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@ -1,4 +0,0 @@
Given the formula $\sin(\alpha + \beta)$:
$$ \sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta) $$
Given the formula $\cos(\alpha + \beta)$:
$$ \cos(\alpha + \beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta) $$

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@ -1,4 +1,3 @@
An **identity** is an equation that is true for all values of the variable for which the expressions in the equation are defined.
# Trigonometric Identities
All of the following only apply when the denominator is not equal to zero.
@ -65,15 +64,3 @@ Getting rid of the exponent:
$$ \sqrt{\frac{576}{625}} = \frac{24}{25} = sin\theta $$
From there, you can find the rest of the identities fairly easily.
# Simplifying trig expressions using identities
Given the difference of square formula:
$$ a^2 - b^2 = (a-b)(a+b) $$
## Examples
Simplify $\tan\theta\sin\theta + \cos\theta$:
1. $\dfrac{\sin\theta}{\cos\theta} * \sin\theta + \cos\theta$
2. $\dfrac{\sin^2\theta}{cos\theta} + \cos\theta$
3. $(\dfrac{\sin^2\theta}{cos\theta} + \cos\theta)\dfrac{\cos\theta}{\cos\theta} = \sin^2\theta*\cos^2\theta + \cos\theta$
Si\

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- An overweight person has extra weight from bones, fat, muscle, body fat, and/or body wader
- Obesity is a condition characterized by excessive and unhealthy bodyfat
# Consequences
## Obesity
- Type II Diabetes (DM)
- **Hypertension**
- Cardiovascular disease
- **Obstructive sleep apnea**
- Osteoarthritis
- Infertility
- Certain cancers
- Gallbladder disease
- Respiratory problems
- Surgical complications
- Clinical depression
- Metabolic syndrome
- **Stroke**
# Underweight
- Fatigue / Anemia
- Nutrient deficiencies
- Lack of energy
- Poor concentration
- Unhealthy hair, skin, nails
- Osteoporosis
- Illness/infection
- Bone fractures
- Amenorrhea
- Infertility
- High risk pregnancy
- Clinical depression
- Low body temperature
# BMI
- A numerical value based on the ratio between a person's height and weight that is used to **classify a person's weight** and **measure risk for disease**
- Can be calculated using:
$$ \dfrac{Weight (kg)}{Height (m)^2} or \dfrac{Weight (lbs)}{Height (in)^2} * 703 $$
Conversions:
- Lbs -> Kg: Divide by 2.2
- Feet -> Inches: Multiply by 12
- Inches -> Meters: Multiply by 2.54 / 100
## Ranges
- Underweight: BMI < 18.5
- Healthy weight: BMI 18.5 - 24.9
- Overweight: BMI 25.0 - 29.9
- Obese: BMI >= Obses
- Obese Class I: BMI 30-34.9
- Obese Class II: BMI 35-39.9
- Obese Class III: BMI >=40
## Limitations
Not always accurate for:
- Highly muscular individuals
- Older adults
- Chronically ill individuals
- BMI does not take gender, age, race, or activity level into account
## NWO
- Normal weight obesity refers to a normal body weight as measured by BMI, but they actually have higher body fat
- Comes with an associated risk of insulin resistance
- Diabetes
- Coronary artery disease
# Body Composition and Fat Distribution
- Body composition is the relative and absolute measurement of body tissues, usually expressed as a percent body fat
- Adipose tissue refers to fat cells
- Total body fat refers to to adipose tissue and essential fat
- Essential fat is fat that is vital for survival; found in cell membranes, certain bones, and nervous tissue.
- **Subcutaneous** is fat accumulation of adipose tissue cells in the tissue under the skin.
- This layer helps to:
- *Insulate the body against cold temps*
- *Protect the body from bumps and bruises*
- **Visceral fat** is the accumulation of adipose cells under the abdominal muscles and over the digestive organs to protect them
- Types of obesity
- **Apple shaped (Central body)**: Central body obesity: Risk of heart diseases, stroke, diabetes, HTN, cancer
- **Gynoid (Pear shaped)**: Not associated w/ Chronic Disease Risk
## Assessment
- Hydrostatic weight (error of 2-3%)
- Air displacement plethysmography- BODPOD (error of 3-5%)
- Dual energy x-ray absorptiometry: DEXA (Error of 1-4%)
- **Bio-electrical impedance** (Error: 3-4%) Sends a shock through your body and measures how long it takes
- Skinfold calipers (Error 3-5%)
- **Waist circumference -> 35 inches for a women** or **>40 inches for a man** is associated with central adiposity and increased health risk, specifically CVD risk
## Health
- Losing as little as 5% of excess body fat
- Can increase HDL cholesterol levels
- Reduce high blood pressure
- Improve glucose tolerance
# Energy Exchange
## Energy In
- Carbs
- Lipids
- Proteins
- Alcohol
## Energy Out (Total Energy Expenditure )
- Basal metabolic rate
- The minimum number of kcals required to maintain normal body function after fasting and resting for 12 hours. **Accounts for ~60-75% of an individual's total energy use**
- Factors that increase BMR include thyroid hormone levels and postexercise recovery
- Factors that decrease BMR include starvation and aging.
- Physical activity
- Thermic effect of food
- Non-exercise activity

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@ -48,10 +48,6 @@ int arr_size = sizeof(arr) / sizeof(arr[0]);
```
# Pointers
`&` gives you the address of a variable
`*` gives you the value in memory that an address points to.
# Formatting specifiers
# Standard library

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- https://www.ankermake.com/blogs/guides/how-to-make-3d-prints-stronger
- https://blog.prusa3d.com/how-to-improve-your-3d-prints-with-annealing_31088/
- https://markforged.com/resources/blog/joinery-onyx
- https://bigrep.com/posts/gyroid-infill-3d-printing/
- https://www.hp.com/us-en/printers/3d-printers/learning-center/3d-printed-joint-design.html
TL;dr:
- Use gyroid infill with an infill density of between 50-80% for structural prints
- Use PLA with a very slow speed, low layer height, and minimal/no cooling
- Use dovetail joints of scale defined in the HP article
- Anneal the print at 110c for ~30 minutes depending on the size and shape of the object