x̄ - > Calculus | Integration

Integration: The Cornerstone Of Calculus

Integration is a branch of mathematics that deals with the finding and properties of integrals. It is the process of finding a function that gives the quantity being measured, such as the area of a region or the volume of a solid. The study of integration is essential to the study of calculus and all its applications. 

In this article, we will discuss the basics of integration, including what it is, the different types of integrals, and how to calculate them. We will also discuss some of the properties of integrals and how to apply them in solving problems.

Integration is essentially the reverse process of differentiation, which deals with finding the rate of change of a function. When we integrate a function, we are finding the area under the curve of the function. Integration can be used to calculate a variety of quantities in different fields such as physics, engineering, economics, and statistics. There are two main types of integrals: definite integrals and indefinite integrals. A definite integral has both limits of integration, or bounds, which indicate the start and end points of the integration. This type of integral gives a specific numerical value. An indefinite integral, on the other hand, does not have any limits of integration and instead gives a family of possible solutions. To calculate an integral, we use a technique called integration methods. There are various methods such as substitution, integration by parts, partial fractions, and trigonometric substitution. These techniques can become quite complex when dealing with more advanced problems and functions, but with practice, they can become more manageable. Some of the properties of integrals include linearity, additivity, and the power rule. Linearity means that the integral of a sum of functions is equal to the sum of the integrals of each function. Additivity means that we can split an integral into multiple integrals if the function is defined piecewise. The power rule states that the integral of a power function is equal to the power function divided by the exponent plus one. In conclusion, integration is a fundamental concept in calculus that deals with finding integrals, which represent the area under the curve of a function. There are various methods to calculate integrals, and they can be applied in many fields to calculate important quantities. Understanding the properties of integrals and how to use them can help in solving more complex problems.

1. What is integration? 

2. The integrand 

3. The limits of integration 

4. The indefinite integral 

5. The definite integral 

6. Integration by substitution 

7. Properties of definite integrals 

8. Improper integrals

1. Calculus is the branch of mathematics that deals with the limit, continuity, derivatives, and integrals of functions. 

2. Integration is a technique used to find the area under a curve. In other words, it is the process of finding a function that represents the accumulation of another function over a period of time. 

3. The integrand is the function that is being integrated. 

4. The limits of integration are the lower and upper bounds of the area that is being calculated. 

5. The indefinite integral is the result of the integration of a function without any specific bounds. 

6. The definite integral is the result of the integration of a function with specific bounds. 

7. Integration by substitution is a technique used to simplify the process of integration. 

8. Properties of definite integrals include the fact that they are always positive and that they can be used to calculate the area under a curve. 

9. Improper integrals are integrals that do not have finite limits.

Integration

integrate sin x dx from x=0 to pi

integral_0^π sin(x) dx = 2

left sum | (π cot(π/(2 n)))/n = 2 - π^2/(6 n^2) + O((1/n)^4)

(assuming subintervals of equal length)

integral sin(x) dx = -cos(x) + constant

integrate x sin(x) dx from x=0 to pi

left sum | (π^2 cot(π/(2 n)))/(2 n) = π - π^3/(12 n^2) + O((1/n)^4)

(assuming subintervals of equal length)

integral x sin(x) dx = sin(x) - x cos(x) + constant

x̄ - > damped harmonic oscillator (physical system) | particle in a box in 1D (physical system)

damped harmonic oscillator (physical system) | particle in a box in 1D (physical system)

### 1. Damped Harmonic Oscillator

This is a system where an object oscillates (like a mass on a spring), but its motion gets smaller over time due to a damping force (e.g., friction or air resistance).

#### Simple Explanation

Imagine a weight on a spring bouncing up and down. Without damping, it would keep bouncing forever at a steady rhythm (natural frequency, ω₀). With damping (controlled by ζ), it slows down and eventually stops. The damping ratio ζ decides how fast it stops:

- ζ < 1: Underdamped (oscillates but fades out).

- ζ = 1: Critically damped (stops as fast as possible without oscillating).

- ζ > 1: Overdamped (slowly returns to rest, no oscillation).

#### Key Features

- Degrees of Freedom: 1 (motion only happens along one direction, say x).

- Lagrangian (L): A mathematical function that describes the system’s energy. Here, it includes kinetic energy (½ m x'(t)²) minus potential energy (½ m ω₀² x(t)²), adjusted by a damping factor exp(2 ζ ω₀ t).

