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📰 Solution: The perimeter of a rectangle is given by $ P = 2(l + w) $, where $ l $ is length and $ w $ is width. Given $ 2(l + w) = 80 $, we simplify to $ l + w = 40 $. The area $ A = lw $. Express $ w = 40 - l $, so $ A = l(40 - l) = 40l - l^2 $. This quadratic equation opens downward, and its maximum occurs at the vertex $ l = \frac{-b}{2a} = \frac{-40}{-2} = 20 $. Substituting $ l = 20 $, $ w = 20 $, so $ A = 20 \times 20 = 400 $. The maximum area is $\boxed{400}$. 📰 Question: An entomologist studying pollination patterns models the number of flowers visited by bees as $ f(t) = -5t^2 + 30t + 100 $. What is the maximum number of flowers the bees visit in a day? 📰 Solution: The function $ f(t) = -5t^2 + 30t + 100 $ is a quadratic opening downward. The vertex occurs at $ t = \frac{-b}{2a} = \frac{-30}{2(-5)} = 3 $. Substituting $ t = 3 $, $ f(3) = -5(9) + 30(3) + 100 = -45 + 90 + 100 = 145 $. The maximum number of flowers visited is $\boxed{145}$. 📰 The Shocking Truth Behind Eic Stock Is It The Next Big Breakout 8037922 📰 Troutdale Verizon Store 8031868 📰 Fxaix Expense Ratio 4176239 📰 Chuck Chuck E Cheese Coupons The Secret Shoppers Want Them Now 6488061 📰 1000 Made Easy Learn How To Invest In Etfs Fast Profitably 5620696 📰 Watch Your Taste Buds Explode The Latest Kamikaze Drink Is Changing Everything 8146163 📰 Stop Corrupt Files In Their Tracks The Ultimate Net Framework Cleanup Utility Tool Revealed 1051707 📰 Good Tv Providers 5534289 📰 Yogi Berra Museum 3364635 📰 Can This Atrium Mychart Tool Change How You Experience Your Healthcare 1148704 📰 Best Mattress Protector 5229218 📰 June Journey 1260099 📰 Cross The Internet How One Builder Built A Megab 927621 📰 Step Into Ultimate Pleasure The Science Behind The Orgasmatrix Breakthrough 9317564 📰 Midnight In Paris 2180879