Evaluate: 1.93 -0.43/(1.9)2+(1. 9*0.4)-(0.4)2
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Evaluate: 1.93 -0.43/(1.9)2+(1. 9*0.4)-(0.4)2
- A.
3.02
- B.
1.589
- C.
3.56
- D.
2.78
Attempted by 11 students.
Show answer & explanation
Correct answer: A
Key insight: use the factorization a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Set a = 1.9 and b = 0.4. Then (1.9^3 - 0.4^3) = (1.9 - 0.4)(1.9^2 + 1.9*0.4 + 0.4^2).
So the expression becomes (1.9^2 + 1.9*0.4 + 0.4^2)/(1.9 - 0.4).
Compute the pieces: 1.9^2 = 3.61, 1.9*0.4 = 0.76, 0.4^2 = 0.16. Sum = 4.53. Denominator = 1.9 - 0.4 = 1.5.
Final division: 4.53 ÷ 1.5 = 3.02. Therefore the value is 3.02.