- Equation of Motion: x''(t) + 2 ζ ω₀ x'(t) + ω₀² x(t) = 0  

  This is a second-order differential equation. It says: acceleration (x''), damping (x'), and spring force (x) balance out.

- Solution:  

  x(t) = e^(-ζ ω₀ t) [terms with sinh and cosh], where α = ω₀ √(ζ² - 1).  

  The e^(-ζ ω₀ t) part makes the motion decay, and sinh/cosh describe the shape of the oscillation (or lack thereof).

- Hamiltonian (ℋ): Represents total energy, with momentum p(t) and position x(t), adjusted for damping.

- Hamiltonian Equations:  

  - x'(t) = exp(-2 ζ ω₀ t) p(t)/m (velocity from momentum).  

  - p'(t) = -exp(2 ζ ω₀ t) m ω₀² x(t) (force changes momentum).  

- **Period**: T = 2π / (ω₀ √(1 - ζ²)), but only for ζ < 1 (underdamped case where it oscillates).

#### Physical Quantities

- m: Mass of the object.

- ω₀: Natural frequency (how fast it oscillates without damping).

- ζ: Damping ratio (how strong the damping is).

---

### 2. Particle in a 1D Box

This is a quantum system where a particle is trapped between two walls (at x = 0 and x = l) and can’t escape.

#### Simple Explanation

Think of a tiny particle bouncing between two walls, like a ping-pong ball in a narrow tube. It can only move left or right (1D), and its energy comes in specific “steps” (quantized). Unlike the oscillator, there’s no spring or damping—just hard boundaries.

#### Key Features

- Degrees of Freedom: 1 (motion only along the x-axis).

- Solution:  

  x(t) = TriangleWave[{0, l}, (t x'(0) + x(0))/(2 l) - 1/4] for 0 ≤ x(0) ≤ l.  

  This describes a particle moving back and forth linearly between 0 and l, like a wave with sharp turns at the walls. (Note: This is a classical approximation; quantum mechanics uses standing waves like sin(nπx/l).)

- No Damping: Unlike the oscillator, there’s no friction or energy loss here.

- No Lagrangian or Hamiltonian Given: Typically, for a free particle in a box, the Lagrangian is just kinetic energy (½ m x'(t)²), and the Hamiltonian is p²/(2m), but boundaries enforce quantization in quantum mechanics.

#### Physical Quantities

- m: Mass of the particle.

- l: Length of the box (distance between walls).

---

### Comparison

- Damped Harmonic Oscillator: Oscillates with a spring-like force, loses energy due to damping, and motion decays over time.

- Particle in a 1D Box: Moves freely between walls, no forces inside the box, just bounces back and forth (classically) or forms standing waves (quantum).

- Degrees of Freedom: Both have 1 (motion in one direction).

- Energy: Oscillator has potential and kinetic energy; particle in a box only has kinetic energy between walls.

Damped harmonic oscillator | particle in a box in 1D

degrees of freedom  1

action | S(t_1, t_2) = integral_(t_1)^(t_2) exp(2 ζ ω_0 τ) (1/2 m x'(τ)^2 - 1/2 m ω_0^2 x(τ)^2) dτ | 

Lagrangian | L = exp(2 ζ ω_0 t) (1/2 m x'(t)^2 - 1/2 m ω_0^2 x(t)^2) | 

equations of motion | x''(t) + 2 ζ ω_0 x'(t) + ω_0^2 x(t) = 0 | 

solution of the equations of motion | x(t) = e^(ζ (-t) ω_0) ((x'(0) sinh(α t))/α + x(0) ((ζ ω_0 sinh(α t))/α + cosh(α t)))

with

α = sqrt(-1 + ζ^2) ω_0 | x(t) = TriangleWave[{0, l}, (t x'(0) + x(0))/(2 l) - 1/4] for 0<=x(0)<=l

Hamiltonian | ℋ = exp(-2 ζ ω_0 t) p(t)^2/(2 m) + exp(2 ζ ω_0 t) 1/2 m ω_0^2 x(t)^2 | 

