P.e.m.b.a.h.a.s.a.n UN 2013.

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1 p.e.m.b.a.h.a.s.a.n UN 2013

2 LOGARITMA = 6 𝒂 𝒍𝒐𝒈 𝒃 𝒏 =𝒏 𝒂 𝒍𝒐𝒈𝒃 𝒂 𝒍𝒐𝒈𝒃 . 𝒃 𝒍𝒐𝒈𝒂 =𝟏 remember 1 𝟑 𝒍𝒐𝒈
𝒂 𝒍𝒐𝒈 𝒃 𝒏 =𝒏 𝒂 𝒍𝒐𝒈𝒃 𝒂 𝒍𝒐𝒈𝒃 . 𝒃 𝒍𝒐𝒈𝒂 =𝟏 𝟑 𝒍𝒐𝒈 𝟐 𝟐 𝟐 𝒍𝒐𝒈 𝟑 𝟑 𝟑 𝒍𝒐𝒈𝟐 𝟐 𝒍𝒐𝒈𝟑 𝟐 . 𝟑 . 1 = 6

3 2 1 1 1 − = 2 – = 6

4 3 −𝟔 𝟕 𝟑 . 𝟒 . 𝟕 𝟑 𝟕 +𝟓 𝟒 𝟕 −𝟐 −𝟏𝟎 +𝟐𝟎 𝟕 =𝟖𝟒−𝟏𝟎+𝟏𝟒 𝟕 =𝟕𝟒+𝟏𝟒 𝟕

5 4 𝟏𝟎 . 𝟓𝟓=𝟓𝟓𝟎 𝒎𝒎 𝟓𝟓 𝒄𝒎

6 5 𝟒 . 𝟐 . 𝟒 . 𝟐 . 𝟏𝟐𝒙+𝟐𝟎−𝟏𝟎𝒙−𝟏𝟐=𝟗𝒙+𝟏𝟓 𝟐𝒙+𝟖=𝟗𝒙+𝟏𝟓 −𝟕=𝟕𝒙 −𝟏=𝒙

7 6 𝟐𝒄+𝟑𝒌=𝟏𝟎𝟏.𝟓𝟎𝟎 𝒄+𝟐𝒌= 𝟓𝟑.𝟓𝟎𝟎 𝒄+ 𝒌= 𝟒𝟖.𝟎𝟎𝟎

8 7 2x – 5y + 20 = 0 ( -5 , 2 ) 2x – 5y + 1 = 0 2x – 5y = 2 . -5 +-5 . 2
( -5 , 2 ) 2x – 5y + 1 = 0 2x – 5y = 2x – 5y = -20 2x – 5y = 0

9 8

10 9 8𝑥+7𝑦≤56 4𝑥−3𝑦≥−12 (1,0) KITA UJI TITIK (1,0) 𝟖 . 𝟏+𝟕 . 𝟎≤𝟓𝟔 BENAR
𝟒 . 𝟏−𝟑 . 𝟎≥−𝟏𝟐 BENAR (1,0) Daerah IV memenuhi

11 10 2𝒙+𝒚=𝟗 𝟓 𝒙+𝟐𝒚=𝟏𝟐 𝒙=𝟐 𝒛=𝟑𝒙+𝟐𝒚 (𝟐,𝟓) 𝒛=𝟑.𝟐+𝟐.𝟓=𝟏𝟔 𝒛=𝟑.𝟒,𝟓+𝟎=𝟏𝟑,𝟓
𝒚= 𝟐𝟒−𝟗 𝟒−𝟏 = 𝟏𝟓 𝟑 =𝟓 𝒙=𝟐 9 𝒛=𝟑𝒙+𝟐𝒚 (𝟐,𝟓) 𝒛=𝟑.𝟐+𝟐.𝟓=𝟏𝟔 maks 6 4,5 12 𝒛=𝟑.𝟒,𝟓+𝟎=𝟏𝟑,𝟓 𝒛=𝟎+𝟐.𝟔=𝟏𝟐

12 11 𝑓 𝑥 = 𝑥 2 −3𝑥−10 𝑘𝑜𝑒𝑓𝑖𝑠𝑖𝑒𝑛 𝑥 2 𝑝𝑜𝑠𝑖𝑡𝑖𝑓 𝑘𝑜𝑒𝑓𝑖𝑠𝑖𝑒𝑛 𝑥 𝑛𝑒𝑔𝑎𝑡𝑖𝑓

13 12 a = b = -c = a+b-c = a+b-c = 6i – j + 8k

14 ____ ____ ____ ____ ____ ____ ____ ____ ____
13 𝑏𝑎𝑟𝑖𝑠 𝑘𝑒 1 𝑘𝑜𝑙𝑜𝑚 𝑘𝑒 1 2 1 1 − − =𝟒 𝟐 . 𝟏 + 𝟏 . 𝟐 ____ ____ ____ ____ ____ ____ ____ ____ ____

