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

@@ -1,8 +1,57 @@
-A vector is a mathematical concept that denotes direction and magnitude. They're often notated using an arrow ($\overrightarrow{v}$), or with a bold, lowercase letter. (**v**).
+A vector is a mathematical concept that denotes direction and magnitude. They're often notated using an arrow ($\vec{v}$), or with a bold, lowercase letter. (**v**).
 
 
-$$\begin{bmatrix}
+Vectors are often denoted as a matrix with two rows: $\begin{bmatrix}1 \\2\end{bmatrix}$
-1 \\
+# Component Form
-2
+If $\vec{v}$ is a vector with the initial point $(x_y,\ y_i)$, and a terminal point $(x_t,\ y_t)$, we can express $\vec{v}$ in component form as $\vec{v} = \langle x_t - x_i,\ y_t, -y_i \rangle$ 
-\end{bmatrix}
+# Magnitude
-$$
+The magnitude of a vector is $|\vec{v}| = \sqrt{a^2 + b^2}$
+
+# Direction
+The direction of a vector is $\theta = \tan^-1(\frac{b}{a})$.
+
+# Addition
+To find $\vec{u} + \vec{v}$, we can put one vector on the end of another vector. The resulting vector will share the same tail as the first vector, and the same head as the second vector.
+
+# Scalar Multiplication
+A **scalar** is just a real number. Scalar multiplication is multiplying a vector with a real number. This will scale or shrink a vector, but does not change the direction it points at.
+
+We do not multiply two vectors together.
+# Unit Vector
+A vector with a magnitude of 1 is a **unit vector**.
+
+If $\vec{v}$ is a nonzero vector, the unit vector can be found using the equation $\vec{u} = \dfrac{1}{|\vec{v}|}\vec{v}$ . In other words, to find a unit vector, divide the vector by its magnitude.
+
+# $i$, $j$ Notation
+Every 2d vector has a horizontal component and a vertical component. The horizontal unit vector could be written as $i = \langle 1, 0 \rangle$, and the vertical unit vector could be written as $j = \langle 0, 1 \rangle$ Every vector can be made up using a combination of these standard unit vectors.
+
+# Trigonometric Form
+Given a vector $\vec{v}$ with a magnitude $|\vec{v}|$ and direction $\theta$:
+
+The component form is given as:
+
+$$ \vec{v} = \langle \cos \theta,\ |\vec{v}|\sin\theta \rangle $$
+
+# Standard position
+- A vector is in standard position if the initial point is at $(0, 0)$.
+
+# The Dot Product
+The dot product of two vectors $\vec{u} = \langle a, b \rangle$ and $\vec{v} = \langle c, d \rangle$ is $\vec{u} * \vec{v} = ac + bd$.
+
+- Given that $\vec{u} = \langle -7, 3 \rangle$, and $\vec{v} = \langle -3, 4 \rangle$, find $\vec{u} * \vec{v}$.
+- $\vec{u} * \vec{v} = -7 * -4 + 3 * 4$
+
+The dot product can be used to find the angle between two vectors.
+
+If $\theta (0\degree < \theta < 180\degree)$, is the angle between two nonzero vectors $\vec{u}$ and $\vec{v}$, then
+$$ \cos\theta = \dfrac{\vec{u}*\vec{v}}{|\vec{u}||\vec{v}|} $$
+
+# Work
+The dot product can be used to compute the work required to move an object a certain distance.
+
+To compute work, you need a force and direction. If the force is applied in the same direction:
+
+$$ W = Fd $$
+
+The work $W$ is done by a constant force $\vec{F}$ in moving an object from a point $P$ to a point $Q$ is defined by:
+$$ W = \vec{F} \cdot\vec{PQ} = |\vec{F}||\vec{PQ}|\cos\theta $$Where $\theta$ is the angle between $\vec{F}$ and $\vec{PQ}$.

