Recent content by Johnny Leong

  1. J

    Which terms should be grouped together for factorization?

    I found that this question cannot be factorized as a very simple answer. If really do factorization, only group several terms together, factorize something out but then cannot proceed.
  2. J

    Which terms should be grouped together for factorization?

    r^2 - xyr + (r^2)s + (x)r^2 - (y)r^2 + rsy Which terms should be grouped together for factorization? Please give some comments.
  3. J

    Sum of (i^2)/(4^i) where i is from 0 to infinity.

    What are you doing, arildno? You are professional but I do not understand. Why you do like this?
  4. J

    Sum of (i^2)/(4^i) where i is from 0 to infinity.

    I mean the approximation should be an upper bound to the accurate answer to the original question.
  5. J

    Sum of (i^2)/(4^i) where i is from 0 to infinity.

    I think Gokul43201's answer would not be a good one because after I have read a book, I found that when we do some approximation, the approximation's value had better dominate the value of the original question.
  6. J

    Sum of i^2/(4^i): 0 to Infinity

    Sum of (i^2)/(4^i) > 1/4 + 1/4 + 9/16 + Sum of 1/(4^i) where 4<=i<=infinity. Can this be a good approximation?
  7. J

    Sum of (i^2)/(4^i) where i is from 0 to infinity.

    Actually, this question could not give an accurate answer. The answer should just be an approximation, right? Because the terms in the summation are not having some sequence properties.
  8. J

    Sum of (i^2)/(4^i) where i is from 0 to infinity.

    Please give me some hints: Sum of (i^2)/(4^i) where i is from 0 to infinity.
  9. J

    Sum of i^2/(4^i): 0 to Infinity

    Please give me some hints: Sum of (i^2)/(4^i) where i is from 0 to infinity.
  10. J

    About aerial dish used in communication

    1. What is the function of the dish? Ans: It is to focus the weak signals so that to intensify them. 2. What wave property is suitable to describe the phenomenon happened in the dish? Ans: Reflection. 3. If an antenna is to be placed in front of the dish, where it should be placed to get...
  11. J

    How to Solve a Trigonometric Equation with Multiple Solutions?

    I have solved the problem, I have made some careless mistakes above. The solution is: tan 2x + sec 2x = cos x + sin x where 0<=x<=360 (sin 2x + 1) / cos 2x = cos x + sin x (cos x + sin x)^2 / cos 2x = cos x + sin x (cos x + sin x) / cos 2x = 1 (cos x + sin x) / [(cos x + sin x)(cos x - sin...
  12. J

    How to Solve a Trigonometric Equation with Multiple Solutions?

    How to solve this equation: tan 2x + sec 2x = cos x + sin x where 0<=x<=360 I solve it in this way but cannot find the right answer: (sin 2x + 1) / cos 2x = cos x + sin x (cos x + sin x)^2 / cos 2x = cos x + sin x (cos x + sin x) / cos 2x = 1 sqrt(2) cos(x - 45) sec 2x = 1 sec 2x cos(x -...
  13. J

    Can Predicate Logic Capture Language and Gender Assumptions?

    Represent this sentence in first-order logic: Every student who takes French passes it. Represent the sentence "All Germans speak the same languages" in predicate calculus. Use Speaks(x, l), meaning that person x speaks language l. What axiom is needed to infer the fact Female(Laura)...
  14. J

    Solving a Trigonometric Equation with Identities

    I have solved the problem. I have used the identities: sin x + sin y = 2 sin (x+y)/2 cos(x-y)/2 and cos 2x = 2 cos^2 (x) - 1. With these two identities, it's easy to solve the problem.
  15. J

    Solving a Trigonometric Equation with Identities

    How to solve: sin x + sin 3x + sin 2x = 1 + cos 2x + cos x, give general solution in radians for x. How to get start? Anyone could help me, please?
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