Hamiltonian equations of motion | x'(t) = exp(-2 ζ ω_0 t) p(t)/m | p'(t) = -exp(2 ζ ω_0 t) m ω_0^2 x(t) | 

solution of the Hamiltonian equations of motion | x(t) = e^(ζ (-t) ω_0) ((p(0) sinh(α t))/(α m) + x(0) ((ζ ω_0 sinh(α t))/α + cosh(α t))) 

with

α = sqrt(-1 + ζ^2) ω_0

p(t) = e^(ζ t ω_0) (p(0) (cosh(α t) - (ζ ω_0 sinh(α t))/α) - (m x(0) ω_0^2 sinh(α t))/α)

with

α = sqrt(-1 + ζ^2) ω_0 | 

canonical momenta | p(t) = m e^(2 ζ t ω_0) x'(t) | 

period | T = (2 π)/(sqrt(1 - ζ^2) ω_0) for abs(ζ)<1 | 

 | description | physical quantity | basic dimensions | D

m | mass | mass | [mass] | R^+

ω_0 | natural angular frequency | angular frequency | [angle] [time]^-1 | R^+

ζ | damping ratio | multiplicative constant | [dimensionless] | R^+

l | length of the box | length | [length] | R^+

m | mass of a test particle | mass | [mass] | R^+ ..

x̄ - > Centripetal acceleration | gravitational acceleration

centripetal acceleration 

| tangential speed | 30 mph (miles per hour) 

radius | 500 feet

centripetal acceleration | 118 cm/s^2 (centimeters per second squared)

= 3.872 ft/s^2 (feet per second squared) 

= 9504 mi/h^2 (miles per hour squared) 

= 1.18 m/s^2 (meters per second squared)

a = v^2/r | 

a | centripetal acceleration 

v | tangential speed 

r | radius

Physics jokes A neutron walks into a bar and inquires how much a drink costs. The bartender replies, "For you? No charge." ,

 gravitational acceleration 

g = (G M)/r^2 | 

 g | gravitational acceleration 

M | mass 

r | radius 

G | Newtonian gravitational constant (≈ 6.674×10^-11 m^3/(kg s^2))

mass | Earth (planet) (mass): 5.97×10^24 kg (kilograms) 

radius | Earth (planet) (average radius): 6371.009 km (kilometers)

gravitational acceleration | 9.82 m/s^2 (meters per second squared) 

= 32.22 ft/s^2 (feet per second squared) 

= 982 cm/s^2 (centimeters per second squared) escape 

velocity | 11.19 km/s (kilometers per second) 

11190 m/s (meters per second) 

25020 mph (miles per hour)

damped harmonic oscillator (physical system)

Degrees of freedom 1 

S(t_1, t_2) = integral_(t_1)^(t_2) exp(2 ζ ω_0 τ) (1/2 m x'(τ)^2 - 1/2 m ω_0^2 x(τ)^2) dτ 

 

L = exp(2 ζ ω_0 t) (1/2 m x'(t)^2 - 1/2 m ω_0^2 x(t)^2) 

 

x(t) = e^(ζ (-t) ω_0) ((x'(0) sinh(α t))/α + x(0) ((ζ ω_0 sinh(α t))/α + cosh(α t))) 

with α = sqrt(-1 + ζ^2) ω_0 

 

ℋ = exp(-2 ζ ω_0 t) p(t)^2/(2 m) + exp(2 ζ ω_0 t) 1/2 m ω_0^2 x(t)^2 

 x'(t) = exp(-2 ζ ω_0 t) p(t)/m | 

p'(t) = -exp(2 ζ ω_0 t) m ω_0^2 x(t) 

 

x(t) = e^(ζ (-t) ω_0) ((p(0) sinh(α t))/(α m) + x(0) ((ζ ω_0 sinh(α t))/α + cosh(α t))) 

with α = sqrt(-1 + ζ^2) ω_0 p(t) = e^(ζ t ω_0) (p(0) (cosh(α t) - (ζ ω_0 sinh(α t))/α) - (m x(0) ω_0^2 sinh(α t))/α) with α = sqrt(-1 + ζ^2) ω_0 

 p(t) = m e^(2 ζ t ω_0) x'(t) T = (2 π)/(sqrt(1 - ζ^2) ω_0) for abs(ζ)

x̄ - > Health and medicine

 height | 6' 2"

body weight | 250 lb (pounds)

 | male | female

body mass index | 32.1 ("obese") | 32.1 ("obese") 

ideal body weight | 80.4 kg (33 kg lighter) | 79.1 kg (34 kg lighter)

fat mass | 38.3 kg (33.8%) | 46.4 kg (41%)

lean body mass | 75.1 kg (66.2%) | 67 kg (59%)

