Mathematics Homework Solutions

Finding trigonometric forms.

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

Sequential Ambiguity

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

proof of the irrationality

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.

Divisibility by 13

Show that any number of the form ABCABC (ex. 356356)is divisible by 13.

Working with the sum of cubes

13+23+33+…. +n3 = (1+2+3+…+n) 2 Please see the attached problem.

applying algorithm to equations

29x + 33Y = 2490 I am looking for the integer values of x and y that satisfy this equation

finding integer values of x and y for the problem posted

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.

Problem Comparisons

I have answered two problems involving the distance of swimmers. My solutions are detailed in the attachment. My professor has emailed me the following statements in two separate emails: EMAIL #1 RE: Q48 Could you draw a graph which shows each swimmer.[distance(y axis) vs. time(x axis)]At point origin one swimmer at 0 dist ...continues

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