Teeb meem yuav tsum tau Solved los ntawm cov kab zauv. Cov tshuaj ntawm muaj teeb meem nyob rau hauv kev kawm txog zauv

Nyob rau hauv lub chav kawm ntawm lub tsev kawm ntawv ntawm kev kawm txog zauv yuav tsum tau mus ntsib cov hom phiaj. Ib txhia yog tamed nyob rau hauv ib tug ob peb kauj ruam, lwm leej lwm tus yuav tsum tau ib tug tej yam puzzle.

Teeb meem yuav tsum tau Solved los ntawm cov kab zauv, tsuas yog nyob rau thawj lub xub ntiag tsis yooj yim. Yog hais tias koj xyaum, cov txheej txheem mus rau tsis siv neeg.

geometric duab

Nyob rau hauv thiaj li yuav to taub cov nqe lus nug, koj yuav tsum tau mus rau cov tub ntxhais. Ua tib zoo txog cov ntsiab lus ntawm cov mob, nws yog zoo dua kom nws rov nyeem ob peb lub sij hawm. Kev sib tw rau kab zauv tsuas yog nyob rau thawj lub xub ntiag tsis yooj yim. Xav txog ib qho piv txwv rau pib qhov uas yooj yim.

Dan duab plaub, nws yog tsim nyog los nrhiav tau nws cheeb tsam. Muab: dav ntawm 48% tsawg tshaj li qhov ntev ntawm lub perimeter ntawm lub duab plaub yog 7.6 centimeters.

Txog cov teeb meem daws nyob rau hauv kev kawm txog zauv yuav tsum tau ceev faj vchityvaniya, logic. Ua ke, qhia rau peb nrog nws. Yuav ua li cas koj yuav tsum tau ua ntej ntawm tag nrho cov mus kawm txog dabtsi? Peb txhais qhov ntev ntawm x. Yog li ntawd, nyob rau hauv no kab zauv, lub dav yuav 0,52h. Peb yuav muab cov puag ncig - 7.6 centimeter. Peb nrhiav semiperimeter, qhov no 7.6 centimeters muab faib los ntawm 2, nws yog sib npaug zos rau 3.8 centimeters. Peb twb tau txais cov kab zauv los ntawm cov uas peb nrhiav tau qhov ntev thiab dav:

0,52h + x = 3.8.

Thaum peb tau txais x (ntev), nws yog ib qho yooj yim mus nrhiav tau thiab 0,52h (dav). Yog hais tias peb paub no ob qhov tseem ceeb, peb yuav nrhiav tau cov lus teb rau lub ntsiab lus nug.

Teeb meem yuav tsum tau Solved los ntawm cov kab zauv, yog tsis nyuaj li thaum lawv zoo li, hais tias peb yuav to taub los ntawm tus thawj piv txwv li. Peb tau pom ib tug ntev x = 2.5 cm, dav (y oboznchim) 0,52h = 1.3 cm. Txav mus rau lub cheeb tsam. Nws yog qhov yooj yim mis S = x * y (rau voos). Nyob rau hauv peb qhov teeb meem S = 3,25. Qhov no yuav tsum tau cov lus teb.

Cia saib cov piv txwv ntawm kev daws cov teeb meem nrog rau kev nrhiav chaw. Thiab lub sij hawm no, peb muab qhov duab plaub. Cov tshuaj ntawm muaj teeb meem nyob rau hauv kev kawm txog zauv ntawm nrhiav perimeter, thaj tsam, txawv cov nuj nqis ntau heev. Peb nyeem cov lus ntawm qhov teeb meem: muab ib cov duab plaub, nws kav ntev npaum yog 3.6 centimeters ntau dav, uas yog 1/7 ntawm lub perimeter ntawm lub daim duab. Nrhiav qhov chaw ntawm lub duab plaub.

Nws yuav ua tau yooj yim rau xaiv lub dav ntawm lub nce mus nce los x, thiab qhov ntev ntawm (x + 3.6) centimeters. Peb nrhiav tau cov puag ncig:

P = 2 + 3.6.

