"> </span>que <span class="blank"> </span>apr<span class="blank _0"></span>esentam <span class="blank _9"> </span>grandezas <span class="blank _9"> </span>relacionadas, <span class="blank _9"> </span>tanto <span class="blank _7"> </span>diretamente</div><div class="t m0 x5 h12 y47 ffd fs5 fc4 sc0 ls0 ws0">quanto <span class="blank _a"> </span>inversament<span class="blank _2"></span>e <span class="blank _d"> </span>proporcionais. <span class="blank _a"> </span>T<span class="blank _0"></span>emos <span class="blank _d"> </span>duas <span class="blank _d"> </span>situações <span class="blank _a"> </span>a <span class="blank _d"> </span>considerar, <span class="blank _a"> </span>a <span class="blank _d"> </span>primeira</div><div class="t m0 x5 h12 y48 ffd fs5 fc4 sc0 ls0 ws0">chamada simples e a segunda, composta. V<span class="blank _2"></span>amos conhec<span class="blank _0"></span>er cada uma delas.</div><div class="t m0 x5 h12 y6a ffe fs5 fc4 sc0 ls0 ws0">Regra de três simples<span class="ffd"> é um pr<span class="blank _0"></span>ocesso prátic<span class="blank _0"></span>o para resolv<span class="blank _0"></span>er problemas que en<span class="blank _0"></span>volv<span class="blank _0"></span>am</span></div><div class="t m0 x5 h12 y6b ffd fs5 fc4 sc0 ls0 ws0">quatro valor<span class="blank _0"></span>es <span class="blank _1"> </span>dos quais <span class="blank _1"> </span>conhecemos três deles. <span class="blank _1"> </span>Devemos, portanto, deter<span class="blank _0"></span>minar <span class="blank _1"> </span>um</div><div class="t m0 x5 h12 y6c ffd fs5 fc4 sc0 ls0 ws0">valor <span class="blank _15"> </span>a <span class="blank _15"> </span>par<span class="blank _1"> </span>tir <span class="blank _15"> </span>dos <span class="blank _b"> </span>três <span class="blank _14"> </span>já <span class="blank _b"> </span>conhecidos. <span class="blank _15"> </span><span class="ffe">Regra <span class="blank _15"> </span>de <span class="blank _15"> </span>três <span class="blank _15"> </span>composta</span> <span class="blank _b"> </span>é <span class="blank _b"> </span>utilizada <span class="blank _b"> </span>em</div><div class="t m0 x5 h12 y4c ffd fs5 fc4 sc0 ls0 ws0">problemas c<span class="blank _0"></span>om mais de duas grandezas.</div><div class="t m0 x5 he y4d ffe fs5 fc4 sc0 ls0 ws0">Ex<span class="blank _0"></span>emplos resolvidos:</div><div class="t m0 x5 h12 y6d ffd fs5 fc4 sc0 ls0 ws0">1) <span class="blank _3"> </span>Para <span class="blank _1"> </span>percorr<span class="blank _0"></span>er <span class="blank _3"> </span>certo <span class="blank _3"> </span>trajet<span class="blank _0"></span>o, <span class="blank _3"> </span>um <span class="blank _3"> </span>carro<span class="blank _0"></span>, <span class="blank _3"> </span>à <span class="blank _3"> </span>velocidade <span class="blank _3"> </span>de <span class="blank _3"> </span>60km/h, <span class="blank _3"> </span>faz <span class="blank _3"> </span>certo <span class="blank _3"> </span>per<span class="blank _0"></span>curso</div><div class="t m0 x5 h12 y6e ffd fs5 fc4 sc0 ls0 ws0">em <span class="blank _d"> </span>4 <span class="blank _f"> </span>horas. <span class="blank _d"> </span>Se <span class="blank _d"> </span>a <span class="blank _f"> </span>velocidade <span class="blank _d"> </span>desse <span class="blank _f"> </span>carr<span class="blank _0"></span>o <span class="blank _f"> </span>fosse <span class="blank _d"> </span>de <span class="blank _d"> </span>80km/h, <span class="blank _d"> </span>em <span class="blank _f"> </span>quantas <span class="blank _f"> </span>horas <span class="blank _d"> </span>seria</div><div class="t m0 x5 h12 y6f ffd fs5 fc4 sc0 ls0 ws0">feit<span class="blank _0"></span>o o mesmo percurso<span class="blank _2"></span>?