ExamHoot

Find the value of ?? in the following expression: (0.73)3+(0.27)3(0.73)20.73×0.27+(0.27)2×(112+120+130+142+156)1=?\frac{(0.73)^3 + (0.27)^3}{(0.73)^2 - 0.73 \times 0.27 + (0.27)^2} \times (\frac{1}{12} + \frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56})^{-1} = ?

Find the value of ?? in the following expression: (0.73)3+(0.27)3(0.73)20.73×0.27+(0.27)2×(112+120+130+142+156)1=?\frac{(0.73)^3 + (0.27)^3}{(0.73)^2 - 0.73 \times 0.27 + (0.27)^2} \times (\frac{1}{12} + \frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56})^{-1} = ?

  1. 4.84.8

  2. 2.42.4

  3. 0.2080.208

  4. 3.63.6

  5. 5.25.2

Show answer & explanation

Correct answer

4.84.8

Explanation

1) The algebraic identity a3+b3a2ab+b2=a+b\frac{a^3 + b^3}{a^2 - ab + b^2} = a + b. Here a=0.73,b=0.27a=0.73, b=0.27, so a+b=1.0a+b = 1.0. 2) Telescoping series: 112+120+130+142+156=(1314)+(1415)++(1718)=1318=524\frac{1}{12} + \frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56} = (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + \dots + (\frac{1}{7} - \frac{1}{8}) = \frac{1}{3} - \frac{1}{8} = \frac{5}{24}. 3) Taking the inverse: (524)1=245=4.8(\frac{5}{24})^{-1} = \frac{24}{5} = 4.8. 4) Result: 1.0×4.8=4.81.0 \times 4.8 = 4.8.

Written by ExamHoot EditorialPublished · Updated

All 20 Simplification questions

  1. 1.Simplify:
  2. 2.Find the value of 17 + 12√2 + 17 - 12√2 .
  3. 3.Simplify:
  4. 4.Approximately evaluate 49.8 × 20.1 × 0.98/4.9 × 9.9 × 3.1 using rounding to one significant figure.
  5. 5.Simplify:
  6. 6.If x = 2 + √3 , find the value of x^2 + 1/x^2 .
  7. 7.Simplify:
  8. 8.Find the value of 12 + 12 + √12 + .
  9. 9.Simplify:
  10. 10.Approximately what is 23.8\% of 489.6 ?
  11. 11.What value should come in place of the question mark ( ?
  12. 12.Evaluate the value of ?
  13. 13.Find the value of ?
  14. 14.What should come in place of ?
  15. 15.Find the value of ?
  16. 16.What value should come in place of the question mark ( ?
  17. 17.Find the value of ?
  18. 18.What should come in place of in the given expression?
  19. 19.Find the value of ?
  20. 20.Evaluate the value of ?