Discrete Math problems: Mathematical induction

1.Use mathematical induction to prove that 2-2*7+2*7^2-.....+2(-7)^n=(1-(-7)^n+1)/4 whenever n is a nonnegative integer. 2.Show that 1^3+2^2+....n^3=[n(n+1)/2]^2 whenever n is a positive integer. 3.Use mathematical induction to show that 3 divides n^3+2n whenever n is a nonnegative integer.

Discrete Math: Mathematical Induction

1.Use mathematical induction to prove that 2-2*7+2*7^2-.....+2(-7)^n=(1-(-7)^n+1)/4 whenever n is a nonnegative integer. 2.Show that 1^3+2^2+....n^3=[n(n+1)/2]^2 whenever n is a positive integer. 3.Use mathematical induction to show that 3 divides n^3+2n whenever n is a nonnegative integer.

Working with a sinusoidal function.

This question concerns the function y/3 = 3+ 4sin [3x+ pi ] Where x is measured in radians. (1) Choose the one option which gives the value of the function when x= pi/2 (2) Choose the one option which gives the period of the function. Options for questions 1 and 2. A 1 B. 2 C. 3 D. 4 E. pi/3 ...continues

Trigonometry questions , Pythagoras theorem, cosine and sine formulas

(i) A herring gull was ringed at Llyn Trawsfynydd Gwynedd (grid reference SH 700360) and was retapped near Criccieth, Gwynedd ( grid reference SH 500380). The ringing report states the Distance as 20km and the Direction as 276 degrees. (a) Use the grid refernces and trigonometry to check that the map bearing of Criccieth fr ...continues

Permutation -Combination

An anthropologist discovers an isolated tribe whose written alphabet contains only six letters called a, b, c, d, e, and f. The same letters cannot be used twice in the same word. If each different sequence of letters constitutes a different word in the language, what is the maximum number of six-letter words that the language ...continues

Evaluating expressions with square roots

Evaluate this expression if K=-4,m=2,and n=16. -3sq.root of n + m +5k.

Linear Programming

Please see the word attachment for questions. I want answer on the excel sheet.

Quantative Methods: Linear Programming

Please find the question as an attachment. Also, please provide the answer in the attached Excel sheet. You will have to use the solver. 1. A hospital is trying how many RN’s to hire to provide the 24-hour-day coverage it needs on the floor. The hospital is concerned with both costs for wages of RN’s hired and level of ca ...continues

Probability: Sample Spaces

Please see http://www.isye.gatech.edu/people/faculty/Robert_Foley/classes/2027/hmwk2.pdf for the fully formatted problems. Probability: This is where the homework 2 is found. I couldn't attach the files for some odd reason. But I ONLY NEED HELP ON PROBLEM # 2, 3, AND 4. 2. Let the sample space be S = {1, 2, 3, 4, 5}. Defi ...continues

Probability

I only need help with problems 1, 2, and 3. Please see the following website for the complete problems:http://www.isye.gatech.edu/people/faculty/Robert_Foley/classes/2027/hmwk3.pdf 1. Suppose that the sample space S = {1, 2, 3, ...}. Let pk = Pr({k}) for k 2 S. In each of the following cases, compute c. (a) Suppose that pk ...continues