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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} $. 📰 This Mountaineer Pharmacy Could Be Your Key To Surviving Any Extremesheres Whats Inside 9260071 📰 Social Security Email Big Beautiful Bill 7512909 📰 30 Year Old Woman 6195565 📰 Amante 7233378 📰 Uncover What Utahjaz Got Everyone Missing Before It Shocked Travelers 792982 📰 This Hidden Ysl Candy Glaze Is Taking Over Glossy Food Trendsyou Need It 535458 📰 Zad 3847943 📰 Final Rust Transformation Tool Proves Power You Never Imagined 1996744 📰 Wake Up Hidden Dragon Scales Found In Ancient Ruinsyou Wont Believe What Follows 1782535 📰 Stuller Redefined The Secret They Never Said 5788721 📰 How To Open A Custodial Account 3437544 📰 Notre Dame Campus 9031168 📰 How A Single Game Became The Most Sold Video Game Evermillions Still Buy It Monthly 4452340 📰 The Shocking Truth About Hog Jowl That Will Make You Craving More Instantly 7766752 📰 Los Cazadores 2195525