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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} $. 📰 Transform Your Look Fast With This Perfect Black Denim Skirt Hack 8398352 📰 City North Apartments 2748187 📰 Finally Got It Done How To Change Time Zone In Outlook Like A Pro 8772736 📰 Perch Sonoinello Cost I Colori Nascosti Che Definiscono La Bellezza 1547837 📰 Delta Force Pc 2624399 📰 Wells Fargo Bank Knoxville Tn Locations 1190704 📰 Red Lobster Stock Shock This Hidden Culinary Secret Is Taking The Sea Restaurant World By Storm 9462810 📰 Command Strike Fps The Ultimate Kill Engage Youll Want To Master Instantly 4604687 📰 Your Outlook Signature Just Got 10X More Professionalheres How To Customize It Instantly 8765074 📰 Batman In New Movie 3291777 📰 Salma Hayek Age 7953465 📰 Youre Missing Out Snnc Stock Price Rises Over 30 In Just One Week 4631548 📰 Afcconne Shocked Everyone The Secret Turkey Route Youve Been Missing 5873772 📰 Bank Of American Visa 4184436 📰 Golden State Warriors Depth Chart 5298127