Quadratic Equation

Quadratic Equation

Quadratic equation is a second order polynomial with 3 coefficients – a, b, c. The quadratic equation is given by: ax2 + bx + c = 0 The solution to the quadratic equation is given by 2 numbers x1 and x2. We can change the quadratic equation to the form of: (x – x1)(x – x2) = 0 Quadratic Formula The solution to the quadratic equation is given by the quadratic formula: The expression inside…

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Normal and Probability Distribution

Normal and Probability Distribution

Normal distribution is a continuous probability distribution. It is also called Gaussian distribution. The normal distribution density function f(z) is called the Bell Curve because it has the shape that resembles a bell. Standard normal distribution table is used to find the area under the f(z) function in order to find the probability of a specified range of distribution. Normal distribution function When random variable X has normal distribution, The probability density function and cumulative…

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Negative Components

Negative Components

Negative exponents rule The base b raised to the power of minus n is equal to 1 divided by the base b raised to the power of n: b-n = 1 / bn Negative exponent example The base 2 raised to the power of minus 3 is equal to 1 divided by the base 2 raised to the power of 3: 2-3 = 1/23 = 1/(2·2·2) = 1/8 = 0.125 Negative fractional exponents The base…

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Logarithm and Natural Logarithm

Logarithm and Natural Logarithm

The base b logarithm of a number is the exponent that we need to raise the base in order to get the number. Logarithm definition When b is raised to the power of y is equal x: b y = x Then the base b logarithm of x is equal to y: logb(x) = y For example when: 24 = 16 Then log2(16) = 4 Logarithm as inverse function of exponential function The logarithmic function,…

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Exponent Rules

Exponent Rules

The base a is raised to the power of n is equal to the multiplication of a, n times: an = a × a × … × a n times a is the base and n is the exponent. Exponents rules and properties Rule name Rule Example Product rules a n · a m = a n+m 23 · 24 = 23+4 = 128 a n · b n = (a · b) n 32…

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Euler’s Constant

Euler’s Constant

e constant or Euler’s number is a mathematical constant. The e constant is real and irrational number. e = 2.718281828459… The e constant is defined as the limit: The e constant is defined as the limit: The e constant is defined as the infinite series: Properties of e Reciprocal of e The reciprocal of e is the limit: Derivatives of e The derivative of the exponential function is the exponential function: (e x)’ = ex…

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