John Rhodes, Math Teacher at Senioritis.io

John Rhodes
July 7, 2023
Calculus

Understanding the Coordinate Plane: A Comprehensive Guide to Locating Points and Analyzing Mathematical Relationships

Coordinate Plane The coordinate plane is a two-dimensional system used in mathematics to locate points using two perpendicular lines known as the x-axis and the y-axis The...

John Rhodes
July 7, 2023
Calculus

Is f(2) Defined and Continuous? Exploring Statements II and III.

Which of the following statements, if true, can be used to conclude that f(2) exists?i. limx→2f(x) exists.ii. f is continuous at x=2.iii. f is differentiable at x=2....

John Rhodes
July 7, 2023
Calculus

Calculating the Average Rate of Change of f(x)=1+3cos(x) over the interval [0, π]

The function f is given by f(x)=1+3cosx. What is the average rate of change of f over the interval [0,π] ? To find the average rate of...

John Rhodes
July 7, 2023
Calculus

Finding the Average Rate of Change of a Function over an Interval: Step-by-Step Guide and Calculation

Selected values of a function f are shown in the table above. What is the average rate of change of f over the interval [1,5] ? To...

John Rhodes
July 7, 2023
Calculus

Comparing and evaluating the function f(x) to determine the true statement: a math analysis.

Let f be the function given by f(x)=(1/7)x^7+12x^6−x^5−(15/4)x^4+(4/3)x^3+6x^2. Which of the following statements is true? To determine which of the following statements is true, we need to...

John Rhodes
July 7, 2023
Calculus

Approximating f′(0.5) using the difference quotient with a small positive value and calculating the difference between the approximation and the actual value of f′(0.5)

Let f be the function given by f(x)=2×3. Selected values of f are given in the table above. If the values in the table are used to...

John Rhodes
July 7, 2023
Geometry

Understanding Alternate Exterior Angles: Properties and Proof of Congruence in Parallel Lines

alternate exterior angles are congruent Alternate exterior angles are pairs of angles that are formed when a transversal intersects two parallel lines Alternate exterior angles are pairs...

John Rhodes
July 7, 2023
Geometry

Understanding the Corresponding Angles Theorem: Exploring the Congruency of Corresponding Angles when Parallel Lines are Cut by a Transversal

if 2 parallel lines are cut by transversals, then corresponding angles are congruent To understand why corresponding angles are congruent when two parallel lines are cut by...