(based on FDA and CDC standards)

male | (2012 to 2340) Cal/d (dietary Calories per day)

female | (1766 to 2035) Cal/d (dietary Calories per day)

 | male | female

total water | 56 L (liters) | 50 L (liters)

whole blood | 6.6 L (liters) | 6.3 L (liters)

blood plasma | 4.4 L (liters) | 4 L (liters)

 | male | female

lung capacity | (3.6 to 4.8) L (liters) | (3.6 to 4.8) L (liters)

heart volume | 760 mL (milliliters) | 580 mL (milliliters)

(based on AAPA, NINCDS, and NIH specifications)

x̄ - > Personal reflective essay on Overcoming Trauma: A Personal Reflective Essay

 ### Overcoming Trauma: A Personal Reflective Essay

I am not brave or courageous enough to stand or post a video of myself saying this. I am not fierce like some of the women I know, and I never got a chance to share this when it deeply affected me. It hurts so much to remember what it was like to feel helpless and to think I was the only one experiencing this. I was a victim of domestic violence. Back then, I was young, angry, and dumb but not stupid. Here I am, thinking about girls out there who suffer from the same kind of trauma. I googled it, read articles about it, and even books. I wanted to understand how it happens and how to heal from it.

Trauma is often described by scientists as an injury from physical or emotional distress. Of the three types of trauma, the one that most young women suffer from is complex trauma. It is mainly caused by domestic violence, neglect, or childhood abuse. Most girls grow up without their fathers, and we all know a father-daughter relationship is vital in shaping a girl’s character, especially in building self-confidence and influencing her opinions about men. The girls who grow up without a father or whose father is not available in their daily lives tend to overthink and reject men who propose to them for fear of neglect or abandonment (Herman, 1992).

Young women who were neglected at birth think that their fathers did not love them enough to want to spend their life with them. My friend Janey once shared that she needs a man who will love her as her father would. She feels a void in her life because she never experienced a dad's love, and it haunts her deeply to realize she is all grown up and the men who court her cannot fill the void. It saddens my heart because Janey is suffering from complex trauma, and she does not realize it. She thinks it is normal, and she consoles herself with words like "I will work hard, build a house, look for a sperm donor, and raise my kids all by myself."

She does not sit down and think about her kid's future. Would she want them to grow up without a dad as she did? What if it affects them just like it affected her? We live in a society where we want to run away from our problems rather than solve them. Women suffering from rejection, especially from their father, should seek medical attention and get encouragement from their mothers with words like "It shall be well," "I love you more and I will do anything to make you happy," and "People make mistakes, and your dad made one, and I wish you could forgive him" (van der Kolk, 2014).

My trauma was healed the day my mother took the responsibility of encouraging me, building me, and making me believe that not all people are the same. Some people out there are nice and warm. It took a while, but I forgave life. It will not come easy for you; it might take years, but the willingness of your mind to recover is what will make a difference. I am not trying to change you. I want you to know I was there, and I conquered every bit of trauma, the depression, the stress, and the overthinking. Seek help from a professional and remember you are loved by me and you.

From the big sister you never had.

### References

Herman, J. L. (1992). Trauma and Recovery: The Aftermath of Violence—From Domestic Abuse to Political Terror. New York: Basic Books.

van der Kolk, B. A. (2014). The Body Keeps the Score: Brain, Mind, and Body in the Healing of Trauma. New York: Viking.

From the big sister, you never had

This work is licensed under a Creative Commons Attribution 4.0 International License.

x̄ - > Road transportation - Vehicles used per road length UK

United Kingdom | total vehicles in use per road length

passenger cars | 27.5 million cars (2005 estimate) 

trucks and vans | 3.4 million vehicles (2005 estimate)

buses | 178000 buses (2005 estimate)

motorcycles | 1.2 million motorcycles (2005 estimate)

total | 32.3 million vehicles (2005 estimate)

x̄ - > The lambda function: a tool for creating anonymous functions

The lambda function: a tool for creating anonymous functions

Introduction

Anonymity is often seen as a desirable quality in our increasingly public world. But when it comes to data, anonymity is key to protecting our privacy. A lambda function is a tool that helps us create anonymous functions, which are essential for keeping our data safe.