15 14

16 15 ` 𝒌𝒐𝒏𝒕𝒓𝒂𝒑𝒐𝒔𝒊𝒔𝒊 𝒅𝒂𝒓𝒊 𝒑→𝒒 𝒂𝒅𝒂𝒍𝒂𝒉 ~𝒒→~𝒑

17 16 𝒅𝒊𝒊𝒏𝒈𝒌𝒂𝒓 𝒊𝒏𝒈𝒌𝒂𝒓𝒂𝒏 𝒅𝒂𝒓𝒊 𝒑→𝒒 𝒂𝒅𝒂𝒍𝒂𝒉 𝒑⋀~𝒒

18 17 𝑳=𝝅 𝒓 𝟐 +𝟐𝝅𝒓𝒕 𝑳=𝝅𝒓 𝒓+𝟐𝒕 𝑳= 𝟐𝟐 𝟕 𝟏𝟒 𝟏𝟒+𝟒𝟎 𝑳=𝟒𝟒 𝟓𝟒

19 18 𝑲=𝟐.𝟏𝟖+𝟒.𝟓+ 𝟐𝟐 𝟕 𝟕=𝟕𝟖

20 19 𝑱 𝑰 𝒅𝒊𝒂𝒈𝒐𝒏𝒂𝒍 𝒃𝒊𝒅𝒂𝒏𝒈 𝒅𝒊𝒂𝒈𝒐𝒏𝒂𝒍 𝒃𝒊𝒅𝒂𝒏𝒈 𝑮 𝑯 𝒔𝒊𝒔𝒊 𝒅𝒊𝒂𝒈𝒐𝒏𝒂𝒍 𝒓𝒖𝒂𝒏𝒈 𝑭 𝑬 𝑫 𝑪

21 20 𝑽= 𝟏 𝟑 𝑳𝒂 . 𝒕 𝑽= 𝟏 𝟑 .𝟏𝟓 . 𝟕.𝟏𝟐 𝑽=𝟓 . 𝟕.𝟏𝟐=𝟒𝟐𝟎

22 21 𝟑 𝒅𝒊𝒔𝒆𝒃𝒆𝒍𝒂𝒉 𝒌𝒂𝒏𝒂𝒏

23 22 𝑪 𝑩𝑪= 𝟏𝟎 𝑺𝒊𝒏 𝟔𝟎 𝒐 𝑺𝒊𝒏 𝟒𝟓 𝒐 𝟏𝟎 𝟔𝟎 𝒐 𝟒𝟓 𝒐 𝑩 𝑨 𝑩𝑪= 𝟏𝟎 𝟏 𝟐 𝟑 𝟏 𝟐 𝟐 = 𝟏𝟎 𝟑 𝟐 . 𝟐 𝟐 =𝟓 𝟔

24 23 𝑺𝒏= 𝟏𝟐 𝟐 𝟐 . 𝟏𝟐𝟓𝟎𝟎𝟎𝟎+𝟏𝟏 . 𝟐𝟓𝟎𝟎𝟎 𝑺𝒏=𝟔 𝟐𝟓𝟎𝟎𝟎𝟎𝟎+ 𝟐𝟕𝟓𝟎𝟎𝟎 𝑺𝒏=𝟔 𝟐𝟕𝟕𝟓𝟎𝟎𝟎 𝑺𝒏=𝟏𝟔.𝟔𝟓𝟎.𝟎𝟎𝟎

25 24 𝒏=𝟑 𝟏𝟓 . 𝟑 𝟒 𝟏𝟓 . 𝟑 𝟐 𝟓 . 𝟑 𝟒 𝟓 . 𝟑 𝟑

26 25 𝟏 𝟐 𝟑 𝟒 𝟓 =𝟏𝟓 𝟏 𝟐 𝟏 𝟐 𝟓 𝟖 𝟐 𝟒 𝟓 𝟒𝟓 𝟐𝟓 𝟏𝟓 𝒎𝒊𝒔𝒂𝒍 𝒓= 𝟏 𝟐 𝒃𝒆𝒏𝒂𝒓

27 26 5 4 1 3 2 10 6 4 5 𝒑= 𝟕 𝟑𝟔

28 27 3 8 𝐶= = 𝟓𝟔

29 28 𝒑= 𝟑𝟎𝟎 𝟏𝟎𝟎𝟎 .𝟏𝟎𝟎% 𝒑=𝟑𝟎%

30 29 9 165 – 169 12 6 𝟑 𝟔 𝟗 𝑴𝒐=𝟏𝟔𝟒,𝟓+ 𝟑 𝟗 . 𝟓=𝟏𝟔𝟒,𝟓+𝟏,𝟔𝟕 𝑴𝒐=𝟏𝟔𝟔,𝟏𝟕

31 30

32 30 Berat badan (kg) xt f d fd 49 – 51 5 -2 -10 52 – 54 17 -1 -17 55 – 57 56 14 58 – 60 10 1 61 – 63 4 2 8 Jumlah 50 -9 𝒙 =𝟓𝟔+ −𝟗 𝟓𝟎 .𝟑=𝟓𝟔−𝟎,𝟓𝟒=𝟓𝟓,𝟒𝟔

