Mathematics | Senioritis

John Rhodes
July 7, 2023
Discrete Math

A Logical Equivalences Proof: Breaking Down the Given Statement and Proving its Truth

p ∧ F ≡ Fp ∨ T ≡ T To prove the given statement using logical equivalences, we’ll break it down into two separate equivalences: 1 To...

John Rhodes
July 7, 2023
Discrete Math

Proving Logical Equivalences: Understanding and Demonstrating Identity, Domination, and Idempotent Laws in Math

p ∧ T ≡ pp ∨ F ≡ p To understand and prove the given expressions, we will use the following properties of logical equivalences: 1 To...

John Rhodes
July 7, 2023
Geometry

The Mathematics Behind the 3-4-5 Triangle: Side Lengths, Angles, and Trigonometric Ratios

3-4-5 triangle A 3-4-5 triangle is a special type of right triangle with side lengths in the ratio of 3:4:5 A 3-4-5 triangle is a special type...

John Rhodes
July 7, 2023
Geometry

Understanding the Side Length Ratios in a 30-60-90 Triangle: Explained with Formulas and Summary

The side ration of a 30-60-90 triangle is … In a 30-60-90 triangle, the ratios of the side lengths are as follows: – The side opposite the...

John Rhodes
July 7, 2023
Geometry

The Side Ratio and Proportions of a 45-45-90 Triangle: Explained and Demonstrated

The side ratio of a 45-45-90 triangle is … The side ratio of a 45-45-90 triangle is 1:1:√2 The side ratio of a 45-45-90 triangle is 1:1:√2....

John Rhodes
July 7, 2023
Geometry

Determining If a Triangle is Obtuse: Using Side Lengths and the Pythagorean Theorem

Regarding side length, a triangle is an obtuse triangle if … A triangle is considered obtuse if one of its angles is greater than 90 degrees A...

John Rhodes
July 7, 2023
Geometry

How to Determine if a Triangle is Acute: The Side Length Approach and Triangle Inequality Theorem

Regarding side length, a triangle is is an acute triangle if … A triangle is considered acute if all three of its angles are acute angles, meaning...

John Rhodes
July 7, 2023
Geometry

Understanding the Pythagorean Theorem: Identifying right triangles and their characteristics

Regarding side length, a triangle is a right triangle if … A triangle is considered a right triangle if it satisfies the Pythagorean theorem, which states that...