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Эл. №ФС77-60625 от 20.01.2015
Инфоурок / Математика / Конспекты / Решение задания для выпускного экзамена по алгебре и началам анализа (11-класс 35-задание)
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35-nji iş. Çep tarap

  1. Aňlatmany ýönekeýleşdiriň:

hello_html_7312fab0.gif= hello_html_606dfa40.gif hello_html_m24162ac3.gif =

= hello_html_m5e4b47bf.gif hello_html_m24162ac3.gif =hello_html_1f325e3c.gif; Jogaby: hello_html_1f325e3c.gif

  1. Deňlemäni çözüň:

hello_html_m4138ef68.gifhello_html_m7e898541.gif0; D=49-24 = 25; => x1≠1; x2=6;

hello_html_m496bad62.gif=hello_html_m6651b6c.gif; hello_html_m30b6662b.gif = hello_html_5f34b418.gif ;

hello_html_35fa9c31.gif= 0; D = 64-28 = 36; x1 = hello_html_m280b1418.gif = hello_html_2c7ea72d.gif = hello_html_m14dab445.gif = 1; x1 = 1;

x2 = hello_html_3f10f0a3.gif = hello_html_598bd53b.gif = hello_html_651880a7.gif = 7; x2 = 7; x1=1, kök deňlemäni kanagatlandyrmaýar.

Jogaby: x=7;

  1. Deňsizligi çözüň:

hello_html_6e9f5463.gifhello_html_m230ba0fa.gif; hello_html_1dc1fed5.gif ;

hello_html_1efe9eb4.gif+ 2hello_html_6b2fd1c.gifk hello_html_50661fa5.gif - hello_html_m418f76f4.gif hello_html_m4bf64df3.gif + 2khello_html_6b2fd1c.gif , kZ. ; hello_html_1daba409.gif + 2hello_html_6b2fd1c.gifk ≤ - hello_html_m418f76f4.gif hello_html_49c132ef.gif + 2khello_html_6b2fd1c.gif , kZ.

hello_html_m55b1fe04.gif- 4hello_html_6b2fd1c.gifk hello_html_m4f3a936b.gif hello_html_38664469.gif - 4khello_html_6b2fd1c.gif , kZ. ; hello_html_m2d0748aa.gif - 4hello_html_6b2fd1c.gifk hello_html_m4f3a936b.gif hello_html_6223d22a.gif - 4khello_html_6b2fd1c.gif , kZ.

4. Harydyň bahasy iki gezek, her gezekde-de şol bir göterim gymmatladyldy. Eger harydyň ilkibaşdaky bahasy 6000 man, ahyrky bahasy bolsa 6615 man bolan bolsa, haryt her gezek näçe göterim gymmatladylypdyr?

Çözülişi:

6000+6000x%+(6000+6000x%)x% = 6615; 6000+60x+(6000+60x)hello_html_3c6980ec.gif =6615;

6000+60x+60x+hello_html_3b88a430.gif hello_html_7a2a5240.gif =6615; 6000+120x+hello_html_3b88a430.gif hello_html_7a2a5240.gif =6615;

hello_html_3b88a430.gifhello_html_7a2a5240.gif+120x – 615 = 0; 3x2+600x-3075 = 0; x2+200x-1025 = 0;

D =b2- 4ac = 40000+4100=44100; x1= hello_html_5b9e419.gif = hello_html_m2069b593.gif =hello_html_16b19bf3.gif = - 205;

x1= hello_html_m17fc82d2.gif = hello_html_7f94c53.gif =hello_html_61bd9d73.gif = 5; Jogaby 5% gymmatlady.

5. Parallel göni çyzyklaryň birinjisinde 10 nokat, ikinjisinde bolsa 9 nokat bar. Depesi bu nokatlarda bolan näçe sany üçburçluk bar?

Üçburçlugyň kesgitlemesinden belli bolşy ýaly 3 nokat 1 gönüde ýatmaýar.