</div><div class="t m0 x5 he y70 ffe fs5 fc4 sc0 ls0 ws3">Resolução:</div><div class="t m0 x5 h12 y71 ffd fs5 fc4 sc0 ls0 ws0">Observe <span class="blank _3"> </span>que <span class="blank _1"> </span>a <span class="blank _3"> </span>velocidade <span class="blank _1"> </span>e <span class="blank _3"> </span>o <span class="blank _1"> </span>tempo <span class="blank _1"> </span>são <span class="blank _3"> </span>grandezas <span class="blank _1"> </span>inversament<span class="blank _0"></span>e <span class="blank _3"> </span>propor<span class="blank _0"></span>cionais, <span class="blank _1"> </span>ou</div><div class="t m0 x5 h12 y72 ffd fs5 fc4 sc0 ls0 ws0">seja, <span class="blank"> </span>quanto <span class="blank"> </span>maior <span class="blank"> </span>a <span class="blank"> </span>v<span class="blank _0"></span>elocidade, <span class="blank"> </span>menor <span class="blank"> </span>o <span class="blank"> </span>tempo, <span class="blank"> </span>ele <span class="blank"> </span>diminui <span class="blank"> </span>em <span class="blank"> </span>r<span class="blank _0"></span>azão <span class="blank"> </span>inversa.</div><div class="t m0 x5 h12 y73 ffd fs5 fc4 sc0 ls0 ws0">Então <span class="blank _1"> </span>podemos <span class="blank _1"> </span>nos <span class="blank _1"> </span>guiar <span class="blank _1"> </span>pelo <span class="blank _1"> </span>esquema <span class="blank _1"> </span>de <span class="blank _1"> </span>\ue67eechas, informando <span class="blank _1"> </span>que <span class="blank _1"> </span>sentidos <span class="blank _1"> </span>iguais</div><div class="t m0 x5 h12 y74 ffd fs5 fc4 sc0 ls0 ws0">nos informam que as gr<span class="blank _0"></span>andezas são diretas e sentidos opost<span class="blank _0"></span>os, grandezas inv<span class="blank _0"></span>ersas:</div><div class="t m0 x5 h12 y75 ffd fs5 fc4 sc0 ls0 ws2">Assim</div><div class="t m0 x5 h12 y76 ffd fs5 fc4 sc0 ls0 ws0">Logo o t<span class="blank _0"></span>empo que ele irá gastar é 3 horas.</div><div class="t m0 x5 h12 y77 ffd fs5 fc4 sc0 ls0 ws0">2) <span class="blank _1"> </span>A <span class="blank _3"> </span>construt<span class="blank _0"></span>ora <span class="blank _1"> </span>ALEGRIA <span class="blank _1"> </span>está <span class="blank _3"> </span>trabalhando <span class="blank _1"> </span>fazendo <span class="blank _1"> </span>a <span class="blank _3"> </span>t<span class="blank _0"></span>erraplanagem <span class="blank _1"> </span>de <span class="blank _1"> </span>um <span class="blank _3"> </span>grande</div><div class="t m0 x5 h12 y78 ffd fs5 fc4 sc0 ls0 ws0">ter<span class="blank _0"></span>reno. <span class="blank _b"> </span>Como <span class="blank _8"> </span>o <span class="blank _8"> </span>terr<span class="blank _0"></span>eno <span class="blank _8"> </span>era <span class="blank _8"> </span>desnivelado, <span class="blank _8"> </span>ela <span class="blank _8"> </span>pretendia <span class="blank _b"> </span>colocar <span class="blank _c"> </span>20 <span class="blank _b"> </span>caminhões</div><div class="t m0 x5 h12 y79 ffd fs5 fc4 sc0 ls0 ws0">idênticos <span class="blank _3"> </span>para <span class="blank _a"> </span>transportar <span class="blank _a"> </span>160m3 <span class="blank _a"> </span>de <span class="blank _a"> </span>terr<span class="blank _0"></span>a <span class="blank _a"> </span>em <span class="blank _a"> </span>8 <span class="blank _a"> </span>horas, <span class="blank _3"> </span>o <span class="blank _a"> </span>que <span class="blank _a"> </span>seria <span class="blank _a"> </span>su\ue67dciente <span class="blank _3"> </span>para <span class="blank _3"> </span>o</div><div class="t m0 x5 h12 y7a ffd fs5 fc4 sc0 ls0 ws0">serviço. <span class="blank _3"> </span>Mas <span class="blank _a"> </span>o <span class="blank _a"> </span>en<span class="blank _1"> </span>genheiro <span class="blank _3"> </span>recalculou <span class="blank _3"> </span>e <span class="blank _a"> </span>veri\ue67dcou <span class="blank _3"> </span>que <span class="blank _a"> </span>serão <span class="blank _a"> </span>necessários <span class="blank _a"> </span>descarregar</div><div class="t m0 x5 h12 y7b ffd fs5 fc4 sc0 ls0 ws0">apenas <span class="blank _1"> </span>125m3. <span class="blank _1"> </span>Por <span class="blank _1"> </span>questão <span class="blank _1"> </span>de <span class="blank _1"> </span>logística, <span class="blank _3"> </span>os <span class="blank _1"> </span>caminhões <span class="blank _1"> </span>irão <span class="blank _1"> </span>trabalhar <span class="blank _1"> </span>apenas <span class="blank _1"> </span>5 <span class="blank _1"> </span>horas.</div><div class="t m0 x5 h12 y7c ffd fs5 fc4 sc0 ls0 ws0">Nessas condições, quant<span class="blank _0"></span>os caminhões serão necessár<span class="blank _0"></span>ios?</div><div class="t m0 x8 h13 y7d fff fs6 fc4 sc0 ls0 ws4"><span class="fc2 sc0">=</span><span class="blank _16"> </span><span class="fc2 sc0">\u21d2</span><span class="blank"> </span><span class="fc2 sc0">8</span></div><div class="t m0 x9 h13 y7d ff10 fs6 fc4 sc0 ls0"><span class="fc2 sc0">x</span></div><div class="t m0 xa h13 y7d fff fs6 fc4 sc0 ls0 ws5"><span class="fc2 sc0">=</span><span class="blank _15"> </span><span class="fc2 sc0">4</span><span class="blank"> </span><span class="fc2 sc0">×</span><span class="blank"> </span><span class="fc2 sc0">6</span><span class="blank _15"> </span><span class="fc2 sc0">\u21d2</span><span class="blank _15"> </span><span class="fc2 sc0">8</span></div><div class="t m0 xb h13 y7d ff10 fs6 fc4 sc0 ls0"><span class="fc2 sc0">x</span></div><div class="t m0 xc h13 y7d fff fs6 fc4 sc0 ls0 ws6"><span class="fc2 sc0">=</span><span class="blank"> </span><span class="fc2 sc0">2</span><span class="fc2 sc0">4</span></div><div class="t m0 xd h13 y7e fff fs6 fc4 sc0 ls0"><span class="fc2 sc0">4</span></div><div class="t m0 xd h13 y7f ff10 fs6 fc4 sc0 ls0"><span class="fc2 sc0">x</span></div><div class="t m0 xe h13 y7e fff fs6 fc4 sc0 ls0 ws0"><span class="fc2 sc0">8</span><span class="fc2 sc0">\u2212</span><span class="blank _17"></span><span class="fc2 sc0">0</span></div><div class="t m0 xe h13 y7f fff fs6 fc4 sc0 ls0 ws0"><span class="fc2 sc0">6</span><span class="fc2 sc0">\u2212</span><span class="blank _17"></span><span class="fc2 sc0">0</span></div><div class="t m0 xf h13 y80 ff10 fs6 fc4 sc0 ls0"><span class="fc2 sc0">x</span></div><div class="t m0 x10 h13 y80 fff fs6 fc4 sc0 ls0 ws7"><span class="fc2 sc0">=</span><span class="blank"> </span><span class="fc2 sc0">\u21d2</span></div><div class="t m0 x11 h13 y80 ff10 fs6 fc4 sc0 