Peb yuav tsis daws tau qhov equation, vim hais tias peb muaj nws nyob rau hauv ob ntau yam. Yog li ntawd, peb saib dua mob. Nws hais tias lub dav yog sib npaug zos rau 1/7 ntawm lub perimeter. Peb tau txais lub equation:

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

Rau qhov yooj yim ntawm cov tshuaj, peb muab ib sab ntawm kab zauv los ntawm 7, li ntawd, peb tau txais tshem ntawm lub feem:

2 + 3.6 = 7x.

Tom qab peb tau txais lub ntsiab x (dav) = 0.72 cm. Paub qhov dav, ntev nrhiav:

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

Tam sim no peb paub qhov ntev thiab dav coj mus rau lub ntsiab lus nug ntawm yog dab tsi lub cheeb tsam ntawm ib tug duab plaub.

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

Cov kaus poom uas mis nyuj

Daws teeb meem siv cov equations ua rau ib tug ntau ntawm teeb meem tom tsev kawm ntawv, txawm lub fact tias no qhov teeb meem pib nyob rau hauv lub plaub qib. Muaj ntau cov piv txwv peb tau kawm nyob rau hauv qhov kev txiav txim ntawm qhov chaw ntawm cov nuj nqis, tam sim no ib tug me ntsis digress los ntawm lub ntsuas. Cia peb kawm saib ib tug yooj yim ua hauj lwm nrog cov kev npaj ntawm lub rooj, lawv pab visually: raws li cov ntaub ntawv los pab nyob rau hauv kev daws ntau pom.

Caw cov me nyuam nyeem cov mob ntawm qhov teeb meem thiab tsim tau ib daim ntawv los pab compiling kab zauv. Qhov ntawd yog qhov mob: muaj ob poom, cov thawj peb lub sij hawm ntau mis nyuj tshaj nyob rau hauv lub thib ob. Yog hais tias tus thawj nchuav tsib litres nyob rau hauv lub thib ob, cov mis nyuj yuav tsum sib npaug muab faib. Lus Nug: yuav ua li cas muaj ntau yam kaus poom los ntawm cov mis nyuj nyob rau hauv txhua?

Yuav kom pab daws yuav tsum tau tsim ib lub rooj. Yuav ua li cas yuav tsum nws zoo li cas?

kev txiav txim siab

	nws yog	nws los ua
1 muaj peev xwm ntawm nyob	3	3 - 5
2 poom	x	x + 5

Yuav ua li cas li no pab nyob rau hauv lub drafting ntawm kab zauv? Peb paub hais tias raws li ib tug tshwm sim cov mis nyuj yog sib npaug zos, lub kab zauv thiaj li yuav raws li nram no:

3 - 5 + x = 5;

2 = 10;

x = 5.

Peb pom ua thawj zaug nqi ntawm cov mis nyuj churns nyob rau hauv lub thib ob, ces tus thawj yog: 5 * 3 = 15 litres ntawm cov mis nyuj.

Tam sim no, ib tug me ntsis piav rau ntawm daim duab saum rooj.

Yog vim li cas peb yog cov thawj ntawm ib tug can sau tias 3: nyob rau hauv lub mob stipulated hais tias cov mis nyuj yog peb lub sij hawm tsawg tshaj li nyob rau hauv lub thib ob kaus poom. Tom qab ntawd peb nyeem hais tias tus thawj 5 litres ntawm cov kaus poom leaked, yog li ntawd ua 3 - 5, thiab lub thib ob nchuav: x + 5. Vim li cas peb muab tso rau ib tug sib npaug zos kos npe rau ntawm lub ob nqe lus? Lub tej yam kev mob ntawm qhov teeb meem hais tias cov mis nyuj tau ua sib npaug.

Yog li ntawd peb tau txais cov lus teb: thawj lub can - 15 litres, thiab lub thib ob - 5 litres ntawm cov mis nyuj.

Kev txiav txim ntawm lub qhov tob

Raws li qhov teeb meem: qhov tob ntawm cov thawj zoo nyob rau hauv 3.4 meters ntau dua qhov thib ob. Tus thawj zoo twb tau nce los ntawm 21,6 meters, thiab lub thib ob - peb lub sij hawm, tom qab no cov kev ua dej muaj tib lub tob. Koj yuav tsum xam dab tsi ntawm qhov tob ntawm txhua zoo yog Ameslikas.

