Izinkinga ukuba Iyaxazululwa by ezothando. Isixazululo ezinkingeni mathematics

Ngokuhamba esikoleni mathematics edingekayo ukuhlangabezana nezinhloso. Abanye walawula ngezinyathelo ezimbalwa, eminye idinga iphazili ezithile.

Izinkinga ukuba Iyaxazululwa by ezothando, kuphela lapho uqala nje ukubona nzima. Uma uprakthiza, inqubo iya othomathikhi.

ngamajamo weJiyomethri

Ukuze uzwisise umbuzo, kudingeka uthole umnyombo. baqonde okushiwo isimo ngokucophelela, kungcono kabusha funda izikhathi eziningana. Izinselele kwesibalo kuphela nzima uma uqala ukumbona. Cabangela isibonelo ukuqala elula.

Dan isikwele, kubalulekile ukuthola endaweni yayo. Sikhishwe: ububanzi at 48% uma kuqhathaniswa nangonyaka ubude azungezwe we isikwele kuyinto 7.6 amasentimitha.

Kucatulula tinkinga tetibalo mathematics kudinga vchityvaniya ngokucophelela, logic. Nobabili, tshelani nathi ukubhekana naso. Yini okudingeka kuqala kunazo zonke okufanele icatshangelwe? Thina selisho ubude x. Ngakho-ke, kulesi equation, ububanzi kuyoba 0,52h. Sitshelwe azungezwe - 7.6 isentimitha. Esimthola semiperimeter, lokhu 7.6 amasentimitha ehlukaniswa 2, kuba elilingana 3.8 amasentimitha. Sikuphathele ezothando ngawo sithola ubude nobubanzi:

0,52h + x = 3.8.

Lapho sithola x (ubude), kulula ukuthola futhi 0,52h (ububanzi). Uma siyazi lezi zimiso ezimbili, sithola impendulo yalo mbuzo main.

Izinkinga ukuba Iyaxazululwa by ezothando, akuyona njengoba kunzima njengoba kubonakala kunjalo, leso sizwisise esibonelweni kuqala. Sithole obuphelele x = 2,5, ububanzi (y oboznchim) 0,52h = 1.3 cm. Yisa endaweni. Kuyinto elula ifomula S = x * y (i calandze). Ngo inkinga yethu S = 3,25. Lokhu kuyoba impendulo.

Ake sibheke izibonelo zokuxazulula izinkinga ngokuthola isikhala. Futhi kulesi sikhathi, sithatha isikwele. Isixazululo izinkinga wezibalo ekutholeni ipherimitha, endaweni, izibalo ezahlukene kaningi. Siyafunda isitatimende yenkinga: inikezwe isikwele, nobude bawo ububanzi 3.6 amasentimitha ngaphezulu, okuyinto 1/7 azungezwe sibalo. Thola indawo isikwele.

Kuyoba elula ukuqoka ububanzi x variable, nobude (x + 3.6) ngamasentimitha. Sithola azungezwe:

P = 2 + 3.6.

Asikwazi ukuxazulula equation, ngenxa yokuthi sinefu kuyo eziguquguqukayo ezimbili. Ngakho-ke, sibheka futhi isimo. Lithi ububanzi ilingana 1/7 azungezwe. Sithola ezothando:

1/7 (2 + 3,6) = x.

Ukuze kube lula isixazululo we gaya ohlangothini kwesibalo ngo-7 lilinye, ngakho sithola ukubabulala ingxenyenamba:

2 + 3.6 = 7x.

Ngemva sithola izixazululo x (ububanzi) = 0.72 cm. Ukwazi ububanzi, ubude yokuthola:

0,72 + 3,6 = 4,32 cm.

Manje siyazi ubude nobubanzi elihambisana umbuzo oyinhloko yini endaweni isikwele.

S = x * y, S = 3,1104 cm.

Amathini ubisi

Ukuxazulula izinkinga besebenzisa zibalo kubangela eziningi nezinkinga esikoleni, naphezu kweqiniso lokuthi lolu daba iqala efunda ibanga lesine. Kunezibonelo eziningi esixoxe ukuzimisela izindawo izibalo, manje digress kancane kusukela geometry. Ake sibone nomsebenzi olula ukulungela amatafula, zisiza zibukeke: nedatha ukusiza ekuxazululeni kubonakale kakhulu.

