Always a good review of all functions
... Watch the video on finding the Read example 2 GCF at kahn Copy the picture showing relative maximum, minimum and x intercepts at the top of pg 315 into your Know it all Books. Review example 4-6 on page 315-316, write down the equivalent statements in the Key concepts box at the bottom of page 316 i ...
... Watch the video on finding the Read example 2 GCF at kahn Copy the picture showing relative maximum, minimum and x intercepts at the top of pg 315 into your Know it all Books. Review example 4-6 on page 315-316, write down the equivalent statements in the Key concepts box at the bottom of page 316 i ...
Proof of a conjecture: Sum of two square integers can
... Now, if c1c2 & c2c3 both satisfy c then equating k we get: Against c1c2, (bα1 ± aβ) = β & (aα1 ± bβ) = β & ignoring (+) sign we have bα1 = β(a + 1) …….. (A) or aα1 = β(b + 1) ……..(B) Similarly, against c2c3 we have bα3 = β(a + 1) ……… (C) or aα3 = β(b + 1) ……… (D) If (A) & (C) or (B) & (D) are true t ...
... Now, if c1c2 & c2c3 both satisfy c then equating k we get: Against c1c2, (bα1 ± aβ) = β & (aα1 ± bβ) = β & ignoring (+) sign we have bα1 = β(a + 1) …….. (A) or aα1 = β(b + 1) ……..(B) Similarly, against c2c3 we have bα3 = β(a + 1) ……… (C) or aα3 = β(b + 1) ……… (D) If (A) & (C) or (B) & (D) are true t ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.