Subjects algebra

Moment Calculation A279Bc

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1. **State the problem:** Calculate the value of $$M_{r\max} = 400 \times 530 \times 0.025 \times 0.85 \times 300 \times \left( 530 - \frac{0.85 \times 300 \times 530 \times 0.025}{2 \times 0.81 \times 0.65 \times 30} \right) \times 10^{-6}$$ 2. **Calculate the denominator inside the parentheses:** $$2 \times 0.81 \times 0.65 \times 30 = 2 \times 0.81 \times 0.65 \times 30 = 31.59$$ 3. **Calculate the numerator inside the fraction:** $$0.85 \times 300 \times 530 \times 0.025 = 0.85 \times 300 \times 530 \times 0.025 = 3378.75$$ 4. **Calculate the fraction inside the parentheses:** $$\frac{3378.75}{31.59} \approx 107.01$$ 5. **Calculate the expression inside the parentheses:** $$530 - 107.01 = 422.99$$ 6. **Calculate the product of the constants outside the parentheses:** $$400 \times 530 \times 0.025 \times 0.85 \times 300 = 400 \times 530 \times 0.025 \times 0.85 \times 300 = 1351500$$ 7. **Multiply the product by the parentheses result:** $$1351500 \times 422.99 = 571676985$$ 8. **Multiply by $10^{-6}$ to get the final result:** $$571676985 \times 10^{-6} = 571.68$$ **Final answer:** $$M_{r\max} \approx 571.68$$