Mema izingane ukufunda isimo yenkinga futhi ukwakha ishadi ukusiza kwekuhlanganisa equation. Yilokho isimo: kukhona amathini amabili, ubisi lokuqala ngokuphindwe kathathu ngaphezu lesibili. Uma kuqala wathela amalitha amahlanu lesibili, ubisi uzobe ihlukaniseke ngokulinganayo. Umbuzo: bangaki amathini ubisi ngamunye?

Ukusiza ukuxazulula isidingo udale ithebula. kufanele injani like?

isinqumo

	kwaba	yaba
1 fantshi	3	3 - 5
2 amakani	x	x + 5

Lokhu kuhlangana kanjani usizo nokubhalwa ezothando? Siyazi ukuthi ngenxa ubisi zazilingana, ezothando ke kuyoba kanje:

3 - 5 + x = 5;

2 = 10;

x = 5.

Sithole ukwenza imali yokuqala ubisi churns lesibili ke eyokuqala kwaba: 5 * 3 = 15 amalitha ubisi.

Manje, incazelo kancane etafuleni umdvwebo.

Kungani thina singabantu sokuqala ikani esinelebuli 3: esimweni wawufuna ukuba ubisi lingaphansi kathathu kunangesikhathi Amathini yesibili. Khona-ke sifunda ukuthi 5 amalitha yokuqala namakani leaked, ngakho baba 3 - 5, kanye yesibili yasithululela: x + 5. Kungani senza Isiboniso elilinganayo phakathi imigomo emibili? Imibandela yenkinga uthi ubisi isibe ngokulinganayo.

Ngakho sithole impendulo: kuqala kungakusiza - 15 amalitha, kanti eyesibili - 5 amalitha ubisi.

Ukunqunywa ukujula

Ngokwe inkinga: womthombo kuqala ku 3.4 amamitha njengengcebo enkulu kunemicebo yesibili ukujula. I kahle kuqala Kwandiswa ngo-21.6 amamitha, kanti eyesibili - kathathu, ngemuva lezi zenzo imithombo ube ukujula efanayo. Udinga ukubala ukuthi izinto zihamba kahle ngamunye ukujula wayedabuka.

Izindlela nokuxazulula izinkinga ziningi, kungenziwa isenzo akha lesi zibalo noma inhlelo yamasu abo, kodwa elula kakhulu ukhethe impendulo yesibili. Ukuya itafula isinqumo sotavim, njengoba kulesibonelo odlule.

isinqumo

	kwaba	yaba
1 kahle	+ 3.4 x	x + 3.4 + 21.6
2 kahle	x	3

Thina uqhubekele ukulungiswa equation. Kusukela ukujula kahle abe okufanayo, it has ifomu elilandelayo:

x + 3.4 + 21.6 = 3;

x - 3 = -25;

-2x = -25;

x = -25 / -2;

x = 12.5

Sathola womthombo yesibili ukujula yokuqala, ungakwazi manje uthole lokuqala:

12,5 + 3,4 = 15,9 m.

Ngemva izenzo ezenziwe elotshiwe impendulo: 15.9 m, 12.5 m.

abazalwane ababili

Qaphela ukuthi le nkinga kuhlukile bonke abanhliziyo odlule ngenxa yesimo wayedabuka inombolo efanayo izinto. Ngakho, ithebula asizayo senziwa oda reverse, okungukuthi, kusukela "waba" 'ubelokhu ".

Isimo: laba bazalwane ababili wabanika nuts ngokulinganayo, kodwa umdala wanika kancane umfowabo 10, ngemva kwalokho Encane kwaba nati izikhathi ezinhlanu. Bangaki nuts manje wonke umfana?

isinqumo

	kwaba	yaba
abaphezulu	x + 10	x
abasebasha	5x - 10	5x

Kulingana:

x = 10 + 5x - 10;

-4h = -20;

x = 5 - nuts kwaba umfowabo omdala;

5 * 5 = 25 - umfowabo omncane.

Manje ungakwazi ukubhala impendulo: 5 nati; 25 namantongomane.

ukuthenga

Isikole kudingeka ukuthenga amabhuku nezincwadi, okokuqala akukhona wesibili ebiza kakhulu ruble 4.8. Udinga ukubala malini ingenye ncwadi futhi ibhuku elilodwa, uma ukuthenga izincwadi amabili nanhlanu nokukodwa notebook wakhokha inani elifanayo lemali.

