1.14.
, . . :
) cos(0,47);
) = -3,1;
) = ;
) = ln(68,214).
.
) . 0,891568.
0,47 = 0,005.
:
cos(0,47) = │sin(0.47)│ ∙ 0.005 = 0,00226443;
δcos(0,47) = │tan(0.47)│ ∙ 0.005 = 0,00253983 ≤ 0.005 = 0,5 ∙ 10-2.
, 0,891568 .
: 0,892.
) . 0,0450492.
= 0,05. :
= │-3,1│ ∙ 0,05 = 0,0225246;
δ = 0,05 = 0,5 ∙ 10-1.
, 0,0450492 .
: 0,04.
) . 4,6378875.
= 0,005. :
= = 1,078077 ∙ 10-3;
δ = = 2,3245002 ∙ 10-4 < 0.5 ∙ 10-3;
, 4,6378845 .
: 4,6378.
) . 4,2226498.
= 0,0005. :
= = 7,3298736 ∙ 10-6;
δ = = 1,7358469 ∙ 10-6 < 0,5 ∙ 10-5.
, 4,2226498 .
: 4,222649.
1.15.
.
= , = 12,34, b = 14,3.
.
( ) . 1.1.
1.1.
=
b + ln(a) b + ln(a) A
12,34 14.3 3.513 3.78 7.30 2.5129 16.81 0.434
ea eb e e e e eb + ln(a) eA
0.005 0.05 0.00071 0.0066 0.0073 0.0004 0.05041 0.0017
.
, , = 0,005, b = 0,05.
= 3,51283. ( . 1.1):
|
|
= = 0,0007117 ≈ 0,00071.
, , . .
= 3,51283 ≈ 3,513.
.
= 3,781534.
b = = 0,0066107 ≈ 0,0066.
, b .
:
= 0,00071 + 0,0066 = 0,00731 ≈ 0,0073;
ln() = = 0,000405 ≤ 0,0005;
b + ln(a) = 0.05 + 0.000405 = 0.050405 ≤ 0.5;
= = = 0,0017.
, .
: = 0,434 0,002.
, .
1.16.
d = (3 0,001) h = (10 0,002) p = (95,5 0,001) . γ .
.
1 .
:
V = h,
γ = .
, p > 0, d > 0, h > 0 γ p d h.
:
2,999 < d < 3,001;
9,998 < h < 10,002;
95,499 < p < 95,501;
3,14159 < π < 3,1416.
γ :
= = 1,350 /3 ( );
= = 1,352 /3 ( ).
, γ,
γ = (1,351 0,002) /3.
: γ = (1,351 0,002) /3.
2 .
,
= = 1,351 /3.
,
ln γ = ln 4 + ln p ln π 2 ln d ln h.
, :
;
δγ = δp + δπ + 2δd + δh = = 8.803 ∙ 10-4
:
Δγ = δγ ∙ γ = 8,803 ∙ 10-4 ∙ 1,351 = 1,2 ∙ 10-3.
, :
γ = (1,351 0,001) /3,
, .
: γ = (1,351 0,001) /3.
1.17.
V = πd3, d = 3,7 0,05 , π = 3,14.
.
d π ,
3 = 8,44;
2 = 21,5.
,
│Δf│ = ,
8,44 ∙ 0,0016 + 21,5 ∙ 0,05 = 0,013 + 1,075 = 1,088 3 ≈ 1,1 3.
V = ≈ (26.5 1.1) 3.
δV = = 0,041 ≈ 4%.
: ΔV = 1,1 3, δV = 4%.
1.18.
= , l ; a b ; s ; p . , p = 20 ; δp = 0,1%; = 3 ; δ = 1%; b = 44 ; δb = 1%; l = 50 ; δl = 1%; s = 2,5 ; δs = 1%.
|
|
.
Ln E = 3ln l + ln p 3ln a ln b ln s ln 4.
, , :
.
,
δ = 3δl + δp + 3 δ + δb + δs = 3 ∙ 0,01 + 0,001 + 3 ∙ 0,01 + 0,01 + 0,01 ≈0,081. , 0,081, . . 8% .
: δ ≈ 8%.
1.19.
z Mathcad , b c , .
z = , a:= 12,34 b:= 14,3.
.
. 1.3 1.5
. 1.3. 1.19
. 1.4. 1.19
. 1.5. 1.19