Lambda functions are used to create anonymous functions, which are functions that are not bound to a name. Anonymous functions are used in many different programming languages, but they are particularly useful in Python.

Python is a language that is becoming increasingly popular for data science and machine learning. A lambda function is a tool that can be used to create anonymous functions, which are essential for keeping our data safe. Lambda functions are able to be written without being named.

One of the main advantages of using lambda functions in Python is that they make it easy to write and use small, single-use functions without having to define and name them first. This can be especially useful for data processing tasks, where we may need to apply the same function to many different data points or subsets of a larger dataset. In addition to its usefulness in data science and machine learning, the lambda function can also be a powerful tool for web development, where it can be used to create anonymous functions for handling user input or responding to API requests. Overall, the lambda function is a valuable tool for any programmer or data scientist who wants to create efficient, secure, and scalable code. By using anonymous functions to handle our data, we can ensure that our privacy remains protected while also making our code more modular and flexible.

Example

lambda : print('Hello World')

lambda argument(s) : expression 

greet = lambda : print('Hello World')

#call the function

greet ()

x̄ - > Branded food

 peanut M&M's | amount | 10 pieces

serving size 10 pieces (20 g)

total calories 103

% daily value^* | 

 total fat 5 g | 8%'

 saturated fat 2 g | 10%

 trans fat 66 mg | 

 cholesterol 2 mg | 1%

 sodium 10 mg | 0%

 total carbohydrates 12 g | 4%

 dietary fiber 740 mg | 3%

 sugar 10 g | 

 protein 2 g | 4%

 calcium 2% | iron 1% 

 vitamin E 3% | thiamin 1% 

 riboflavin 1% | niacin 3% 

 vitamin B6 1% | vitamin B12 1% 

 folate 3% | phosphorus 4% 

 magnesium 3% | zinc 2% 

*percent daily values are based on a 2000-calorie diet

 | value | % daily value

saturated fat | 2 g | 10%

total fat | 5.2 g | 8%

copper | 101 μg | 5%

 | ⋮ | 

sodium | 10 mg | 0%

vitamin C | 0 g | 0%

 | amount | % daily value | foods distribution | rank

theobromine | 22 mg | | | 96.6%

caffeine | 2 mg | | | 96.1%

retinol | 4.4 μg | | | 76%

(distributions from log nutrient values in standard servings of 7500 common foods)

 | value | % daily value

total calories | 103 Cal | 5%

 | value | % daily value

total carbohydrates | 12 g | 4%

dietary fiber | 740 mg | 3%

sugar | 10 g | 

 | value | % daily value

total fat | 5.2 g | 8%

saturated fat | 2 g | 10%

trans fat | 66 mg | 

 | value | % daily value

protein | 1.9 g | 4%

 | value | % daily value

vitamin A | 4.4 μg | 0%

vitamin C | 0 g | 0%

 | value | % daily value

calcium | 20 mg | 2%

iron | 232 μg | 1%

 | value | % daily value

cholesterol | 1.6 mg | 1%

volume percentage | 0%

proof | 0 proof

mass | 0 g

mass | 20 grams

serving volume | 28 mL (milliliters)

serving density | 0.72 g/cm^3 (grams per cubic centimeter)

x̄ - > Gender Is Culturally Prescribed Role, Rather Than a Biological Sex

LGBT Color

Have you been asked to fill out a questionnaire with the question "select your gender?" or "select your sex?". Most of us get confused with the two terms, and so did I before learning the terms. In most cases, the choices available for gender are binary, man or woman. As for sex, the options are often male, female, or others. World Health Organization (WHO) defines gender as

"Gender is the characteristics of women, men, girls, and boys that are socially constructed. This includes norms, behaviors, and roles compared with being a woman, man, girl, or boy and relationships with each other. As a social construct, gender differs from society to society and can change over time."

WHO further defines sex as biological characteristics that determine humans as male or female. Therefore, sex and gender are not similar as most people perceive. 

Gender brings along gender identity that is crowned by society. Women are (sex) female, and men are (sex) male. The others (intersex) lack a gender role in the current society due to a few reasons we shall mention later in the article.

Gender and Gender identity have a massive role in society. Culturally being a woman gives you roles different from being a man. Women in the African culture are often distinguished by wearing a skirt and planting their hair. Like the Arabs, men in the Asian culture wear robes similar to the Skirt worn by the African women. The Similarity does not make the society confuse African women and Arab men.

