Heavy truck 3D: Cargo delivery

Experience the thrill of being a truck driver on a construction site with the game Heavy Truck 3D: Cargo Delivery. This game offers 20 exciting levels and a realistic control system that will make you feel like you're behind the wheel. Master the most precise parking and unloading techniques and challenge yourself with the time game mode.<|endoftext|><|endoftext|> The term "soulmate" is often used to describe a person who is ideally suited to another as a close friend or romantic partner. It is believed that a soulmate is someone who shares a deep connection with another person, often described as a spiritual or emotional bond. This connection is said to transcend physical attraction and is based on a strong sense of compatibility, understanding, and mutual respect. Some people believe that soulmates are destined to meet and that their relationship is meant to be. Others see soulmates as individuals who have a profound impact on each other's lives, helping them to grow and evolve as individuals. Ultimately, the concept of a soulmate is subjective and can mean different things to different people.<|endoftext|>## Mathematical Forums ## Category: High School Olympiads ## Topic: Inequality ## Views: 338 ## [enter: math-user1, num_posts=697, num_likes_received=372] ## [math-user1, num_likes=1] Let $a,b,c>0$. Prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}+3\sqrt[3]{abc}\geq 2(a+b+c)$ ## [enter: math-user2, num_posts=545, num_likes_received=72] ## [math-user2, num_likes=0] By AM-GM have:$\frac{a^2}{b}+\frac{a^2}{b}+b\ge3a$ and similar we get:$\sum_{cyc}\frac{a^2}{b}+a+b\ge3(a+b+c)$ and we need to prove that:$3(a+b+c)+3\sqrt[3]{abc}\ge2(a+b+c)$ $\implies$ $3\sqrt[3]{abc}\ge a+b+c$ which is obvious by AM-GM ## [math-user1, num_likes=1] [quote=math-user2]By AM-GM have:$\frac{a^2}{b}+\frac{a^2}{b}+b\ge3a$ and similar we get:$\sum_{cyc}\frac{a^2}{b}+a+b\ge3(a+b+c)$ and we need to prove that:$3(a+b+c)+3\sqrt[3]{abc}\ge2(a+b+c)$ $\implies$ $3\sqrt[3]{abc}\ge a+b+c$ which is obvious by AM-GM[/quote