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a.
b. ∑ (x-xr)² = (5,1 - 5,3)² + 2 (5,2 - 5,3)² + 2 (5,3 - 5,3)² + 2 (5,4 - 5,3)²
= (-0,2)² + 2 (-0,1)² + 2 (0)² + 2 (0,1)²
= 0,04 + 0,02 + 0 + 0,02
= 0,08
stdev =√ [ ∑(x - xr)² / (n -1) ]
= √ [ 0,08 / (7-1) ]
= √ 0,0133
= 0,11
= 0,1
c. ∑ x = 5,2+5,3+5,1+5,4+5,2+5,4+5,3
= 36,9
∑ x² = 5,2²+5,3²+5,1²+5,4²+5,2²+5,4²+5,3²
= 194,59
Δx = √ n ∑ x² - (∑x)² / n-1
Δx =
=
=
= 0,005
ketidakpastian relatif = Δx/xr . 100%
= 0,005/5,3 x 100%
= 0,1 %
d. x = 5,3 +/- 0,1
UK 2.8
a. lihat lampiran
b. m = y₁ - y₂ / x₁ - x₂
= 100,200 - 100,025 / 80 - 10
= 0,175 / 70
= 0,0025
pers garis :
y - y₁ = m (x - x₁)
y - 100,200 = 0,0025 (x - 80)
= 0,0025x - 0,200
y = 0,0025x - 0,200 + 100,200
y = 0,0025x + 100
c. Panjang logam saat t = 0 --> x = 0
y = 0,0025(0) + 100
= 100 C
pers umum pemuaian panjang :
l = lo (1 + αt)
y = 0,0025x + 100
= 100 (1 + 0,0025/100 x)
= 100 (1 + 0,000025 x)
y = l
lo = 100
α = 0,000025
x = t
sehingga koefisien muai α = 0,000025
d) sehingga bahan yang dimaksud adalah = aluminium