Tolong dibantu kak nomer 14 dan 15 beserta caranya ya
Matematika
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Pertanyaan
Tolong dibantu kak nomer 14 dan 15 beserta caranya ya
1 Jawaban
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1. Jawaban DB45
Percerminan
y = 2x
m = 2 --> tan A = 2 = y/x
r = √(x²+y²)= √5
sin A = y/r= 2/√5
cos A = x/r= 1/√5
sin 2A = 2 sin A cos A = 2(2/√5)(1/√5)= 4/5
cos 2A =√( 1 - sin² 2 A) = √(1 - (4/5)² = +_ 3/5
cos 2A = - 3/5 ( dikuadran II)
( x')= (x) cos 2A + (y) sin 2A
x' = 7(-3/5) + (-1) (4/5)
x' = -21/5 - 4/5 = -25/5 = -5
(y') = (x)(sin 2A) + (y) cos 2A
y' = 7 (3/5)+ (-1)(-4/5)
y' = 21/5 + 4/5 = 25/5 = 5
bayangan x',y' = (-5, 5)
2.
⁴log (3-x) + ²log x > 1/2
²log (3-x)¹/² + ²log x > ²log 2¹/2
²log x√(3-x) > ²log √2
x √(3-x) > √2
x²(3-x) > 2
3x² - x³ - 2 >0
x³ - 3x² + 2 > 0 dgn syarat 3-x > 0 atau x > 0
(x-1)(x² - 2x -2) > 0
x = 1 , x = 1 - √3, x = 1 + √3 , x < 3 ,x > 0
x > 1 + √3
1 - √3 < x < 1
x < 3
x> 0
HP
0 < x < 1 atau 1 +√3 < x < 3