Putter King Adventure Golf

Putter King Adventure Golf is a top-rated 3D golf game. It features high-quality graphics and impressive sound. The courses are located all around the world. You can also share your results with friends on Facebook and Twitter. Choose from a variety of entertaining animated characters, each with their own unique abilities. Your goal is to navigate the ball through various obstacles and into the hole. The game offers 24 distinct themed holes, as well as 3 user-created holes and 4 game modes (championship, timed, multiplayer, and training).<|endoftext|><|endoftext|> # 2015 AMC 10B Problems/Problem 1. ## Contents. 1 Problem 2 Solution 3 Video Solution 4 See Also ## Problem. What is the value of $2+4+6+8+10+12+14+16+18+20$? $\textbf{(A)}\ 90\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 110\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 130$ ## Solution. We can pair the numbers up as follows: $(2+20)+(4+18)+(6+16)+(8+14)+(10+12)$. Each pair adds up to $22$, and there are $5$ pairs, so the sum is $22 \cdot 5 = \boxed{\textbf{(B)}\ 100}$. ## Video Solution. https://youtu.be/8WrdYLw9_ns ~savannahsolver <|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:$\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c$ and by AM-GM again:$3\sqrt[3]{abc}\ge3\frac{3abc}{a+b+c}$ so we should prove that:$\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}