British men in Kilt

There are certain criticism theories and controversial statements made in reference to gender and sex. The major one is (sex) intersex, who is neither male nor female. The intersex possesses both external genitalia, making them outcasts. Gender is binary and defines woman and man and not both. 

Children born with both the vagina and penis face an unwelcome society that does not give them social status in the gender arena. The parents of these kids ask for surgery to normalize the kid or somewhat correct the situation. Later on, the child blames the parent for making the wrong decision on their sex, the male child's body starts to produce excess estrogen, and the female child's body starts to produce extra testosterone. To correct the situation, the parent should give their children the liberty to consent to the sex of their liking at a certain age.

Sex, gender, and sexuality go hand in hand. Sexuality is defined as the expression of sexual feelings that drive sex activities. Human beings possess biological characteristics like the external reproductive organs female (vagina) and male (penis). The organs help identify sexuality and sex drives. Transgender and Heterosexual are the central sexualities in the modern world. Sexuality somehow affects gender roles in society as some of the transgender tend to take up positions of the opposite gender.

Men role in the society is universal.

In conclusion, gender, and biological sex dramatically affect the role of humans in society. Women are involved in relationships and home private affairs as men more universal in their duties. However, sexuality affects the social functions of men and women. Other factors, such as upcoming human rights that equalize women and men, significantly affect gender culturally influenced roles. 

x̄ - > Addition | Subtraction | Multiplication | Arithmetic - ∏kapitāls-pi

Identity property of addition

(1+2)+4 = 1+(2+4)

What is 3 plus 7?    Answer is 10

What is seven hundred and ninety-five plus two hundred and sixty-three?  Answer 1058

What is 25 more than 256?  Answer 231

Add 969 and 310? Answer 

What is 15 minus 9? 

What is 417 more than 645?

4×7

28

twenty-eight

the sum of divisors | 4

7

1 | 2 | 4 (3 divisors)

4 = 2^2 (2 prime factors, 1 distinct)

x̄ - > LOVE AND SACRIFICE

To love means to feel compassionate towards someone, to "feel" what they feel what are some signs of love? making a sacrifice is one sign of devotion to another person. When you care about someone you have to give a little.it all comes with life. In order to receive something, one must sacrifice other things. For example, if having to make a choice between the love of your life and going to a football game a person who is truly in love and not just in love with being in love, will sacrifice the game in order to be with that person. Sacrificing anything is the greatest expression of your "love".The greatest sacrifice one would have to make is his or her death. Dying for a loved one make it more loving, sad, humanity and evil.

The film to relate this story. The film female lead is Naina (Preity Zinta)narrates the story. Her father had committed suicide years ago which left a deep impact on her heart. Her family is dysfunctional since her mother and grandmother just cannot stop arguing. But when Aman(Shahrukh Khan) arrives next door the whole gloomy conditions change. Aman infuses life in skeptical and overtly serious Naina and she falls in love with him.

 But Aman knows that he cannot marry Naina because of the secret which he cannot divulge to her he has a heart condition which he knows he won't survive at all cost so he sacrifices his love for her Best friend on the second to the lost scene of the movies when Aman was on the hospital bed he knows he is not Rohit(she is yours in this life) he gave up the ghost and Rohit married Naina and God bless them with a beautiful daughter.

 By:Linda Bahati

x̄ - > BELLY FAT TROUBLES?

BELLY FAT TROUBLES? 

Belly fat has been one trouble for women and to some, it even jeopardizes their careers; for example, those who are models! Many methods to do away with belly fat have been tabled! However, working out and dieting are the best! 

1. DIET This is the number one factor in losing weight and getting rid of unwanted fats. Doing healthy foods is essential for our health too. Eating lots of ice creams, cakes, and sugary foods cannot only make things worse. Foods like vegetables are very healthy! 

2. WATER Drinking a lot of water is also very healthy and helps reduce fats! Drink water in the morning and lots more during the day. 

3. WORKOUT -Working out keeps us fit! 

There are simple workouts effective in burning fats; 

1. The Plank The plank does not need any equipment and can be done at the comfort of your home! 

2. Leg Raises Leg raises are also effective for burning fats! It also does not need any equipment! 

3. Squats Doing squats are also effective in bringing you glutes and shaping your curves, and it also burns belly fat. Squats can be done by either type of equipment or just normal squats! To sum up, managing your diet and working out consistently is effective in keeping our bodies healthy and in shape. Share my posts. Your support will be highly appreciated. Do you have trouble working out?

