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# Discrete Math

### Venn Diagram Post Survey

Creating a venn diagram post survey. Construct a Venn diagram, label your diagram clearly. Use your diagram to answer the following questions A survey asked participants many questions. Among the questions were these two: Do you own an Ipod? Are you over the age of 45? 33 did own an Ipod 57 were over the age of 45

### Gaussian Prime Factorizations and Binary Operations on Sets

Please see the attached file. Find the Gaussian prime factorizations of....

### Rigid Body Dynamics

(Please refer attachment for detailed problem description) Problem 1 : The 40 kg disc is released from rest with the spring compressed. At the instant shown (see attachment) it has a speed of 4 m/s and the spring is unstretched. From this poinr determine the distance d that the disc moves down the 30 degree ramp before moment

### Riemann Sum Proof Infinite Series

Show that: &#8721;&#8734;k=0 [(-1)^k * (pi)^2k][(2k)! * (2)^2k] = 0 This is the Riemann sum from 0 to infinity (see attached)

### Can lim x->0+ f '(x) and lim x->0- f '(x) exist and differ?

Suppose f(x) is differentiable at ALL x in R. Is it possible for lim x->0+ f '(x), and lim x->0- f '(x) to exist and NOT be equal?

### Finite mathematics six questions

1.Simplify the expression 3&#8730; (-1000) 2.Total profit is defined as total revenue minus total cost. R(x) and C(x) are the revenue and cost from the sale of x televisions. If R(x)= 240x - 0.9x^2 and C(x) - 4000 + 0.6x^2, find the profit from the sale of 100 televisions. 3.Simplify the complex fraction X/x+1 9/ x^2

### Discrete Math

I need help in solving the attached problem. Thanks!

### A student thinks of a polynomial p(x) of arbitrary degree, and non-negative integer coefficients.

A student thinks of a polynomial p(x) of arbitrary degree, and non-negative integer coefficients. How can you determine the student's polynomial by asking for two values of her polynomial, say p(a) and p(b), where a and b are positive integers? Hint: A positive integer n can be written uniquely in base k, where k is a positive

### R-module proof..

Any help is greatly appreciated. Please see the attached file. If R is a principal ideal domain....

### R-module proof rings

Any help would be greatly appreciated. Please see the attached file. Thank you! Let R be a ring with identity. Recall that the non-zero R-module M is simple...

### Finiteness of Sets

Give examples to show that the finiteness of the collections in parts c and d is essential. c) for any finite collection G1, G2, ...., Gn of open sets, intersection (at the top of the intersection sign is n and at the bottom is i=1) of Gi is open. d) For any finite collection F1, F2, ...., Fn of closed sets, union sign (

### Using a Modified Tree Diagram

Ernesto is going to choose 2 flowers. First, he will choose a flower for his mother the second flower he chooses will be for his sister. The florist has two blue flowers, 1 red flower and 1 yellow flower. Please draw a tree diagram to show all of Ernesto's possible choices Can you do this in a computation manner?

### Logic: Diplomat Row Example

Please see the attached file for the fully formatted problems. On Diplomat Row, an area of Washington, DC. there are five houses. Each owner is a different nationality, each has a different pet, each has a favorite food, each has a different drink, and each house is painted a different colour. All Statements: (1) Green H

### Set Operations and Venn Diagrams

Please see the attached file for the fully formatted problems. Auto Accessories Unlimited surveyed 155 customers to determine information...

### Bolzano's Theorem : How many iterations of the Bisection algorithm are necessary to approximate this root?

Please see the attached file for the fully formatted problem. Bolzano's Theorem : How many iterations of the Bisection algorithm are necessary to approximate this root?