33 31

34 31 𝒇𝒌 𝟕 𝟏𝟐 𝟐𝟎 𝟑𝟏 𝟑𝟕 𝟒𝟎 𝟏𝟎 𝟒 𝟏𝟎 − 𝟕 𝟓 .𝟓=𝟑𝟕,𝟓 𝑲 𝟏 = 𝟑𝟒,𝟓+

35 32 𝒇 𝒙 = 𝟑𝒙+𝟏 𝟐𝒙−𝟓 𝟑 . (−𝟓) − 𝟏 . 𝟐 𝒇′ 𝒙 = 𝟐𝒙−𝟓 𝟐 𝒇′ 𝒙 = −𝟏𝟕 𝟐𝒙−𝟓 𝟐

36 33 𝒇 𝒙 =𝒔𝒊𝒏𝟒𝒙+𝒄𝒐𝒔𝟑𝒙 𝒇′ 𝒙 = 𝟒 𝒄𝒐𝒔 𝟒𝒙 − 𝒔𝒊𝒏 𝟑𝒙 𝟑

37 34 𝑳𝒊𝒎 𝒙→𝒂 𝒇(𝒙) 𝒈(𝒙) = 𝒇(𝒂) 𝒈(𝒂) 𝑳𝒊𝒎 𝒙→−𝟑 𝟒𝒙+𝟖 𝟐 𝟒(−𝟑)+𝟖 𝟐 = −𝟒 𝟐 =−𝟐

38 35 𝒔𝒕𝒂𝒔𝒊𝒐𝒏𝒆𝒓 𝒇 ′ 𝒙 =𝟎 𝒇 𝒙 = 𝟐𝒙 𝟑 − 𝟑𝒙 𝟐 +𝟓 𝟔𝒙 𝟐 −𝟔𝒙=𝟎 𝒙 𝟏 =𝟎 𝟔𝒙(𝒙−𝟏)=𝟎
𝒇 ′ 𝒙 =𝟎 𝟔𝒙 𝟐 −𝟔𝒙=𝟎 𝒙 𝟏 =𝟎 𝒇 𝟎 =𝟐.𝟎−𝟑.𝟎+𝟓=𝟓 𝟔𝒙(𝒙−𝟏)=𝟎 (𝟎,𝟓) 𝒙 𝟐 =𝟏 𝒇 𝟏 =𝟐.𝟏−𝟑.𝟏+𝟓=𝟒 𝒙 𝟏 =𝟎 (𝟏,𝟒) 𝒙 𝟐 =𝟏

39 36 𝒙 𝟐 −𝟒𝒙+𝟑=𝟎 𝑫=(−𝟒) 𝟐 −𝟒.𝟏.𝟑 𝑫=𝟏𝟔−𝟏𝟐=𝟒 𝒙 𝟐 −𝟑𝒙+𝟐 = 𝒙−𝟏
𝑳= 𝑫 𝑫 𝟔 𝒂 𝟐 = 𝟒 𝟒 𝟔 . 𝟏 𝑳= 𝟖 𝟔 = 𝟒 𝟑

40 37 𝒕=𝟐− −𝟏 =𝟑 −𝟏 𝟐 𝟓 𝒚=𝒙+𝟑 𝟐 𝑽= 𝟏 𝟑 𝝅 𝟑 ( ) 𝟐 𝟐 + 𝟓 𝟐 + 𝟐 . 𝟓 𝑽=𝝅 𝟒+𝟐𝟓+𝟏𝟎 =𝟑𝟗𝝅

41 38 = 𝟐 𝒙 𝟑 + 𝒙 𝟐 +𝒙 𝟎 𝟑 =𝟐 . 𝟐𝟕+𝟗+𝟑 =𝟓𝟒+𝟏𝟐=𝟔𝟔

42 39 𝟑𝒙 𝟐 𝟒𝒙−𝟏 𝒅𝒙 = 𝟏𝟐𝒙 𝟑 − 𝟑𝒙 𝟐 𝒅𝒙 = 𝟏𝟐 𝟒 𝒙 𝟒 − 𝟑 𝟑 𝒙 𝟑 +𝑪=𝟑 𝒙 𝟒 − 𝒙 𝟑 +𝑪

43 40 𝒙 𝟐 + 𝒚 𝟐 +𝟏𝟎𝒙−𝟐𝒚−𝟏𝟎=𝟎 −𝟓 𝟏 𝟔 𝒙 𝟐 + 𝒚 𝟐 +𝟏𝟎𝒙 −𝟐𝒚 +𝟐𝟓+𝟏 − 𝟑𝟔=𝟎
−𝟓 𝟏 𝟔 𝒅𝒊𝒌𝒂𝒍𝒊𝒌𝒂𝒏 (−𝟐) 𝒅𝒊𝒌𝒖𝒂𝒅𝒓𝒂𝒕𝒌𝒂𝒏 𝒙 𝟐 + 𝒚 𝟐 +𝟏𝟎𝒙 −𝟐𝒚 +𝟐𝟓+𝟏 − 𝟑𝟔=𝟎 𝒙 𝟐 + 𝒚 𝟐 +𝟏𝟎𝒙−𝟐𝒚−𝟏𝟎=𝟎

44 Thank You !