education/nutrition/Review.md

@@ -0,0 +1,116 @@
+# Macronutrients
+- We need a larger amount
+- Provides Calories
+## Carbohydrates
+- Provides 4 calories per gram
+- The storage form of carbohydrates in the body is as glycogen (very branched sugar). Stored in muscles and in liver
+- Only **monosaccharides** can be directly absorbed. Everything else must be broken down first.
+### Simple
+- Mono/Disaccharides
+Monosaccharides include:
+- Glucose
+- Fructose (fruit sugar)
+- Galactose
+Disaccharides include:
+- Sucrose (glucose + fructose)
+- Maltose (glucose + glucose)
+- Lactose (glucose + galactose)
+### Complex
+- Polysaccharides
+Polysaccharides include:
+- Starches
+	- Amalose
+	- Amalopectin (More branched)
+- Fiber
+	- Photosynthesis +Sun + carbon + hydrogen + oxygen
+
+## Protein
+- Provides 4 calories per gram
+- Protein is composed of amino acids
+- There are **9 essential** amino acids
+- There are **11 non-essential** amino acids
+	- Donkey bridge: If it starts with the letter A, it's a non-essential amino acid
+- Protein has nitrogen alongside hydrogen, carbon, and 
+- To use protein as energy, it must be **deanimated**.
+## Lipids/Fats
+- Provides 9 calories per gram
+- Fat is composed of hydrocarbon chains
+- Tryglicerine - 3 fatty acid chains, with glycerol backbone
+### Saturated Fats
+- Saturated fats have no double bonds
+### Unsaturated Fats
+- Unsaturated fats have one or more double bond
+
+### HDL (High Density Lipoprotein)
+- We want high HDL levels
+- Takes cholesterol out of the cells to the liver to be excreted
+### LDL (Low Density Lipoprotein)
+- We want low LDL levels
+- Takes cholesterol into arteries
+### oLDL (Oxidized Low Density Lipoprotein)
+- Damaged LDL
+- Deposits plaque
+# Micronutrients
+- Smaller Amounts
+- Don't provide calories
+## Vitamins
+## Minerals
+
+## Water
+- Not a macro or micronutrient, but still one of the 6 major nutrition groups
+## Alcohol
+- While not in a food group, provides 7 calories per gram
+
+# Digestive System
+1. Mouth
+	- Digestion of carbs/starches, and fats begin here.
+	- Mechanical digestion (chewing)
+	- Chemical digestion (amalayses (starch) and lipases (fat) in the mouth)
+2. Esophagus
+	- Peristalsis is an involuntary relaxation and contraction of muscles to move food down 
+1. Gastroesophageal/Lower Esophageal/Cardiac Sphincter
+	- When this sphincter misfires, it can cause heartburn or gastroesphageal reflex disease (GERD)
+2. Stomach
+	- Protein 
+3.  Pyloric Sphincter
+4. Small Intestine (DJI)
+	1. Duodenum
+	2. Jejunum
+	3. Ilium
+5. Ilieocecal Valve
+
+# DRI (Dietary Reference Intakes)
+## EAR (Estimated Average Requirement)
+- Meet the requirements of 50% of healthy individuals
+## RDA (Recommended Daily Allowance)
+- 97.5% of healthy people
+- EAR plus a margin of safety
+## AI (Adequate Intake)
+- The average amount of nutrients a healthy population needs to consume
+## UL (Upper Limit)
+- Prevents overconsumption
+## AMDR (Acceptable Macronutrient Distribution Range)
+- Carbs: 45-65% / kCal
+- Protein: 10-35% / kCal
+- Fats: 20-35% / kCal
+## EER (Estimated Energy Requirements)
+- Average estimated caloric needs
+- Actual needs vary
+
+# Hormones
+## Insulin
+Insulin is made by the beta cells in the pancreas, and promotes absorption of glucose from the blood into liver, fat, and skeletal muscles.
+- Insulin is released when blood sugar levels are too high
+## Glucagon
+Glucagon is a peptide hormone, produced by the alpha cells of the pancreas. It's the opposite of insulin, and it increases blood sugar levels. 
+- Glucagon is released when blood sugar levels are too low
+## Ghrelin
+Ghrellin is known as the "hunger hormone", and it increases the drive to eat. It increases gastric motility and stimulates the secretion of gastric acid.
+## Leptin
+Leptin's primary role is to regulate long-term energy balance. High leptin levels indicate to the brain that energy reserves are high.
+
+# Study Types
+## Exprimental
+- A systematic way of testing a hypothesis
+## Epidemiological
+- Observations of the occurrence, distribution, and associations