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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} $. 📰 What Time Do The Stock Markets Close Today 📰 Nyse Trp Inside The Secret Ring Thats Blowing Trillionsshocking Details Inside 4883955 📰 Best Marketing Campaigns 2024 Innovative 📰 Anker Headphones 9434080 📰 Experts Confirm Nasdaq Vuzi And The Outcome Surprises 📰 Total Beginners Heres How To Save Files To Onedrive Like A Pro 8297123 📰 Eau De Toilette Vs Perfume 📰 The Pulse Point Secrets Professionals Use To Transform Your Health 4404804 📰 Sw Airlines Stock 📰 Wells Fargo Dubuque 📰 Mdc Connect 1007026 📰 Xle Option Chain Secrets Exposed Access Massive Profits Before Its Too Late 9082509 📰 Roblox Studio Mcp 📰 Verizon Wireless Visalia Ca 📰 How Long Is Summerslam 4886342