Txoj kev ntawm kev daws teeb meem yog heev heev, yuav ua tau los ntawm cov kev ua constituting qhov sib npaug los yog lawv system, tiam sis feem ntau yooj yim thib ob xaiv. Mus rau ib tug txiav txim sotavim rooj, raws li nyob rau hauv lub yav dhau los piv txwv.

kev txiav txim siab

	nws yog	nws los ua
1 zoo	+ 3.4 x	x + 3.4 + 21.6
2 zoo	x	3

Peb npaj mus rau qhov kev npaj ntawm cov kab zauv. Txij li thaum lub zoo tob ua tib yam, nws muaj cov nram qab daim ntawv:

x + 3,4 + 21,6 = 3;

x - 3 = -25;

-2x = -25;

x = -25 / -2;

x = 12.5

Peb pom tus thawj tob ntawm lub thib ob zoo, muaj peev xwm tam sim no nrhiav tau cov thawj:

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

Tom qab lub ua tej yam ua yog kaw lus teb: 15,9 m, 12.5 m.

ob tug kwv tij

Nco ntsoov tias qhov teeb meem no yog txawv los ntawm tag nrho cov yav tas los sawv daws yuav vim hais tias ntawm tus mob yog Ameslikas tib yam pes tsawg tus ntawm cov khoom. Raws li, qhov kev pab lub rooj yog ua nyob rau hauv lub rov qab kev txiav txim, piv txwv li, los ntawm "ua" ib tug "tau".

Mob: lub ob kwv tij tau muab sib npaug ceev, tab sis cov laus muab nws me ntsis tij laug 10, tom qab ntawd tus yau yog tus ceev tsib lub sij hawm ntau. Yuav ua li cas muaj ntau yam ceev yog tam sim no txhua txhua tus tub?

kev txiav txim siab

	nws yog	nws los ua
senior	x + 10	x
yau	5x - 10	5x

Equates rau:

x = 10 + 5x - 10;

-4h = -20;

x = 5 - ceev yog nws tus tij laug;

5 * 5 = 25 - tus yau tij laug.

Tam sim no koj muaj peev xwm sau tau cov lus teb: 5 ceev; 25 ceev.

purchase

Lub tsev kawm ntawv xav tau kev pab mus yuav cov phau ntawv thiab phau ntawv sau, cov thawj yog kim kim thib ob ntawm 4.8 rubles. Koj yuav tsum xam ntau npaum li cas yog ib phau ntawv thiab ib phau ntawv, yog hais tias tus purchase ntawm nees nkaum-tsib phau ntawv thiab ib tug phau them tus nqi qub nyiaj.

Ua ntej cov tswv yim rau cov tshuaj, nws yog tsim nyog los teb cov lus nug nram qab no:

• Yuav ua li cas yog nws nyob rau hauv qhov teeb meem?
• Yuav ua li cas npaum li cas koj puas tau them?
• Yuav ua li cas mus yuav?
• Yuav ua li cas qhov tseem ceeb yuav tsum equalized nrog txhua lwm yam?
• Yuav ua li cas koj yuav tsum paub?
• Yuav ua li cas yog tus nqi muab rau x?

Yog hais tias koj tau teb tag nrho cov nqe lus nug, ces npaj mus rau ib tug txiav txim siab. Nyob rau hauv qhov kev piv txwv, raws li cov nqi ntawm x yuav tau txais raws li cov nqi ntawm ib tug phau ntawv sau, thiab tus nqi ntawm cov phau ntawv. Xav txog ob qho kev xaiv:

1. x - tus nqi ntawm ib tug phau ntawv sau, ces x + 4.8 - nqi ntawm cov phau ntawv. Raws li nyob rau hauv no, peb tau kab zauv: 5 = 21x (x + 4.8).
2. x - tus nqi ntawm cov phau ntawv, ces x - 4.8 - nqi phau ntawv sau. Cov kab zauv muaj rau hauv daim: 21 (x - 4.8) = 5x.

Koj muaj peev xwm xaiv rau lawv tus kheej ib tug yooj yim dua kev xaiv, ces peb yuav daws tau qhov ob npaug thiab sib piv cov lus teb, raws li ib tug tshwm sim, lawv yuav tsum tau tib yam.