### Dynamics and Kinematics

For detailed description with figs. please refer the attachment. Prob. 1 : A box slides down a ramp with two straight segments and on leaving the ramp it slides on a rough horizontal surface and then impacting a spring. To determine kinetic energy, velocity at different points and the compression of the spring. Prob. 2 : A

### Goal Programming (Lindo) - First West Chemical

First West Chemical First West Chemical Company produces two chemical ingredients for pharmaceutical firms; formula X and formula Y. Production of each ingredient requires two processes. A unit of Formula X requires 4 hours in process 1 and 3 hours in process 2. A unit in formula Y requires 2 hours in process 1 an

### Propositional logics

Problem: If Cleopatra was powerful, then she was venerated, but if she was not powerful, then she was not venerated and she was feared. If Cleopatra was either venerated or feared, then she was a queen. Cleopatra was a leader if she was a queen. Can you prove that Cleopatra was powerful? a leader? a queen? Do not use

### Finding a Recursive Algorithm

23. Give a recursive algorithm for computing n * a using only addition, where n is a positive integer and a is a real number (add a to itself n times).

### Logic : Determine whether each of the following is a tautology, a contradiction or neither.

13. Determine whether each of the following is a tautology, a contradiction, or neither. * (a) [( P fa] P. (b) Pe=>PA(PvQ). (c) P=.Q.=›PA—Q. * (d) P=IP (P (e) P A (Q v .1=› P (f) IQ A (P P. (g) ( P <=). Q) <=> (—Pv Q)v(—P AQ). (h) [P(Qv R)] [(Q R)v (R (i) P A(P Q) A —Q. (j) (PvQ).Q P. (k) [P (Q A R)] [R = (P Q)].

### Set Proofs without using Venn Diagrams

3. Prove, without using Venn diagrams that a) A intersect ( B union C) = A intersect B) union (A intersect C) and b) A union ( B intersect C) = (A union B) intersect (A union C), for all sets A, B, C 4. Prove, without using Venn diagrams, that the statements i) A subset of B ii) A intersect B = A, and iii) A union

### Finite Math : Linear Equations, Optimization, Probability and Basic Statistics

Week 5 ________________________________________ 1.) ________________________________________ 2.) Find the solution of the following system of linear equations: x + 2y - 7z = -1 3x + 7y - 24z = 6 x + 4y - 12z = 26 ________________________________________ 3.) A cookie company makes three kinds of co

### Algorithm Timing

How much time does an algorithm take to solve a problem of size n if this algorithm uses 2n^2 + 2^n bit operations, each requiring 10^-9 second, with these values of n? i) 10 ii) 20 iii) 50 iv) 100 I need help with a question, the attachment contains the question as well as what I think is the answer. Could someone ple

### List the first 10 terms of each of these sequences

Please see the attached file for the fully formatted problems. Practice problem 20 List the first 10 terms of each of these sequences. a) The sequence whose nth term is the larges integer k such that k! <= n; b) The sequence whose nth term is 3^n - 2^n; c) The sequence whose nth term is sqrt(n) ; d) The sequence whos

### Discrete Math : 'Onto' Functions

To figure how many 'one-to-one' functions' there are from a set with 3 elements to a set with 4 elements --would be-- 4!/(4-3)! or 24. How do you figure out how many 'onto' functions there are from a set with 4 elements to a set with 3 elements? Please give solution and detailed explanation. Thank you.

### Proof methods & strategy

Problem: Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive?

### M/M/1 Simulation

The fraction of the time that the server is busy (&#961;) = &#955;/ &#956; Without using &#955; (Lambda) and &#956; (Mu) in the equations and using only information from excel simulator output, can I use the IF Statement in excel to approximate the fraction of time that the server is busy(&#961;)? Why or why not? Please se

### Is the Set a Group?

Decide whether each of the given sets is a group with respect to the indicated operation. 1- For a fixed positive integer n, the set of all complex numbers x such that x^n=1(that is, the set of all nth roots of 1),with operation multiplication. 2-The set of all complex numbers x that have absolute value 1, with operation m

### Bijection is Homeomorphism

Let f : M -> N be a continuous bijection. M is compact. Show that f is a homeomorphism. Isn't a homeomorphism by definition a bijection? And since M is compact, will it not be true that N will be compact too?

### Proof : Differentiability

Suppose f(b) = f'(b) = 0 and a < b. Show that if f''(x) ≥ 0 for x є [a,b], then f(x) ≥ 0 for x є [a,b].