Suppose that n ≥ 2 bidders are submitting bids to win an item that is worth 100 to each of them. a bid is any number from [0,100]. the highest bid wins the item. if m bidders submit the highest bid then they share the item, so each receives a benefit of 100/m. all bidders—not just the highest bidders—pay a price equal to their bid. letting bi denote bidder i’s bid, bidder i’s payoff then equals (100/m) - bi when i submitted the highest bid and a total of m bidders submitted the highest bid, and equals -bi if i’s bid was not the highest. find all nash equilibria.

4 + 5 7/9= 9 7/9

step-by-step explanation:

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

2/3

step-by-step explanation:

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.