vault backup: 2024-09-30 15:18:49

IT/Hashicorp Nomad.md

@@ -0,0 +1,18 @@
+# Terminology
+## Cluster Terms
+
+| Phrase      | Definition                                                                                                                                                                                                     |
+| ----------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
+| agent       | A process running in server or client mode.                                                                                                                                                                    |
+| client/node | A Nomad client is responsible for running tasks assigned to it. A client registers itself with servers and watches for work to be assigned. When running the agent, the client may be referred to as a *node*. |
+| server      | A Nomad server manages all jobs and clients, monitors tasks, and controls which tasks get placed on which nodes.                                                                                               |
+| dev_agent   | The development agent is an agent configuration that provides useful defaults for running a single node cluster of nomad.                                                                                      |
+
+## Work terms
+| Phrase                    | Definition                                                                                                                                                                                                                                                                        |
+| ------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
+| task                      | The smallest unit of work in Nomad. Tasks are executed by task drivers like `docker` or `exec`, which allows Nomad to be flexible in the types of tasks it supports. Tasks specify their required task driver, configuration for the driver, constraints, and resources required. |
+| group                     | A series of tasks that run on the same Nomad client.                                                                                                                                                                                                                              |
+| job                       | The core unit of *control* for Nomad and defines the application and its configuration. It can contain one or many tasks                                                                                                                                                          |
+| job_specification/jobspec | A job specification, also known as a jobspec.                                                                                                                                                                                                                                     |
+| allocation                | An allocation is a mapping between a task group in a job and a client node. When a job is run, Nomad will chose a client capable of running it and allocates resources on the machine for the ask(s) in the task group defined for the job.                                       |

education/math/MATH1060 (trig)/Graphing.md

@@ -1,3 +1,5 @@
+
+# Sine/Cosine
 ![A graph of sine and cosine](./assets/graphsincos.png)
 
 Given the above graph:
@@ -13,8 +15,6 @@ Given the above graph:
 | $y = cos(2x)$    | Horizontal shrink by a factor of 2 |
 # Periodic Functions
 A function is considered periodic if it repeats itself at even intervals, where each interval is a complete cycle, referred to as a *period*.
-
-
 # Sinusoidal Functions
 A function that has the same shape as a sine or cosine wave is known as a sinusoidal function.
 
@@ -33,3 +33,55 @@ How to find the:
 
 
 $$ y = A * \sin(B(x-\frac{C}{B})) $$
+# Tangent
+$$ y = tan(x) $$
+![Graph of tangent](assets/graphtan.png)
+To find relative points to create the above graph, you can use the unit circle:
+
+If $tan(x) = \frac{sin(x)}{cos(x})$, then:
+
+| $sin(0) = 0$                              | $cos(0) = 1$                              | $tan(0) = \frac{cos(0)}{sin(0)} = \frac{0}{1} =0$                |
+| ----------------------------------------- | ----------------------------------------- | ---------------------------------------------------------------- |
+| $sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $tan(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2} = 1$ |
+| $sin(\frac{\pi}{2}) = 1$                  | $cos(\frac{\pi}{2}) = 0$                  | $tan(\frac{\pi}{2}) = \frac{1}{0} = DNF$                         |
+Interpreting the above table:
+- When $x = 0$, $y = 0$
+- When $x = \frac{\pi}{4}$, $y = 1$
+- When $x = \frac{\pi}{2}$, there's an asymptote
+
+Without any transformations applied, the period of $tan(x) = \pi$. Because $tan$ is an odd function, $tan(-x) = -tan(x)$. 
+# Cotangent
+$$ y = cot(x) $$
+![Graph of cotangent](assets/graphcot.svg)
+
+To find relative points to create the above graph, you can use the unit circle:
+
+If $cot(x) = \frac{cos(x)}{sin(x)}$, then:
+
+| $sin(0) = 0$                              | $cos(0) = 1$                              | $cot(0) = \frac{sin(0)}{cos(0)} = \frac{1}{0} = DNF$             |
+| ----------------------------------------- | ----------------------------------------- | ---------------------------------------------------------------- |
+| $sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $cot(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2} = 1$ |
+| $sin(\frac{\pi}{2}) = 1$                  | $cos(\frac{\pi}{2}) = 0$                  | $tan(\frac{\pi}{2}) = \frac{1}{0} = DNF$                         |
+
+Without any transformations applied, the period of $cot(x) = \pi$. Because $cot$ is an odd function, $cot(-x) = -cot(x)$. 
+
+# Features of Tangent and Cotangent
+Given the form $y = A\tan(Bx - C) + D$ (the same applies for $\cot$)
+- The stretching factor is $|A|$
+- The period is $\frac{\pi}{|B|}$
+- The domain of $tan$ is all of $x$, where $x \ne \frac{C}{B} + \frac{\pi}{2} + {\pi}{|B|}k$, where $k$ is an integer. (everywhere but the asymptotes)
+- The domain of $cot$ is all of $x$, where $x \ne \frac{C}{B} + \frac{\pi}{|B|}k$, where $k$ is an integer (everywhere but the asymptotes)
+- The range of both is $(-\infty, \infty)$
+- The phase shift is $\frac{C}{B}$
+- The vertical shift is $D$
+# Examples
+> Given $-2\tan(\pi*x + \pi) - 1$
+
+ $A = -2$, $B = \pi$, $C = -\pi$, $D = -1$
+  
+| Transformation | Equation                  |
+| -------------- | ------------------------- |
+| Stretch        | $\|-2\| = 2$              |
+| Period         | $\frac{\pi}{\|\pi\|} = 1$ |
+| Phase shift    | $\frac{-\pi}{\pi} = -1$   |
+| Vertical shift | $-1$                      |

education/software development/ECE1400/C.md

@@ -32,6 +32,9 @@ C99 adds a `long long` int
 ## Floats
 A float is a decimal value. Slower arithmetic and inexact values are both drawbacks of using floats.
 
+## Characters
+In C, a `char` denotes a single byte of arbitrary encoding. 
+
 ## Variables
 A variable must be declared before it is assigned.