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How To Fix Age of Wonders 4 Not Launching Error On PC | Fix Age of Wonders 4 Won't Launch Error https://lnkd.in/gDFUYZnB

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Hi. Sometimes simple things need simple solutions.

🔍 Exploring Extremum Points: A Math Adventure! I recently encountered an intriguing problem raised by Lee Chan Lye: https://lnkd.in/dZVShfmb Given x, y, z≥0, maximize the function f(x,y,z)= x^3*y + y^3*z + z^3*x subject to the constraint of x+y+z=3. Using partial derivatives, we found a minimum value of 3 (which is not too bad!). However, the maximum we obtained was less than the expected maximum value of 2187/256 which can be computed with x=9/4, y=3/4 and z=0. But here’s where it gets even more fascinating: when we initially set z=0 and simplify our expression to focus on f(x,y)= x^3*y while substituting y=3−x, we unearth that hidden treasure! 🎉 Using the technique of differentiation, we immediately arrive at the maximum value of 2187/256. This exploration reminds us that sometimes a different approach—like carefully choosing our variables—can lead to remarkable discoveries. 🍬 Math is not just about crunching numbers; it’s about delving into possibilities and enjoying the journey along the way. I would love to hear your thoughts and insights on this problem—what approaches or techniques do you find most effective in optimization? Happy calculating, everyone! #Mathematics #Optimization #Calculus #ProblemSolving #MathAdventure #Learning #Innovation #STEM

Easy and quick fix😜

(5,3), (2,6),(3,4) A different approach to solve this problem using inequality If a>b=> (1+1/a)(1+2/b)<(1+1/b)(1+2/b) =>2b^2<(b^2+3b+2) => b^2-3b-2<0 =>( 3-sqrt(13))/2 <b <(3+sqrt(13))/2 => 0<b<=3 (using b is positive integer) => b=1,2,3 Only for b=3 a=5, so one solution is (5,3) No a possible now if b>=a then replacing b with a in case a>b, we get possible value of a as 1,2 3 So only solution here is (2,6)(3,4)

Figure out what you can control and what you can't. Then decide if what you can't is ok with you.

Please subscribe to my channel! Thank you! 📌 Struggling with memory lapses and need a quick fix? Look no further! In this action-packed video, (Improve Your Memory FAST with the 80-20 Rule) we'll show you how to harness the power of the 80-20 rule (Pareto Principle) to elevate your memory game to new heights. Discover how this simple shift can transform your recall abilities instantly! #learning #learningjourney #learninghacks #memoryhacks #studyhacks #studytips #letsconnect #personaldevelopment https://lnkd.in/dhivQqV4

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