ls0"><span class="fc2 sc0">x</span></div><div class="t m0 x12 h13 y80 fff fs6 fc4 sc0 ls0 ws6"><span class="fc2 sc0">=</span><span class="blank"> </span><span class="fc2 sc0">3</span></div><div class="t m0 x13 h13 y81 fff fs6 fc4 sc0 ls0 ws0"><span class="fc2 sc0">2</span><span class="fc2 sc0">4</span></div><div class="t m0 x14 h13 y82 fff fs6 fc4 sc0 ls0"><span class="fc2 sc0">8</span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pfa" class="pf w0 h0" data-page-no="a"><div class="pc pca w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y83 w3 h14" alt="" src="https://files.passeidireto.com/c5122ea8-ec8f-4696-a609-a943a1623b8e/bga.png"><div class="c x0 y66 w2 h10"><div class="t m0 x5 he y67 ffe fs5 fc4 sc0 ls0 ws3">Resolução.</div><div class="t m0 x5 h12 y68 ffd fs5 fc4 sc0 ls0 ws0">Dev<span class="blank _0"></span>emos <span class="blank _f"> </span>analisar <span class="blank _d"> </span>as <span class="blank _f"> </span>grandezas <span class="blank _d"> </span>número <span class="blank _d"> </span>de <span class="blank _d"> </span>caminhões <span class="blank _f"> </span>com <span class="blank _d"> </span>horas <span class="blank _d"> </span>e <span class="blank _f"> </span>também <span class="blank _d"> </span>com</div><div class="t m0 x5 h12 y69 ffd fs5 fc4 sc0 ls0 ws0">volume <span class="blank _f"> </span>de <span class="blank _f"> </span>forma <span class="blank _f"> </span>separada. <span class="blank _f"> </span>Obser<span class="blank _1"> </span>v<span class="blank _0"></span>amos <span class="blank _e"> </span>que <span class="blank _f"> </span>aumentando <span class="blank _e"> </span>o <span class="blank _f"> </span>núm<span class="blank _1"> </span>er<span class="blank _0"></span>o <span class="blank _e"> </span>de <span class="blank _f"> </span>horas <span class="blank _f"> </span>de</div><div class="t m0 x5 h12 y84 ffd fs5 fc4 sc0 ls0 ws0">trabalho<span class="blank _0"></span>, <span class="blank _6"> </span>podemos <span class="blank _6"> </span>diminuir <span class="blank _18"> </span>o <span class="blank _18"> </span>número <span class="blank _6"> </span>de <span class="blank _18"> </span>caminhões, <span class="blank _6"> </span>logo <span class="blank _18"> </span>temos <span class="blank _18"> </span>grandezas</div><div class="t m0 x5 h12 y85 ffd fs5 fc4 sc0 ls0 ws0">inv<span class="blank _0"></span>ersamente <span class="blank _18"> </span>propor<span class="blank _0"></span>cionais. <span class="blank _18"> </span>Agora, <span class="blank _18"> </span>aumentando <span class="blank _6"> </span>o <span class="blank _18"> </span>volume <span class="blank _18"> </span>dev<span class="blank _0"></span>emos <span class="blank _18"> </span>ter <span class="blank _18"> </span>mais</div><div class="t m0 x5 h12 y86 ffd fs5 fc4 sc0 ls0 ws0">caminhões, <span class="blank _7"> </span>então <span class="blank _9"> </span>temos <span class="blank _7"> </span>grandezas <span class="blank _7"> </span>diretament<span class="blank _0"></span>e <span class="blank _7"> </span>proporcionais. <span class="blank _7"> </span>Guiando-nos <span class="blank _9"> </span>pelo</div><div class="t m0 x5 h12 y87 ffd fs5 fc4 sc0 ls0 ws0">esquema de \ue67eechas:</div><div class="t m0 x5 h12 y88 ffd fs5 fc4 sc0 ls0 ws0">C<span class="blank _0"></span>oncluímos que serão necessários 25 caminhões.