Tus thawj txoj kev

Cov tshuaj ntawm cov thawj kab zauv:

5 = 21x (x + 4.8);

4,2h = x + 4.8;

4,2h - x = 4.8;

3.2x = 4.8;

x = 1.5 (rubles) - tus nqi ntawm ib tug phau ntawv sau;

4.8 + 1.5 = 6.3 (rubles) - tus nqi ntawm ib tug tib phau ntawv.

Lwm txoj kev los daws tau qhov equation (qhib parenthesis):

5 = 21x (x + 4.8);

21x = 5x + 24;

16X = 24;

x = 1.5 (rubles) - tus nqi ntawm ib tug phau ntawv sau;

1.5 + 4.8 = 6.3 (rubles) - tus nqi ntawm ib tug tib phau ntawv.

Qhov thib ob txoj kev

5x 21 = (x - 4.8);

5x = 21x - 100,8;

16X = 100,8;

x = 6.3 (rubles) - nqi rau 1 phau ntawv;

6.3 - 4.8 = 1.5 (rubles) - tus nqi ntawm ib tug phau ntawv.

Raws li yuav pom los ntawm cov piv txwv, cov lus teb yeej zoo tib yam, yog li ntawd, qhov teeb meem yog solved kom raug. Saib rau hauv txoj cai kev txiav txim siab, nyob rau hauv peb tus yam ntxwv tsis muaj cov lus teb yog tsis zoo.

Tseem muaj lwm yam teeb meem yuav tsum tau solved nrog kev pab los ntawm kab zauv, xws li lub zog. Xav txog nyob rau hauv ntau yam nyob rau hauv cov nram no piv txwv.

ob lub tsheb

Nyob rau hauv seem no peb yuav tsom ntsoov rau cov lus tsa suab kev pab raws qib. Yuav tsum tau mus daws tau lawv, koj yuav tsum paub cov nram qab no txoj cai:

S = V * T,

S - nrug, V - tshaj tawm, T - lub sij hawm.

Cia peb xav txog ib qho piv txwv.

Ob lub tsheb tshuav ib txhij los ntawm point A taw tes B. Tus thawj tag nrho deb mus ncig nyob rau tib lub ceev, hauv thawj ib nrab ntawm lub thib ob txoj kev taug kev mus rau ntawm ib tug ceev ntawm 24 km / h, thiab lub thib ob - 16 km / h. Nws yog tsim nyog los mus txiav txim cov kev ceev ntawm lub thawj tsav tsheb rau taw tes B yog hais tias lawv tuaj nyob rau tib lub sij hawm.

Yuav ua li cas peb yuav tsum tau rau cov muab tso ua ke ntawm kab zauv: lub ntsiab nce mus nce los V ₁ (cov kev ceev ntawm lub thawj lub tsheb), me: S - txoj kev T ₁ - thawj lub sij hawm nyob rau hauv lub tsheb txoj kev. Kab zauv: S = V ₁ * T _1.

Ntxiv: hauv thawj ib nrab ntawm lub thib ob lub tsheb txoj kev (S / 2) tsav tsheb ntawm ib tug ceev V ₂ = 24 km / h. Peb muab tau cov kev qhia: S / 24 * 2 = T _2.

Cov tom ntej no yog ib feem ntawm txoj kev nws mus rau tus ceev V ₃ = 16 km / h. Peb tau S / 2 = 16 * T _3.

Ntxiv nws yog pom los ntawm cov kev mob uas lub tsheb tuaj txog ib txhij, yog li T ₁ = T ₂ + T _3. Tam sim no peb muaj qhia qhov nce mus nce los T _1, T _2, T ₃ ntawm peb yav dhau los tej yam kev mob. Peb muab tau cov kab zauv: S / V ₁ = (S / 48) + (S / 32).

S txais lub tsev thiab kom daws tau qhov equation:

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.