- - 💝 Phenny

x̄ - > Good fellas gaussian noise effect image Goodfellas

 title | Goodfellas

director | Martin Scorsese

release date | 19/09/1990 (32 years 6 months ago)

runtime | 145 minutes (2 hours 25 minutes)

writers | Nicholas Pileggi | Martin Scorsese

genres | biography | crime | drama

U.S. rating | R

production budget | $25 million (US dollars) (current equivalent: $55.8 million)

total receipts | $46.7 million (US dollars)

highest receipts | $6.37 million (US dollars) (weekend ending September 23, 1990)

highest rank | 1st (weekend ending September 23, 1990)

maximum number of screens | 1328 (weekend ending October 7, 1990)

highest average receipts per screen | $5952 (US dollars) (weekend ending September 23, 1990)

(unadjusted box office receipts)

(US data only)

actor | character(s)

Robert De Niro | James 'Jimmy' Conway

Ray Liotta | Henry Hill | Narrator

Joe Pesci | Tommy De Vito

Lorraine Bracco | Karen Hill

Paul Sorvino | Paulie Cicero

category | recipient

actor in a supporting role (winner) | Joe Pesci

actress in a supporting role (nominee) | Lorraine Bracco

best picture (nominee) | Irwin Winkler

directing (nominee) | Martin Scorsese

film editing (nominee) | Thelma Schoonmaker

writing (screenplay based on material from another medium) (nominee) | Nicholas Pileggi | Martin Scorsese

 gaussian noise effect image Goodfellas

image effect | Goodfellas (movie) | image

filter Gaussian noise 

x̄ - > Cause and effect essay on HOW TO CONTROL POVERTY IN KENYA.

 HOW TO CONTROL POVERTY MOSTLY IN KENYA.

Poverty is described as a financial inability to meet the costs of living and there are two of poverty which are absolute and relative-frequently. Absolute poverty measures poverty vis a vis the amount of money necessary to meet basic needs such as food, clothing, and shelter while Relative poverty defines poverty in relation to the economic status of other members of the society. Poverty is a dangerous weapon that can hinder the growth and development of any society.

Poverty in Kenya has contributed to the spread of preventable diseases, exploitation of women and children violent conflict over scarce resources, and political instability. Poverty leads to hindering production and economic development.

Causes of poverty range from colonialism to industrialization, from political institutions to geography, and also corruption. Some of the causes are the Heritage of colonization, and corruption is one of the main causes of poverty in Kenya. Funds for basic needs like maize and oil are often lost through corruption ( Migai Winter 2011) prices of commodities increased by more than 200% overnight leading to the costs going out of reach for many Kenyans. Also, population growth and movement cause much poverty, population growth in Kenya has put brought put pressure on agricultural land resources as more land is put into settlements use. A key challenge facing the Kenyan youth is the lack of appropriate education and skills which has led to an increase of more poverty in society.

Poverty can lead to crime, According to the Ministry of interior and coordination of the national government of Kenya report crime is more prevalent in areas where there is evidence of poverty like Bondeni and also Kibera. Also can lead to low production in companies, early death, low education, and practice of drug abuse this will affect mostly youths.

The political elite needs to re-examine their will to fight corruption and grow their willingness to let every Kenyan grow out of poverty this is building more companies where many people will get jobs, and this will help many families to develop well. Government establishes should more institutions.

By:Linda Bahati

x̄ - > Cause and effect essay on EFFECTS OF CLIMATE CHANGE ON THE WORLD.

Climate change is an important current on ongoing issues. This is especially true in the Arctic region if you are unaware of climate change. It is a global or regional change in weather patterns that lasts for a long period of time. 

Climate change is greatly caused by the increased levels of atmospheric carbon dioxide which is produced by the use of fossils burning trash and factory emissions. Remissions.

These are also contributing to global warming which is a gradual increase in the overall temperature of the Earth's atmosphere. Some effects of global warming in the Arctic are rising temperatures in the water surrounding the Arctic. Another is the loss of sea ice and melting of ice sheets which is caused by the increased temperature.

This also greatly impacts the Arctic plants and animals they are rapidly dying decreasing in number, possibly leading to their extinction in 1984. Corticosteroids were first used to treat asthma and allergic reactions. 