Ngaphambi kokuqhubeka ikhambi, kubalulekile ukuphendula imibuzo elandelayo:

• Kuyini e inkinga?
• Kungakanani awuzange ukhokhe?
• Yini ukuthenga?
• Iziphi izindinganiso nemigomo kungenziwa equalized nomunye?
• Yini odinga ukuyazi?
• Ibaluleke ngani bathathwa x?

Uma uke liyiphendula yonke imibuzo, bese uqhubekela phambili isinqumo. Kulesi sibonelo, njengoba ukubaluleka x kungenziwa ezamukelwa njengemiBhalo intengo incwajana yamaphuzu futhi izindleko izincwadi. Cabanga ngemisebenzi ongakhetha kuyo ezimbili kungenzeka:

1. x - ukubaluleka notebook ke x + 4.8 - intengo yebhuku. Ngokusekelwe lokhu, sithola kwesibalo: 5 = 21x (x + 4.8).
2. x - izindleko incwadi ke x - 4.8 - intengo amanothibhuku. I kwesibalo ine uhlobo: 21 (x - 4.8) = 5x.

Ungakhetha bona kukho kuwusizo kakhudlwana, ke thina ukuxazulula zibalo ezimbili bese uqhathanisa izimpendulo, ngenxa yalokho, kumele kube esifanayo.

Indlela yokuqala

Isixazululo of the equation lokuqala:

5 = 21x (x + 4.8);

4,2h = x + 4.8;

4,2h - x = 4.8;

3.2x = 4.8;

x = 1.5 (ruble) - ukubaluleka eyodwa notebook;

4.8 + 1.5 = 6.3 (ruble) - izindleko ibhuku elilodwa.

Enye indlela yokuxazulula le kwesibalo (ukuvulwa abakaki):

5 = 21x (x + 4.8);

21x = 5x + 24;

16x = 24;

x = 1.5 (ruble) - ukubaluleka eyodwa notebook;

1.5 + 4.8 = 6.3 (ruble) - izindleko ibhuku elilodwa.

Indlela yesibili

5x 21 = (x - 4.8);

5x = 21x - 100,8;

16x = 100,8;

x = 6.3 (ruble) - lamakamelo mayelana 1 ncwadi;

6.3 - 4.8 = 1.5 (ruble) - izindleko notebook.

Njengoba singabona kusukela izibonelo, izimpendulo ayafana, ngakho-ke, inkinga isixazululekile kahle. Watch out for isinqumo esifanele, kusibonelo yethu akanayo impendulo alivumi.

Kukhona nezinye izinkinga ukuba ixazululwe ngosizo ezothando, ezifana ukunyakaza. Cabanga ngokuningiliziwe ngalezi zibonelo.

izimoto ezimbili

Kule ngxenye sizogxila imisebenzi ezinyakazayo. Ukuze sikwazi ukuzixazulula, odinga ukukwazi mithetho elandelayo:

S = V * T,

S - ibanga, V - velocity, T - isikhathi.

Ake sicabangele isibonelo.

Ababili imoto kwesokunxele kanyekanye ukusuka endaweni A ukhombe B. Ibanga lokuqala Imininingwane uhambo ijubane lokukhanya alishintshi, engxenyeni yokuqala ka indlela yesibili ihamba ngesivinini of 24 km / h, kanti eyesibili - 16 km / h. Kuyadingeka ukuba lunquma isivinini umshayeli wokuqala ukhombe B uma beza ngesikhathi esifanayo.

Esikudingayo tekuhlelwa kwemisebenti ezothando: main variable V ₁ (ijubane emotweni lokuqala), ezincane: S - indlela T ₁ - okokuqala endleleni yemoto. Isibalo: S = V ₁ * T _1.

Eminye: Engxenyeni yokuqala yekhulu lesibili imoto endleleni (S / 2) waxosha ngesivinini V ₂ = 24 km / h. We ukuthola inkulumo ethi: S / 24 * 2 = T _2.

Inkulumo eyalandela enesihloko esithi endleleni lwahamba ngesivinini V ₃ = 16 km / h. We ukuthola S / 2 = 16 * T _3.