10 nokatly gönüniň 1 depesinden hello_html_2b992cac.gif üçburçluk emele gelýär. 9 nokatly gönüniň 1 depesinden hello_html_m4119dd8e.gif üçburçluk emele gelýär.

10hello_html_2b992cac.gif + 9hello_html_m4119dd8e.gif = 10·hello_html_m2ffd6c12.gif + 9·hello_html_442a4946.gif = 360+405=765; Jogaby: 765 üçburçluk bar.




6. hello_html_66beb351.gif funksiýanyň grafiginde hello_html_m14c4ea61.gif nokada iň golaý nokady tapyň.

B(x,y) – i[ golav nokat bolsun. A(2; -1,5) ; y = x2 – 2;

L(x) = ǀABǀ=hello_html_m221e5ce8.gif = hello_html_md8477f6.gif ;

Lˊ(x)= hello_html_m6f76ba6b.gif = hello_html_453a5199.gif ; Lˊ(x)= 0; hello_html_m3a62825e.gif=0; => x=1;

x2 + x + 1 = 0; hakyky köki ýok.

y = x2 – 2 = 1 – 2 = - 1; => B(1; -1);

7. Berlen çyzyklar bilen çäklenen figuranyň meýdanyny hasaplaň:

hello_html_11852162.gif hello_html_249ee4a2.gif;

hello_html_m31128e6d.gif => hello_html_m5fd4980c.gif = hello_html_3b70014d.gif ;

hello_html_7a2a5240.gif- 5hello_html_3b70014d.gif= 0; D = 25 – 16 = 9;

x1 = 1; x2 = 4;

S= hello_html_70ba2f0c.gif – x – 4)dx =

= hello_html_3ace7559.gif + hello_html_52638c78.gif – 4)dx =

= hello_html_m1373fc3c.gifhello_html_m6195b74b.gif + hello_html_4c6e15f3.gifhello_html_m6195b74b.gif – 4x│hello_html_m6195b74b.gif =

- hello_html_m5d44bbef.gif + hello_html_2b6e6a20.gif – 12 = hello_html_m1350bf44.gif – 12 = hello_html_ma244389.gif = hello_html_78170999.gif = 4,5;

Jogaby: 4,5.























35-nji iş. Sag tarap

  1. Aňlatmany ýönekeýleşdiriň:

hello_html_m3b26b6da.gif= hello_html_6018561e.gif · hello_html_m1f701ef3.gif = hello_html_m6aa91b24.gif · hello_html_m1f701ef3.gif = hello_html_m4fdab470.gif = 12;

  1. Deňlemäni çözüň:

hello_html_684e6071.gifhello_html_2ccad714.gif0; x1 ≠ 1; x2 ≠ - 4;

hello_html_m4d51b16a.gif= hello_html_m74e5532a.gif; hello_html_2ccad714.gif = hello_html_m571a1bf0.gif ;

hello_html_1bf95cf5.gif= 0; D = 16+20 = 36; x1 = hello_html_m280b1418.gif = hello_html_4df9614e.gif = hello_html_49ca7444.gif =-5; x1=-5;

x2 = hello_html_3f10f0a3.gif = hello_html_7b420d70.gif = hello_html_m32ca33e1.gif = 1; x2 = 1; kök deňlemäni kanagatlandyrmaýar.

Jogaby: x=5;

  1. Deňsizligi çözüň:

hello_html_69cce482.gifhello_html_1d5c0faf.gif

hello_html_m2bf5a2e4.gif+ 2hello_html_6b2fd1c.gifk < hello_html_50661fa5.gif – 2x < hello_html_m53e690d0.gif + 2hello_html_6b2fd1c.gifk, k€Z. ; - hello_html_m2bf5a2e4.gif + 2hello_html_6b2fd1c.gifk < hello_html_50661fa5.gif – 2x < hello_html_m2bf5a2e4.gif + 2hello_html_6b2fd1c.gifk, k€Z. ;

hello_html_7a3de2f.gif- hello_html_6b2fd1c.gifk > x > - hello_html_7a3de2f.gif - hello_html_6b2fd1c.gifk, k€Z.