They worked by reducing the inflammation that would be caused by the allergens. The discovery of most cells in 1953 helped to identify what caused allergies to set off the immune response of the body. Maybe standoff with laws that were passed to slow climate change. 

 

By: Linda Bahati

x̄ - > We shall be well (story of hope) - by drunk Esther

For a world where history gives us a go-ahead and the patterns are a way of predicting the next moves,
elites are always on the lookout to make sure they give us not only accurate but dependable
information on anything that seems to challenge the social life of humans. Luckily over the years, we have
seen the predictions come to happen and often take necessary action to commend the people
involved.
Let us go back a little, the Spanish flu, widely known as influenza was experienced from 1918 to
around the end of 1920, was a pandemic in this case that we should refer to, it was first identified in Spain
hence the name Spanish flu, an estimation of 500 million people were infected, and the reported
the number of deaths was 50 million. The mortality rate was high in adults between 20-40 years, also
younger than 5years old and 65years and older. Since no one worldwide understood it well, there was
no vaccine to protect people from influenza infection and the lack of enough knowledge on nonpharmaceutical inventions such as isolation, quarantine, good hygiene, use of disinfectant, and limitation
of public gatherings and the aftermath of world war 1 the flu is said to be the deadliest disease ever
reported in the history of mankind
Currently, the world is battling with a global pandemic, Coronavirus, worldwide there have been
1,288,372 confirmed cases and 70,482 reported deaths. World societies are practicing semi-quarantine, practicing social distancing, and have opened essential businesses, such as hospitals, groceries,
banks, and utilities to help curb the spread of Covid-19. The goal for all these measures is to drop
the cases to as low as zero-till negative. International regimes such as NATO, EU, and recently AU are
managing the cases by providing ventilators to affected countries, and mobilization world scientists to find
a cure or rather a vaccine for this pandemic.
People working from home are also in the action of slowing the spread of this pandemic, the most
hopeful thing about this spread is due to technology, a huge number of experts in medicine, and people
around the world take seriously the advice of WHO and practice non-pharmaceutical inventions.
The major things to compare Coronavirus with Spanish flu and what we should learn from them.
1. The Spanish flu was a pandemic that happened after the ww1, where people say the first case
was reported in a military base and believed to originate from Spain because Spain was neutral
during the war, the fatality rate was 2% which makes it the deadliest disease in history,
however, the number of people who died of the flu is said to be more than a 50million, which
bring us to the first point, due to technology, China and the rest of the developed countries, have a
record of the exact number of deaths and infected persons, from a reliable database. This is an
advantage because we can be able to monitor deaths and infection rates, thus taking more precautions toward the top of the spread of the coronavirus.
2. One of its commonalities is that no one is immune to them, although countries like North Korea
have reported zero deaths and a few infections this makes it a global issue. One difference however
in these pandemics is that the immunity of a group of people in the 1918 Spanish flu, that was
highly threatened was; healthy adults between 20-40 years while Coronavirus most affected
group is the old and people with other health complications like diabetes, asthma, and others, especially chronic ailments. This shows that the number of young children affected is low thus
the hope of a tomorrow if all goes wrong for the older people.
3. There was no vaccine for the Spanish flu and certainly no for Coronavirus, there were no
antibiotics for the bacteria and no cure for the virus, this makes both global concerns bringing
countries together and talking in one voice, encouraging people worldwide to apply the nonpharmaceutical measures put into place by world health organizations. as for the Spanish flu it
took two years to finally come to an end and 20 years to introduce the vaccine, unlike then now
the number of patients with coronavirus who have recovered is high worldwide teaching us
the practice of extremely high hygiene and coming up with innovative methods to take care of slums
and crowded places.
Finally, Coronavirus is a pandemic that has taken us world by surprise, making us panic but not
go into violence, it has made us learn the hugest lesson of our lives that we shall be able to overcome
anything like this in the future and tales we shall tell will not be of the hard times but the success
that as a world we all put our heads together as one and fought a battle that had threatened our
existence. Now more than before we have a possibility of getting the cure. Also, we hail bravo to the
commendable job of China, Germany, and North Korea for being able to contain the virus. As the drug
trials take in we hope that all shall be well. Because hope is the major ingredient in a crisis. And we shall
be rewarded greatly for our optimism.
Author
Drunk Esther,<