Recent content by Johnny Leong

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.

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.

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

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

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.

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?

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.

Please give me some hints: 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.

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...

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...

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 -...

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)...

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.

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?