I have a not so great teacher this term for my multivariable class and now I'm completely lost. We're supposed to be on arithmetic and geometric means but I have no idea how to do anything since my teacher makes us go to the board all the time to figure out things on the spot. We've been given a take home test for which we're allowed to get any and all the help we want. I'm terrified of failing because I only have a vague idea of how to solve these problems.

1. There are many quadrilaterals ABCD with AB=10, BC=8, CD=11, DA=15. Show that if ABCD is the quadrilateral with the greatest area, then the points A, B, C, and D are concyclic. What is its area?

2. Find the largest value of constant k so that x^3+1_>_kx (that's greater or equal to)

a) solve using calculus

b)solve not using calculus

3. Find the maximum value of 4xy^2(10-x-y) over positive numbers x and y.

a)solve using calculus

b)solve not using calculus

4. The region R shown to the right is bounded above by a circular arc of radius 5 centered at the origin and below by a horizontal line segment. FInd the minimum and maximum value of y/(1+x^2^+y^2) over R.

a) solve using calculus

b) solve not using calculus

I will be eternally grateful to whoever can help since my grade is on the line. Please ~bows~

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