Ngaphezu kwalokho ke kubonakala isimo ukuthi izimoto efika kanyekanye, ngaleyo ndlela T ₁ = T ₂ T _3. Manje sinesizathu sokusho variable T ₁ T _2, T ₃ kwezimiso wethu odlule. We ukuthola ezothando: S / V ₁ = (S / 48) + (S / 32).

S ukwamukela iyunithi nokuxazulula ezothando:

1 / V ₁ = _1/48 + _1/32;

1 / V _{1 = (2/96) + (3/96} ) ;

1 / V ₁ = 5/96;

V ₁ = 96/5;

V ₁ = 19.2 km / h.

Lona impendulo. Izinkinga ukuba Iyaxazululwa by ezothando, nzima efika kuqala. Ngaphezu inkinga ngenhla wabonisa ungahlangana ukusebenza, lokho kuchazwa ngawo kulesi sigaba esilandelayo.

umsebenzi umsebenzi

Ukuxazulula lolu hlobo lomsebenzi odinga ukukwazi ifomula:

A = VT,

lapho A - umsebenzi, V - umkhiqizo.

Ukuze uthole incazelo eningiliziwe mayelana nesidingo nikeza isibonelo. Isihloko "Inkinga Zokuxazulula equation" (grade 6) ayikwazi ukuqukatha izinkinga ezinjalo, njengoba kuyintando ezingeni nzima, kodwa nokho, unikeze isibonelo ukuze uthole inkomba.

Funda ngokucophelela imigomo: abasebenzi amabili asebenza ndawonye enza lwa cebo izinsuku nambili. Udinga ukucacisa kuthatha isikhathi esingakanani umsebenzi wokuqala ukwenza imithetho efanayo ngokwabo. It is ukuthi wenza izinsuku ezimbili bomsebenzi njengoba umuntu wesibili ngezinsuku ezintathu ezaziwayo.

Xazulula izinkinga kwakhiwa zibalo kudinga izimo uyifunda ngokucophelela. Into yokuqala Sifundeni inkinga umsebenzi akachaziwe, khona-ke thatha it njengoba iyunithi, okungukuthi, A = 1. Uma inkinga libhekisela inombolo ethile izingxenye, noma amalitha, umsebenzi kufanele uthathe le datha.

Thina selisho throughput we lokuqala nelesibili olusebenza V ₁ V _2, ngokulandelana, kulesigaba, mhlawumbe sifinyelela kwesibalo ezilandelayo:

1 = 12 (V ₁ + V _2).

Yini le kwesibalo kusitshela? Lokho wonke umsebenzi kwenziwa ngabantu ezimbili amahora ayishumi nambili.

Khona-ke singasho ukuthi: 2V ₁ = 3V _2. Ngenxa owokuqala enza okuningi njengoba wesibili ka ezintathu izinsuku ezimbili. Sinohlelo of zibalo:

12 1 = (V1 + V2);

2V = 3V _{1 2.}

Ukulandela imiphumela ukuxazulula uhlelo, siye etholwe ezothando nomunye variable:

1 - 8V = 12V _{1 1;}

V ₁ = 1/20 = _0,05.

Lona umkhiqizo wokuqala ukusebenza. Manje singakwazi ukuthola isikhathi lapho ukuba sibhekane ngokuphumelelayo wonke umsebenzi umuntu wokuqala:

A = V ₁ * T _1;

1 = 0.05 * T _1;

T ₁ = 20.

Njengoba per unit isikhathi kwavunyelwana ngosuku, impendulo iwukuthi: izinsuku ezingu-20.

kabusha inkinga

Uma yingcweti kahle amakhono ukuze uxazulule izinkinga kule nhlangano, futhi nezinjongo umsebenzi uhlangabezana nobunzima, kungenzeka ukuba kuvelwe ukuthola traffic. Kanjani? Uma uthatha isibonelo zokugcina, isimo kuyoba kanje: Oleg futhi Dima liyasondela nomunye, zivele ngemuva kwamahora angu-12. Lamangakhi indlela ukuba anqobe ukungazithandi Oleg, uma wazi ukuthi amahora amabili sihamba ibanga indlela alinganayo Dima amahora amathathu.