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### FAQ

Is there a formula/algorithm to find out the radius of n circles needed to fill a circular area? (The radius of the circular area is provided)

I will assume that each of the small circles that have to touch two other small circles can be touching additional small circles. I presume what you mean by "needed to fill a circular area" is that the n small circles cannot be made any larger and still fit into the large circle, which is the same as stating that the large circle is as small as possible to contain the n small circles.Since the scales are arbitrary, make 1 be the radius of the small circles and make x be the radius of the large circle that encloses all of the small circles. Then, you want to know if there is a formula x(n) for n=3, 4, 5, ... in some closed form. (For n=2, you can't have a small circle touching two other small circles, but in any case that is a trivial solution.)This is known as a packing problem. Your specific example is Circle packing in a circle. I don't know that there is a closed form formula for x(n). Since the packing is optimal (not all of them have been proven to be optimal), it means that, for n circles, the large circle cannot be smaller than radius x.The more general cases are explained by the Wikipedia article Packing problems.

How does one get invited to the Quora Partner Program? What criteria do they use, or is it completely random?

I live in Germany. I got an invite to the Quora partner program the day I landed in USA for a business trip. So from what I understand, irrespective of the number of views on your answers, there is some additional eligibility criteria for you to even get an email invite.If you read the terms of service, point 1 states:Eligibility. You must be located in the United States to participate in this Program. If you are a Quora employee, you are eligible to participate and earn up to a maximum of $200 USD a month. You also agree to be bound by the Platform Terms (https://www.quora.com/about/tos) as a condition of participation.Again, if you check the FAQ section:How can other people I know .participate?The program is invite-only at this time, but we intend to open it up to more people as time goes on.So my guess is that Quora is currently targeting people based out of USA, who are active on Quora, may or may not be answering questions frequently ( I have not answered questions frequently in the past year or so) and have a certain number of consistent answer views.Edit 1: Thanks to @Anita Scotch, I got to know that the Quora partner program is now available for other countries too. Copying Anuta’s comment here:If you reside in one of the Countries, The Quora Partner Program is active in, you are eligible to participate in the program.” ( I read more will be added, at some point, but here are the countries, currently eligible at this writing,) U.S., Japan, Germany, Spain, France, United Kingdom, Italy and Australia.11/14/2018Edit 2 : Here is the latest list of countries with 3 new additions eligible for the Quora Partner program:U.S., Japan, Germany, Spain, France, United Kingdom, Italy, Canada, Australia, Indonesia, India and Brazil.Thanks to Monoswita Rez for informing me about this update.

How can I get more people to fill out my survey?

Make it compellingQuickly and clearly make these points:Who you are and why you are doing thisHow long it takesWhats in it for me -- why should someone help you by completing the surveyExample: "Please spend 3 minutes helping me make it easier to learn Mathematics. Answer 8 short questions for my eternal gratitude and (optional) credit on my research findings. Thank you SO MUCH for helping."Make it convenientKeep it shortShow up at the right place and time -- when people have the time and inclination to help. For example, when students are planning their schedules. Reward participationOffer gift cards, eBooks, study tips, or some other incentive for helping.Test and refineTest out different offers and even different question wording and ordering to learn which has the best response rate, then send more invitations to the offer with the highest response rate.Reward referralsIf offering a reward, increase it for referrals. Include a custom invite link that tracks referrals.

4 inlet pipes with circular cross-section take 9 hours to fill a cistern. How many pipes of half the radius are needed to fill it in 6 hours, if the speed of water is thrice the earlier speed?

Let radius = r speed = vno of pipes = 4total time = 9 hoursSo, total volume = (pie * r^2) * 9 * v * 4Now, new radius = r/2new speed= 3vtotal time = 6 hours n of pipes be xSo, (pie * r^2) * 9 * 4 = (pie * (r/2)^2) * 6 * 3v * xi.e x = 88 Pipes are required.

How would you write a program that fills in a two dimensional array in a circular fashion with the integers from 1 to N²?

Fill the matrix with 0.Then write a recursive routine to fill top row,right column,bottom row and left column with sequential numbers and then issue a recursive call with rest of the matrix with modified boundary indices. It will work for all sizes MxN( including a)M=1, b)N=1, c)M=N, d)both M,N equal to 1)./*sri-starting row index,sci-starting column index,eri-ending row index,eci-ending column index*/void spiral(int A[][20],int m,int n,int num,int sri,int sci,int eri,int eci){int i,j,if(num=m*n){ for(j=sci,j=eci&&A[sri][j]==0&&num=m*n,j++) A[sri][j]=num++, for(i=sri+1,i=eri&&A[i][eci]==0&&num=m*n,i++) A[i][eci]=num++, for(j=eci-1,j=sci&&A[eri][j]==0&&num=m*n,j--) A[eri][j]=num++, for(i=eri-1,i=sri-1&&A[i][sci]==0&&num=m*n,i--) A[i][sci]=num++, spiral(A,m,n,num,++sri,++sci,--eri,--eci),}}