Find the trigonometric form of the complex number where 0 <= theta < 2pi on the equation: r= 1/2 - [(sqrt(3)/2)i]
Working with sequential ambiguity.
In a specific sequence to create, a1 has the elements x1 and y1, a2 has the elements x2 and y2, a3 has the elements x3 and y3, The relationship between each term cannot be bijective, however it has a bounded range of finite whole numbers. Create a rule such that f(x1,y2)=x2 and f(x2,y3) = x3. The rule must be su ...continues
On Monday, May 26th/03, I posted the following question to which a solution was provided by Remus Nicoara, PhD (IP). I thank Remus for his assistance and solution. I'm interested in knowing what the solution would look like if for each term, the y elements are randomly determined. Original Question In a specific sequence t ...continues
2. Apply the proof of the irrationality of sqrt(2) to a) sqrt(3) and b) sqrt(4). If the proof breaks down, indicate precisely why. 3. Euler's phi-function is defined such that for n > 0, phi(n) = |{m < n: gcd(m,n)=1}|. So, e.g., phi(4) = |{1,3}| = 2; phi(5) = |{1,2,3,4}| = 4. a. Show that for prime p, phi(p) = p-1. ...continues
Working with Pythagorean triples.
Find a pythagorean triple with sides (x^2)-1, (y^2)-1, (z^2)-1, where x,y,z are integers.
Show that any number of the form ABCABC (ex. 356356)is divisible by 13.
Working with the sum of cubes.
Please see the attached file for the fully formatted problems. Problem 3: This problem itself is directly creating perceptual curiosity and at the cognitive level it is against what is known in the mathematics. The problem is: 13+23+33+…. +n3 = (1+2+3+…+n) 2 Visual representation of problem: Sum of the cubes equa ...continues
Algorithms : Finding integer values of x and y
A store offers 2 models of scooter, a $29 model and a $33 one. An order was placed with a warehouse which totalled $2490 but the details had been lost. Can you tell the order clerk howl many of each model to send to the store? I have been applying algorithm to equations and am trying to solve integer values for this problem.
Word Problems : Relative Speed of Swimmers
(#48) Two swimmers start at opposite ends of a pool 89 feet long. One person swims at the rate of 19 feet per minute and the other swims at a rate of 53 feet per minute. How many times will they meet in 33 minutes? (#33) Two swimmers start at opposite ends of a 90-foot pool. One swims 30 feet per minute and the other at 20 ...continues
Application of Mathematical Induction Application of Mathematical Induction Fibonacci Numbers :- The Fibonacci numbers are numbers that has the following properties. If Fn represents the nth Fibonacci number, F1 = 1, F2 =1, F3 =2, F4=3, F5 = 5 etc. We can find the Fibonacci number ...continues