4. Harydyň bahasy iki gezek, her gezekde-de şol bir göterim arzanladyldy. Eger harydyň ilkibaşdaky bahasy 20000 man, ahyrky bahasy bolsa 11250 man bolan bolsa, haryt her gezek näçe göterim arzanladylypdyr?

Çözülişi:

20000-20000x%-(20000-20000x%)x% = 11250;

20000-200x-(20000-200x)hello_html_3c6980ec.gif =11250; 20000-200x>0; 100>x;

20000-200x-200x+2x2 = 11250; 2x2 – 400x + 8750 = 0; x2-200x+4375 = 0;

D =b2- 4ac = 40000-17500=22500; x1= hello_html_64894b90.gif = hello_html_m29fd3f55.gif =hello_html_m4f3723b4.gif = 25;

x2= hello_html_ba8001d.gif = hello_html_40657304.gif =hello_html_m7937fd70.gif = 175;dal kök.

Jogaby 25% arzanladylypdyr.

5. Parallel göni çyzyklaryň birinjisinde 9 nokat, ikinjisinde bolsa 7 nokat bar. Depesi bu nokatlarda bolan näçe sany üçburçlyk bar?

Üçburçlugyň kesgitlemesinden belli bolşy ýaly 3 nokat 1 gönüde ýatmaýar.

9 nokatly gönüniň 1 depesinden hello_html_m5c3eebf8.gif üçburçluk emele gelýär. 7 nokatly gönüniň 1 depesinden hello_html_2b992cac.gif üçburçluk emele gelýär.

9hello_html_m5c3eebf8.gif + 7hello_html_2b992cac.gif = 9·hello_html_maf09cb5.gif + 7·hello_html_m2ffd6c12.gif = 189+252=441; Jogaby: 441 üçburçluk bar.





6. hello_html_m7c8cc142.gif funksiýanyň grafiginde hello_html_m7ba4f1ff.gif nokada iň golaý nokady tapyň.

B(x,y) – iň golaý nokat bolsun. A(16; 2,5) ; y = x2 + 2;

L(x) = ǀABǀ=hello_html_m56f3e556.gif = hello_html_m4b9d6349.gif ;

Lˊ(x)= hello_html_m565ad266.gif = hello_html_1590ed03.gif ; Lˊ(x)= 0;

hello_html_21714387.gif= 0; => x = 2;

x2 + 2x + 4 = 0; hakyky köki ýok.

y = x2 + 2 = 2 + 2 = 4; => B(2; 4);

7. Berlen çyzyklar bilen çäklenen figuranyň meýdanyny hasaplaň:

hello_html_11852162.gif hello_html_16dc8884.gif;

hello_html_66f040a0.gif => hello_html_472563cb.gif = hello_html_6b68b677.gif;

hello_html_7a2a5240.gif- 5hello_html_3b70014d.gif= 0; D = 25 – 16 = 9;

x1 = 1; x2 = 4;

S= hello_html_70ba2f0c.gif – x – 4)dx =

= hello_html_3ace7559.gif + hello_html_52638c78.gif – 4)dx =

= hello_html_m1373fc3c.gifhello_html_m6195b74b.gif + hello_html_4c6e15f3.gifhello_html_m6195b74b.gif – 4x│hello_html_m6195b74b.gif =

- hello_html_m5d44bbef.gif + hello_html_2b6e6a20.gif – 12 = hello_html_m1350bf44.gif – 12 = hello_html_ma244389.gif = hello_html_78170999.gif = 4,5;

Jogaby: 4,5.





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Дата добавления 20.09.2015
Раздел Математика
Подраздел Конспекты
Просмотров151
Номер материала ДA-053411
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