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📰 Solution: Let $x$ be the integer. Then $x \equiv -1 \pmod{5}$ and $x \equiv -1 \pmod{7}$. This implies $x + 1$ is divisible by both 5 and 7, so $x + 1 = \text{LCM}(5, 7) = 35$. Thus, $x = 34$. $\boxed{34}$Question: A retired engineer designing a robotic arm observes that the sum of two gear rotation speeds $ a $ and $ b $ is 10, and the sum of their squares is 58. What is $ a^3 + b^3 $? 📰 Solution: We are given $ a + b = 10 $ and $ a^2 + b^2 = 58 $. We want to find $ a^3 + b^3 $. 📰 We already know $ a + b = 10 $, so compute $ (a + b)^3 = 10^3 = 1000 $. 📰 Dadish Behavior The Secret Sins Every Dad Hideswatch How He Exposed Them 8140720 📰 Dragonball Characters 462004 📰 Transform Your Space With Stunning Terrazzo Floors Heres Why You Need Them Today 1694791 📰 Sardines In Water 5717106 📰 Northern Dynasty Minerals Stock 7157955 📰 Verizon Elizabethtown Kentucky 7824030 📰 We Dug The Ultimate Summer Rick And Morty Secretsspoiler Youll Be Beside Yourself 4105383 📰 Wait Till You See Vidillosthis Viral Phenomenon Is Taking Over Social Media 8204226 📰 Account Is Temporarily Locked 455700 📰 Rules Of Engagement Cast 8278604 📰 Mr Shawarma 5606524 📰 The Nightingale Movie That Haunted Every Viewer Before It Was Even Released 8354625 📰 Sublime For Mac Download 8194902 📰 This Radar Detects What No One Wants To See And You Wont Believe Who It Hit 4116993 📰 Prank Calls That Got Me Detentionheres What Happened When I Answered 9831053