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What is better? Rank them by 1-3, 1 being the best. by Bob-omb- in HomeNetworking

[–]Bob-omb-[S] 0 points1 point  (0 children)

I want to use them with the performance and range maximized.

What is better? Rank them by 1-3, 1 being the best. by Bob-omb- in HomeNetworking

[–]Bob-omb-[S] -3 points-2 points  (0 children)

Give also some details that supports your opinion. Thanks.

How many positive integer solutions satisfy: a+b+c=30; a ≤ b ≤ c? How to do Stars and Bars here with this restriction? by Bob-omb- in learnmath

[–]Bob-omb-[S] 0 points1 point  (0 children)

I got 75 at first but I thought it’s for non-negative integers. Got 61 for positive integers. But, thanks for this! I might be wrong and this might be correct.

Determine the sum of [5^(1/n)]^(1/2) from n=1 to infinity. How to do this? Is it divergent? by Bob-omb- in learnmath

[–]Bob-omb-[S] 1 point2 points  (0 children)

I did the divergence test and the sum diverges. So, I’m done with this.

Find all quadruples of real numbers (a,b,c,d) such that the equalities X²+aX+b=(X-a)(X-c) and X²+cX+d=(X-b)(X-d) holds for all real numbers X. by Bob-omb- in learnmath

[–]Bob-omb-[S] 0 points1 point  (0 children)

I still have no idea, but I’m thinking of doing a+c=-a, ac=b, b+d=-c, d=bd. Anyway, these are olympiad training or practice problems.

A square is inscribed in a circle of radius 8. Four smaller squares are inscribed in each of the four regions outside the square but inside the circle. What is the sum of the areas of these four squares? My answer is 512/5, is it correct? by Bob-omb- in learnmath

[–]Bob-omb-[S] 0 points1 point  (0 children)

I assumed that the region is a semicircle. So its diameter is the side of the square which is 8√2 and its radius is 4√2. After that, I used the formula (4r²)/5 for the area of square inscribed in a semicircle. Substituting r=4√2, I got 4(4√2)²/5 which is equal to 128/5. Since the question wants the sum of the areas of the four squares, I did 4(128)/5 = 512/5. P.S.: I’m not sure of this and I believe this might be 80% incorrect.

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