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📰 Solution: We start with the given equations $ a + b = 10 $ and $ a^2 + b^2 = 58 $. First, we compute $ ab $ using the identity $ (a + b)^2 = a^2 + 2ab + b^2 $. Substituting, $ 100 = 58 + 2ab $, so $ ab = 21 $. Next, we use the identity for $ a^3 + b^3 $: $ a^3 + b^3 = (a + b)^3 - 3ab(a + b) $. Plugging in the values: $ a^3 + b^3 = 10^3 - 3 \times 21 \times 10 = 1000 - 630 = 370 $. Thus, the total water efficiency cubed is $ \boxed{370} $. 📰 Question: An organic chemist synthesizes a compound with molecular formula $ C_nH_{2n} $, where the ratio of carbon to hydrogen atoms satisfies $ \frac{a}{b} = 3 $ and their sum is $ a + b = 16 $. Find the value of $ a^2 - b^2 $. 📰 Solution: Given $ \frac{a}{b} = 3 $, let $ a = 3b $. Substituting into $ a + b = 16 $: $ 3b + b = 16 $, so $ b = 4 $ and $ a = 12 $. Now, $ a^2 - b^2 $ factors as $ (a - b)(a + b) = (12 - 4)(16) = 8 \times 16 = 128 $. Therefore, the value is $ \boxed{128} $. 📰 Passagem Aerea 6583474 📰 Dont Miss Outjoinbrands Is Changing The Game See How Easily You Can Participate 7426146 📰 Kendrick Smile 2870794 📰 Dojo 2856686 📰 The Shocking Truth About The Best Barcode Font For Exceldownload Now 8226888 📰 5 Mastering Pivot Tables Just Got Easier The Calculated Field That Experts Swear By 9097854 📰 You Wont Believe How To Unblock Papas Freezeria In Secondsno Account Required 3068201 📰 Hungary National Football Team Vs Portugal National Football Team Stats 2712148 📰 Herb Alpert Herb Alpert 5401889 📰 Yayas Exposed The Madness Behind Her Risewho Saw This Coming 5954284 📰 Shocking Breakdown How Fast Does Hipaa Handle Your Records Request 3149691 📰 This Mario Hat Secret Will Make You Snort Literallyand Youll Lose Your Mind 3956004 📰 This Prudential Stock Breakout Is Musks Secret To Massive Gainsdont Miss Out 9506278 📰 Best Breakfast San Francisco 4589222 📰 S Pneumoniae Pneumonia 1645947