What I Learned Today 12/1/14

I hope you had a HAPPY THANKSGIVING! Gobble Gobble!! Here I am with my mom and step-dad eating lots of yummy food, then Grampa Ernie being silly, then Grama Hilma being silly with fake teeth! I got to spend my whole Thanksgivibg break with them!

Minecraft Homeschool: Ancient Civilization

For the MCHS team build we were supposed to put in defense to protect the castle. I put a hall full of traps to prevent the enemy from going through the front gate. Because the front gate is the most easily passed through by any enemies, I used redstone to create traps. (the redstone is in the three pictures titled redstone) in the hall; the first trap was an arrow slit that shoots arrows. (at the first bit of redstone on the redstone pictures, the redstone pointing into the hall.) There are two grey things pointing at each other, and they are called hoppers. I have set a piece of cobblestone in the hoppers and then, whenever the hopper that has the comparator (the red and white thing) in front of it, it turns on powering redstone that goes to the dispenser, and the dispenser shoots an arrow. The next trap has two pathways and a lava pit. There are two pressure plates before the pathways. Those power a block with a redstone torch on it, turning it off and that retracts the pistons, dumping the enemy into the lava pit. If the enemy passes through that, I have a murder hole. (a murder hole is a hole in the front gate where they drop burning charcoals, lava, or steaming water.) The line of pressure plates powers redstone that turns off one redstone torch, turning on the other that powers a dispenser that releases lava from the ceiling. I have never survived through it myself or anyone willing to try to get through, so I think that anyone who tries to get through the gate is a goner.

Pre-Algebra:

There are three sections I'm learning, but here is just the first one. I get two weeks to do these instead of my usual one. The first section desks with the LEAST COMMON MULTIPLE:

Important: Let n be a positive integer. The prime factorization of any multiple of n includes the prime factorization of n. this is, every prime in the prime factorization of n is the prime factorization of every multiple of n, and is raised to at least as great a power in the multiple as it is in n.

Important: to find the prime factorization of the least common multiple of a group of numbers, we first find the prime factorization of each number. The prime factorization of the least common multiple is the product of the highest power of each prime factor that appears in the prime factorizations of the numbers.

Important: let a and b be positive integers. Every multiple of lcm[a, b] is a common multiple of a and b, and every common multiple of a and b is a multiple of lcm[a, b].

Important: for any positive integers a, b, and n, we have

Lcm[na, nb] = n lcm[a, b]