PreCalculus - TeacherWeb
... (apply One-to-One Property of Exponential Functions) For b > 0 and b ≠ 1, bx = by if and only if x = y. Example: If 3x 35 , then x = 5. If x = 5, then 3x 35 . 2nd method: Take a logarithm of each side. How to Solve Logarithmic Equations: 1st method: If the equation is “single log single lo ...
... (apply One-to-One Property of Exponential Functions) For b > 0 and b ≠ 1, bx = by if and only if x = y. Example: If 3x 35 , then x = 5. If x = 5, then 3x 35 . 2nd method: Take a logarithm of each side. How to Solve Logarithmic Equations: 1st method: If the equation is “single log single lo ...
10-3
... 10-3 Variables on Both Sides Additional Example 3 Continued First solve for the price of one doughnut. Let d represent the price 1.25 + 2d = 0.50 + 5d of one doughnut. ...
... 10-3 Variables on Both Sides Additional Example 3 Continued First solve for the price of one doughnut. Let d represent the price 1.25 + 2d = 0.50 + 5d of one doughnut. ...
Solving Quadratic Equations Notes Part Two
... 2. imaginary number: a number that when squared gives a negative result 3. quadratic equation: an equation where the highest exponent of the variable is a square 4. zeros of a function: also called a root of the function, it is the x value(s) that produce a function value of zero 5. zero product pro ...
... 2. imaginary number: a number that when squared gives a negative result 3. quadratic equation: an equation where the highest exponent of the variable is a square 4. zeros of a function: also called a root of the function, it is the x value(s) that produce a function value of zero 5. zero product pro ...
Determinants
... To illustrate the method of second-order determinants, we will assume two loop equations as follows: 10I1 + 5I2 = 15 2I1 + 4I2 = 8 We want to find the value of I1 and I2. To do so, we form a determinant with the coefficients of the unknown currents. A coefficient is the number associated with an unk ...
... To illustrate the method of second-order determinants, we will assume two loop equations as follows: 10I1 + 5I2 = 15 2I1 + 4I2 = 8 We want to find the value of I1 and I2. To do so, we form a determinant with the coefficients of the unknown currents. A coefficient is the number associated with an unk ...
Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model.PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.