ppt gradien
TRANSCRIPT
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Wednesday, May 3, 2023 1
GRADIEN/KEMIRINGAN
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Wednesday, May 3, 2023 2
ILUSTRASI TENTANG GRADIEN/KEMIRINGAN
A BC
D
E
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GRADIEN/KEMIRINGANWednesday, May 3, 2023
Kata sang supir:Tidak ada tantangan yang berarti.Gradien = 0
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Wednesday, May 3, 2023 4
Kata supir:
Saya harus menekan pedal gas lebih dibanding jalanan datar
Artinya ada tantangan dengan adanya kemiringan (gradient) , karena harus menekan pedal gas, Menambah kecepatan kendaraan maka gradient positif
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Wednesday, May 3, 2023
Tantangan lebih besar.Bagaimanakah gradienya?
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???
Wednesday, May 3, 2023
Aku menekan pedal gas sampaimentok, tetapi mobil tetap tidakmau melaju.
Tantangan sangat besar, karenasaking besarnya sehingga mobiltidak mau melaju.Artinya gradientnya sangat besar,begitu besarnya disebut takterhingga
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Wednesday, May 3, 2023
Saya tidak perlu menekan pedal gas, malah sayaharus nginjak pedal rem untuk mengurangi kecepatan.Berarti gradient negatif
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PADA BIDANG CARTESIUS
a
b
cD
e
f
Garis manakah:Yang gradiennya=0Yang gradiennyapositifYang gradiennyanegatifYang gradiennyaTak terhingga
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Wednesday, May 3, 2023 95
m
3 M
5m
3 M
4M
4 M
KESIMPULANGRADIEN = JARAK VERTIKAL JARAK HORISONTAL
Manakah yang lebihBesar tantanganyaPosisi (i) atau (ii)?
(i) (ii)
Menghitung besar gradien
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MENGHITUNG GRADIEN
Gradien garis AB, ditulis mAB = 3/6 = ½Jika kita tinjau dengan koordinatnya:
A(4,-1) dan B(10,2), maka mAB = Kesimpulan: Jika A(x1,y1) dan B(x2,y2) maka mAB = …..
A
B3
6
●
●
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Hitunglah gradien-gradien berikut:1. m AB= 2. m AC= 3. m CD=
ED
CB
A
KESIMPULAN:.DUA TITIK SEMBARANG YANG TERLETAK PADA SATU GARIS, MAKA GRADIENYA SAMUA SAMA, YAITU = GRADIEN GARIS TERSEBUT
●
●
●
●
●
−36 =
−12
−48 =
−12
−24 =
−12
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EXAMPLE
1. Hitunglah gradien dari dua titik berikut!a. A(2,3) dan B(6,5) Jawab: mAB= y2-y1 x2-x1
= 5-3 6-2 = 1/2
2. Hitung nilai a, jika garis
yang melalui titik (2a,-3)
dan titik (4a,5), memiliki
gradiaen 2.
Jawab: 2 = 5-(-3)
4a-2a
2 = 8/2a
4a=8, a= 2
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3 HITUNGLAH GRADIEN DARI RUAS GARIS BERIKUT
D
E
G
F
CB A
JAWAB:OA = 6/4=3/2BC = 0/5=0DE = -8- (-2) -3-(-7) = -6/4 = -3/2FG = -2-(-7) 5 – 5 = 5/0 = ∞
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HUBUNGAN GRADIEN DAN PERSAMAAN GARIS:1. GARIS-GARIS YANG SEJAJAR
GRADIEN GARIS A= 2GRADIEN GARIS B=2GRADIEN GARIS C=2GRADIEN GARIS D=2KESIMPULAN:…GARIS-GARIS YANG SEJAJAR GRADIENYASAMA
a b c d
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2. GRADIEN GARIS-GARIS YANG SALING BERPOTONGAN TEGAK LURUS
LK
Garis k dan l saling tegak lurus.Gradien garis k = 2Gradien garis l=-1/2Kesimpulan:Jika garis k dan garis l saling tegak lurus maka berlaku:m k x m l = -1
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a
b
c
d
e
f
g
h
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d
b
c
a
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a
c
cb
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Kuadran 1
Kuadran 3
Kuadran 2
Kuadran 4
A
ED
C
B
34
OA=√32 + 42
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Wednesday, May 3, 2023 20
a. X=5b. X=-3
c. y=-3
X=5X=-3
Y=-3
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Rabu 3 Mei 2023
I LOVE YOU MATH
1 2 3O 4 5 76 8 9 10 X→
→ Y
21
109
76543
8
-1-2-3-4-5-6
-1-2-3-5 -4-6