</div><div class="t m0 x15 h13 y89 fff fs6 fc4 sc0 ls0 ws4"><span class="fc2 sc0">=</span><span class="blank _19"> </span><span class="fc2 sc0">×</span><span class="blank _1a"> </span><span class="fc2 sc0">\u21d2</span><span class="blank _16"> </span><span class="fc2 sc0">=</span><span class="blank _1b"> </span><span class="fc2 sc0">\u21d2</span><span class="blank"> </span><span class="fc2 sc0">8</span></div><div class="t m0 x16 h13 y89 ff10 fs6 fc4 sc0 ls0"><span class="fc2 sc0">x</span></div><div class="t m0 x17 h13 y89 fff fs6 fc4 sc0 ls0 ws5"><span class="fc2 sc0">=</span><span class="blank _15"> </span><span class="fc2 sc0">1</span><span class="fc2 sc0">0</span><span class="blank"> </span><span class="fc2 sc0">×</span><span class="blank"> </span><span class="fc2 sc0">2</span><span class="fc2 sc0">0</span></div><div class="t m0 x18 h13 y8a fff fs6 fc4 sc0 ls0 ws0"><span class="fc2 sc0">2</span><span class="fc2 sc0">0</span></div><div class="t m0 x19 h13 y8b ff10 fs6 fc4 sc0 ls0"><span class="fc2 sc0">x</span></div><div class="t m0 x1a h13 y8a fff fs6 fc4 sc0 ls0 ws0"><span class="fc2 sc0">1</span><span class="fc2 sc0">6</span><span class="fc2 sc0">0</span></div><div class="t m0 x1a h13 y8b fff fs6 fc4 sc0 ls0 ws0"><span class="fc2 sc0">1</span><span class="fc2 sc0">2</span><span class="fc2 sc0">5</span></div><div class="t m0 x1b h13 y8a fff fs6 fc4 sc0 ls0"><span class="fc2 sc0">5</span></div><div class="t m0 x1b h13 y8b fff fs6 fc4 sc0 ls0"><span class="fc2 sc0">8</span></div><div class="t m0 x1c h13 y8a fff fs6 fc4 sc0 ls0 ws0"><span class="fc2 sc0">2</span><span class="fc2 sc0">0</span></div><div class="t m0 x9 h13 y8b ff10 fs6 fc4 sc0 ls0"><span class="fc2 sc0">x</span></div><div class="t m0 x11 h13 y8a fff fs6 fc4 sc0 ls0 ws0"><span class="fc2 sc0">8</span><span class="fc2 sc0">\u2212</span><span class="blank _17"></span><span class="fc2 sc0">0</span><span class="fc2 sc0">\u2212</span><span class="blank _17"></span><span class="fc2 sc0">0</span></div><div class="t m0 x1d h13 y8b fff fs6 fc4 sc0 ls0 ws0"><span class="fc2 sc0">1</span><span class="fc2 sc0">0</span><span class="fc2 sc0">\u2212</span><span class="blank _17"></span><span class="fc2 sc0">0</span><span class="fc2 sc0">\u2212</span><span class="blank _17"></span><span class="fc2 sc0">0</span></div><div class="t m0 x1e h13 y8c fff fs6 fc4 sc0 ls0"><span class="fc2 sc0">8</span></div><div class="t m0 x1f h13 y8c ff10 fs6 fc4 sc0 ls0"><span class="fc2 sc0">x</span></div><div class="t m0 x20 h13 y8c fff fs6 fc4 sc0 ls0 ws6"><span class="fc2 sc0">=</span><span class="blank"> </span><span class="fc2 sc0">2</span><span class="fc2 sc0">0</span><span class="fc2 sc0">0</span><span class="blank"> </span><span class="fc2 sc0">\u21d2</span></div><div class="t m0 x21 h13 y8c ff10 fs6 fc4 sc0 ls0"><span class="fc2 sc0">x</span></div><div class="t m0 x22 h13 y8c fff fs6 fc4 sc0 ls0 ws8"><span class="fc2 sc0">=</span><span class="blank"> </span><span class="fc2 sc0">\u21d2</span></div><div class="t m0 x23 h13 y8c ff10 fs6 fc4 sc0 ls0"><span class="fc2 sc0">x</span></div><div class="t m0 x24 h13 y8c fff fs6 fc4 sc0 ls0 ws6"><span class="fc2 sc0">=</span><span class="blank"> </span><span class="fc2 sc0">2</span><span class="fc2 sc0">5</span></div><div class="t m0 x25 h13 y8d fff fs6 fc4 sc0 ls0 ws0"><span class="fc2 sc0">2</span><span class="fc2 sc0">0</span><span class="fc2 sc0">0</span></div><div class="t m0 x11 h13 y8e fff fs6 fc4 sc0 ls0"><span class="fc2 sc0">8</span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div>
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