Purchase Solution

# Average area of inscribed triangle

Not what you're looking for?

Find the average area of an inscribed triangle in the unit circle.Assume that each vertex of the triangle is equally likely to be at any point of the unit circle and that the location of one vertex does not affect the likelyhood the location of another in any way.
(note that the maximum area is achieved by the equilateral triangle, which has side length sqrt(3) and area 3sqrt(3)/4. How does the maximum compare to the average?)

(there is a Hint: In order to reduce the problem to the calculation of a double integral, place one of the vertices of the triangle at (1,0), and use the polar angles teta1 and teta2 of the two other vertices as variables.What is the region of integration?)

##### Solution Summary

This shows how to find the average area of an inscribed triangle in the unit circle.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Probability Quiz

Some questions on probability