Felkészülés a 4. dolgozatra - kidolgozott feladatok

FELKSZLS A NEGYEDIK (UTOLS!) DOLGOZATRA MOST VAGY SOHA!

KTISMERETLENES EGYENLET RENDSZEREK 1. Helyettests mdszervel oldd meg a kvetkez egyenlet rendszereket (Dolgozat 1a. feladat) a) M(3,1) b) M(1,4) 2x + y = 7 4x 3y = 16 3x 2y = 7 x + 2y = 7 2. Ellentett egytthatk mdszervel oldd meg a kvetkez egyenlet rendszert (Dolgozat 1b. feladat) a) M(4, 1) b) M(0,5; 0,25) 6x +6y = 18 2x + 8y = 3 4x + 9y = 7 8x + 4y = -3 SZVEGES FELADATOK - Dolgozat 2a s 2b feladat (3-10) 3. Kt szm sszege 5, klnbsge 7. Mely szmokrl van sz?

A -1 s a 6 szmokrl van sz 4. Hatrozd meg azokat a szmokat, melyek klnbsge -4, az els szm 2/3-nak s a msodik szm 4/5-nek az sszege pedig 12 A keresett szmok a 6 s a 10.

2 x + y = 7 3x 2y = 7

y=2x+7 y=23+7 3x 2(2x+7) = 7 y=6 + 7 3x + 4x 14 = 7 y = 1 7x 14 = 7 7x = 7+14 M(x,y)=(3,1) 7x = 21 x=21: 7 x = 3

4 x 3y = 16 x + 2y = 7

x=2y+7 x=24+7 4(2y+7) 3y = 16 x=8 + 7 8y + 28 3y = 16 x = 1 11y +28 = 16 11y = 2816 M(x,y)=(1, 4) 11y = 44 /(1) 11y=44 y=44: 11 y = 4

6x+6y=18 /2 4x+9y=7 /(3)

12x +12y=36 /2 12x27y=21 /(3)

15y=15 4x + 9(1)=7 y=15 : (15) 4x9=7 y= 1 4x=9+7 4x=16 x=16:4 x=4

M(x,y)=( 4,1)

2x+8y = 3 /4 8x+4y = 3

8x +32y=12 8x+4y = 3

36y=9 8x + 4(0,25)= 3 y=9 : 36 8x+1=3 y=1:4 8x=31 y = 0,25 8x=4 x=4:8 x=0,5

M(x,y)=( 0,5; 0,25)

122

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5. Hromszg egyik bels szge 45,a msik kt szg klnbsge pedig 15. Szmtsd ki a hromszg szgeit

A hromszg szgei: = 75, =60, =45

6. Az egyenl szr kerlete 26 cm. A szrnak fele 1-el kisebb mint alapja. Szmt ki a hromszg oldalait. A hromszg oldalai: a= 6 cm s b = 10 cm 7. Ha egy trt szmlljhoz hozzadunk 4-et, nevezjbl pedig kivonunk 1-et, kettt kapunk. Ha a szmlljbl kivonunk 1-et, nevezjhez pedig hozzadunk 1-et, akkor viszont -et kapunk. Melyik ez a trt?

8. Szmtsd ki az ABC hromszg szgeit (, , ) ha tudjuk: + = 58 40 s - = 15 20

=45

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9. A 8.4 osztlyban 25 tanul van. A fik tlag tmege 66 kg, lnyok pedig 49. Az egsz osztly tmege 1480 kg. Hny fi s hny lny van az osztlyban? A 8.4 osztlyban 15 fi s 10 lny van. 10. A derkszg hromszg befoginak sszege 27 cm. Ha az egyik befogt 2 cm-rel cskkentjk, a msikat 3 cm-rel nveljk, a hromszg terlete nem vltozik. Szmtsd ki a hromszg befoginak hosszt.

( )148049661650148049y2566

1480 =49y +66x y25x 25=y+x

lnyok -y fik -x

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cm 12a1527a2715a

27ba

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KP (dolgozat 3.a, 3.b, 3.c feladat) 11. a) Szmtsd ki a kp felsznt s trfogatt, ha d=82 cm, H=2 cm. 11. b) Szmtsd ki a kp tengelyes metszetnek terlett, felsznt s trfogatt ha s=17 cm, d=16 cm.

11. c) A kp alapjnak kerlete 123pi cm, alkotja pedig 12 cm. Szmtsd ki felsznt s trfogatt

r

H ?s ?r?V ?F

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12.a) A kp palstterlete 60pi cm2, alapterlete pedig 36pi cm2. Szmtsd ki a kp alkotjt s trfogatt

12.b) A kp palstterlete 24 pi cm2, alapterlete pedig 16pi cm2. Szmtsd ki a kp alkotjt s trfogatt

12.c) A kp trfogata 9pi cm3. Szmtsd ki a kp felsznt ha H=3 cm.

12.d) A kp trfogata 18pi cm3, magassgnak s sugarnak arnya 2:1. Szmtsd ki kp felsznt

r

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13.a) Derkszg melynek oldalai a=5 cm s c=13 cm, forog az a befogo krl. Szmtsd ki az gy kapott alakzat F s V.

13.b) Derkszg melynek oldalai b=1 cm s c=2 cm, forog a b befogo krl. Szmtsd ki az gy kapott alakzat F s V. 13.c) Az egyenl szr hromszg, melynek alapja 14 cm, szra pedig 15 cm, magassga krl forog. Szmtsd ki a kapott forgstest felsznt s trfogatt

r=b

H=a

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GMB (DOLGOZAT 4.a s 4. b feladat) 14. a) Szmtsd ki a gmb felsznt s trfogatt ha r=35 cm

14. b) A gmb felszne 200pi cm2. Szmtsd ki trfogatt

14. c) A gmb trfogata 4 pi 3 cm3. Szmtsd ki felsznt. 14. d) Szmtsd ki a flgmb felsznt s trfogatt ha r=22 cm

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VEGYES FELADATOK (DOLGOZAT 5. FELADAT) 15.a) Egy kp alak ednyben melynek magassga 6 cm tmrje 12 cm vz van. Ezt a vizet tntttk egy henger alak ednybe melynek tmrje 12 cm. Az ednyben milyen magasan lesz a vz? KP ALAK EDNY A vz trfogata nem vltozik azzal hogy tntjk egyik ednybl a msikba Az ednyben H=2 cm magasan lesz a vz. 15.b) Egy henger alak ednyben (d=4 cm, H=3 cm) bor van. Mekkora sugar gmbbe tudjuk ezt a bort tnteni? HENGER ALAK EDNY Az adott trfogat bort tntjk egy gmbbe (keressk a gmb sugart)

A keresett gmb sugara r=3 cm

r

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cm 12d6cmH

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cm 6r2:12r

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15.c) Egy r=33 cm sugar gmb alak ednyben folyadk van. Ezt a folyadkot tntjk egy 63 cm magassg kpba. Mekkora kell hogy legyen a kp sugara? GMB ALAK EDNY Az adott trfogat folyadkot tntjk egy kp alak ednybe (keressk a kp sugart)

A kp sugara r=36 cm. 15.d) 8 darab 4 cm sugar lomgolyt felolvasztanak s egy golyba ntttek. Szmtsd ki az gy kapott goly tmrjt.

1 goly trfogata 8 goly trfogata: Nagy goly trfogata = 8 kisgoly trfogata A kapott goly tmrje d=16 cm.

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Documents

Felkészülés a 4. dolgozatra - kidolgozott feladatok