matematika_VII.pdf

2. ucnobis Semotana da monacemebTan dakavSireba:
vTqvaT, pirveli sadguridan gaiyida x litri benzini, maSin meore
sadguridan gaiyideboda 5x litri. pirvelSi darCenili benzinis
raodenobaa (2 3000- x ) litri, xolo meoreSi (2 800-5x ) litri.
3. gantolebis Sedgena:
4. gantolebis amoxsna:
234 Tavi 4 • erTwevri da mravalwevri
2300 − x= 2800 − 5x.
4x = 500 , x = 125.
5. pasuxi: pirveli saduridan gaiyida 125 l benzini, meoridan — 125×
5 l=625 l.
gantolebis Sedgena am amocanaSic cxrilis gamoyenebiT SeiZleba:
benzingasamarTi
I sadguri
benzingasamarTi
I I sadguri
iyo gaiyida darCa
2 300 l xl (2 300–x)l
2 800 l 5xl (2 800–5x)l
algebruli meTodi warmatebiT SegviZlia gamoviyenoT geometriuli
amocanebis amosaxsnelad.
amocana 4. AC fuZis mqone tolferda ABC samkuTxedSi gavlebulia
AD biseqtrisa. C wverosTan mdebare gare kuTxe 1,5-jer metia ADC
kuTxeze. vipovoT ABC samkuT xedis kuTxeebi.
B
moc: ΔABC, AB = BC ,
AD biseqtrisaa,
∠ DCK = 1, 5∠ADC
amoxsna:
u.g. ∠A, ∠B, ∠C
I. sityvieri modeli:
mocemulobis Tanaxmad ∠ DCK = 1, 5∠ADC
II. ucnobis Semotana da monacemebTan dakav Sireba:
A
C K
0
vTqvaT ∠ ACD = x . maSin,
0
∠ BAC = x ,
0
x
∠ DAC = ,
2
0
0 0 x
∠ ADC = 180 − ( x + ),
2
0 0
∠ DCK = 180 −x.
III. gantolebis Sedgena:
0
0 0 0 0 x
180 − x = 1,5(180 − ( x + )).
2
IV. gantolebis amoxsna:
0 0 0 9 0
180 − x = 270 − x ,
4
9 0 0 0 0
x − x = 270 −180
4
5 0 0 0 0
x = 90 , x = 72 .
0 0 4
0
V. pasuxi: ∠ A=∠ C = 72 , ∠ B= 180 −( ∠ A+∠ C)
= 36 .
D