Qhov no yog cov lus teb. Teeb meem yuav tsum tau Solved los ntawm cov kab zauv, nyuab thaum xub thawj siab ib muag. Nyob rau hauv tas li ntawd mus rau saum toj-qhia teeb meem yuav tau sib ntsib los ua hauj lwm, yog dab tsi nws yog los sib tham nyob rau hauv lub tom ntej no seem.

txoj hauj lwm neeg ua hauj lwm

Yuav kom daws tau qhov no hom ntawm hauj lwm uas koj yuav tsum paub cov mis:

A = VT,

qhov twg A - yog lub chaw ua hauj lwm, V - productivity.

Yog xav paub piav qhia ntawm qhov yuav tsum tau muab ib qho piv txwv. Subject "txog cov teeb meem Daws kab zauv" (qib 6) yuav tsis muaj tej teeb meem, vim nws yog ntau theem tsis yooj yim, tab sis muab ib qho piv txwv rau siv.

Ua tib zoo nyeem cov nqe lus: Ob tug neeg ua hauj lwm ua hauj lwm ua ke thiab nqa tawm ib lub hom phiaj rau kaum ob hnub. Koj yuav tau xyuas seb yuav ua li cas ntev nws yuav siv sij hawm thawj neeg ua hauj lwm ua tib yam kev cai rau lawv tus kheej. Nws yog lub npe hu hais tias nws ua rau ob hnub tus nqi ntawm cov ua hauj lwm raws li tus neeg thib ob nyob rau hauv peb hnub.

Daws cov teeb meem compiling sib npaug yuav tsum tau ua tib zoo nyeem tej yam kev mob. Tus thawj tshaj plaws peb kawm tau los ntawm qhov teeb meem uas ua hauj lwm tsis txhais, ces muab nws li ib chav tsev, uas yog, A = 1. Yog hais tias qhov teeb meem yog hais txog mus rau ib tug tej yam muaj pes tsawg tus ntawm qhov chaw, los yog litres, lub chaw ua hauj lwm yuav tsum tau los ntawm no cov ntaub ntawv.

Peb txhais lub throughput ntawm tus thawj thiab thib ob kev khiav hauj lwm los ntawm V ₁ thiab V _2, ntsig txog, nyob rau ntawm no theem, tejzaum nws nqus cov nram qab no kab zauv:

1 = 12 (V ₁ + V _2).

Yuav ua li cas no kab zauv qhia rau peb? Hais tias tag nrho cov ua hauj lwm yog ua los ntawm ob tug neeg nyob rau hauv kaum ob teev.

Tom qab ntawd peb yuav hais tias: 2V ₁ = 3V _2. Vim hais tias cov thawj ib tug tsis ntau li ntau raws li lub thib ob ntawm peb nyob rau hauv ob hnub. Peb muaj ib tug kev sib npaug:

12 1 = (V1 + V2);

2V = 3V _{1 2.}

Tom qab qhov kev tshwm sim ntawm kev daws cov system, peb twb tau txais cov kab zauv nrog ib tug kuj tsis paub meej:

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

V ₁ = _1/20 = _0,05.

Qhov no yog thawj ua hauj lwm productivity. Tam sim no peb muaj peev xwm nrhiav tau lub sij hawm nyob rau hauv uas mus rau tiv nrog tag nrho cov ua hauj lwm thawj thawj tus ua:

A = V ₁ * T _1;

1 = 0.05 * T _1;

T ₁ = 20.

Txij li thaum ib chav tsev lub sij hawm tau txais cov hnub, cov lus teb yog: 20 hnub.

reformulation ntawm qhov teeb meem

Yog hais tias koj muaj zoo mastered rau lub kev txawj ntse los daws kom tau teeb meem nyob rau hauv lub zog, thiab nrog lub hom phiaj ntawm txoj hauj lwm uas koj muaj ib co teeb meem, nws yog tau mus ua hauj lwm tawm kom tau tsheb. Yuav ua li cas? Yog hais tias koj noj cov xeem Piv txwv li, tus mob yuav ua tau li nram no: Oleg thiab Dima yog tsiv ntawm txhua lwm yam, lawv tshwm sim tom qab 12 teev. Pes tsawg txoj kev uas yuav kov yeej nws tus kheej Oleg, yog tias koj paub tias nws yog ob teev kis ib tug deb sib npaug zos txoj kev Dima peb teev.