Answer:
Sure, here are the definitions, examples, and explanations for each term:
1. Definitions: A definition is a statement that gives a clear and concise explanation of the meaning of a word or term. Definitions are used to help people understand what a word or term means in a particular context.
Example 1: The definition of "phototropism" is the movement or growth of a plant in response to light.
Example 2: The definition of "respiration" is the process by which living organisms take in oxygen and release carbon dioxide.
Example 3: The definition of "genetic variation" is the differences in genetic traits among individuals of the same species.
Example 4: The definition of "inflation" is the sustained increase in the general price level of goods and services in an economy over a period of time.
2. Theorems: A theorem is a statement that has been proven to be true using rigorous mathematical reasoning. Theorems are used to explain and predict phenomena in mathematics and other fields of study.
Example 1: The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Example 2: The Fundamental Theorem of Calculus states that differentiation and integration are inverse operations of each other.
Example 3: The Law of Sines is a theorem that relates the sides of a triangle to the sines of the opposite angles.
Example 4: The Binomial Theorem is a formula that can be used to expand the power of a binomial expression.
3. Formulas: A formula is a mathematical expression that shows the relationship between two or more variables. Formulas are used to solve problems and make predictions in many areas of study.
Example 1: The formula for calculating the area of a rectangle is A = 1 x w, where A is the area, I is the length, and w is the width.
Example 2: The formula for calculating the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.
Example 3: The formula for calculating the kinetic energy of an object is KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass, and v is the velocity.
Example 4: The formula for calculating the present value of an investment is PV = FV / (1+r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years.
4. Step-by-Steps: Step-by-steps are instructions that explain how to perform a particular task or solve a problem. They are used to help people understand complex procedures and complete tasks in a consistent and efficient manner.
Example 1: The step-by-step process for solving a linear equation involves isolating the variable on one side of the equation by performing the same operation on both sides.
Example 2: The step-by-step process for changing a tire on a car involves loosening the lug nuts, lifting the car, removing the flat tire, placing the spare tire on the car, tightening the lug nuts, and lowering the car.
Example 3: The step-by-step process for conducting a laboratory experiment involves setting up the experiment, collecting data, analyzing the data, and drawing conclusions.
Example 4: The step-by-step process for writing a research paper involves choosing a topic, conducting research, creating an outline, writing a draft, revising the draft, and finalizing the paper.