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Assignment:Find the solution set of inequality 880.180 ≤2/3×14.3×1000×0.785×0.5×(sin(3.1416x))^3/3.1416+(x×14.3×1000×0.785×(1-sin(2×3.1416x)/(2×3.1416x))/(1.25-3x)×0.4375/3.1416×((sin(3.1416x)+sin(1-2x)) ) ) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
880.180 ≤2 / 3 × 14.3 × 1000 × 0.785 × 0.5 × ( sin ( 3.1416 * x ) ) ^ 3 / 3.1416 + ( x × 14.3 × 1000 × 0.785 × ( 1 - sin ( 2 × 3.1416 * x ) / ( 2 × 3.1416 * x ) ) / ( 1.25 - 3 * x ) × 0.4375 / 3.1416 × ( ( sin ( 3.1416 * x ) + sin ( 1 - 2 * x ) ) ) ) (1)
From the definition field of divisor
2 × 3.1416 * x ≠ 0 (2 )
From the definition field of divisor
1.25 - 3 * x ≠ 0 (3 )
From inequality(1):
x ≤ -11.346318 或 -5.551781 ≤ x ≤ -5.389406 或 -1.6412 ≤ x ≤ -1.394777 或 0.261638 ≤ x ≤ 0.416667 或 1.064028 ≤ x ≤ 1.185008 或 x ≥ 4.345156
From inequality(2):
x < 0 或 x > 0
From inequality(3):
x < 0.416667 或 x > 0.416667
From inequalities (1) and (2)
x ≤ -11.346318 或 -5.551781 ≤ x ≤ -5.389406 或 -1.6412 ≤ x ≤ -1.394777 或 0.261638 ≤ x ≤ 0.416667 或 1.064028 ≤ x ≤ 1.185008 或 x ≥ 4.345156 (4)
From inequalities (3) and (4)
x ≤ -11.346318 或 -5.551781 ≤ x ≤ -5.389406 或 -1.6412 ≤ x ≤ -1.394777 或 0.261638 ≤ x < 0.416667 或 1.064028 ≤ x ≤ 1.185008 或 x ≥ 4.345156 (5)
The final solution set is :
x ≤ -11.346318 或 -5.551781 ≤ x ≤ -5.389406 或 -1.6412 ≤ x ≤ -1.394777 或 0.261638 ≤ x < 0.416667 或 1.064028 ≤ x ≤ 1.185008 或 x ≥ 4.345156Your problem has not been solved here? Please take a look at the hot problems !