1. Use mathematical induction to solve the following: 1 1 (a) Find a formula for 1 by examining the values of this expression for + +...+ 1.2 2.3 n(n + 1) small values of n. (b) Show that 7" – 1 is a multiple of 6 for all n e N
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- I don't need a code for these questions. I just need them answered Nine steel specimens were submerged in seawater at various temperatures, and the corrosion rates were measured. The results are presented in the following table:Temperature (OC)Corrosion(mm/yr.)26.6 1.5826 1.4527.4 1.1321.7 0.9614.9 0.9911.3 1.0515 0.828.7 0.688.2 0.59a. Construct a scatterplot of corrosion (y) vs. temperature (x). Verify that a linear model is appropriate.b. What is the least-square line (trendline/regression line) for predicting corrosion from temperature?c. Two steel specimens whose temperatures differ by 10OC are submerged in seawater. By how much would you predict their corrosion rates differ?d. Predict the corrosion rate for steel submerged in seawater at a temperature of 20OC.e. Construct a table with predicted values from the original dataset.f. Compute the residuals. Which point has the residual with the largest magnitude?g. What is the correlation between temperature and corrosion rate? What…Please show the steps on how to accomplish this task 2. For equation X^2=X among infinite from left numbers there are 3 known solution: 0= ...00000, 1= ...00001 and 5^2^infinity = ...12890625. Give last 8 digits of one more solution whose last digit is 6: ...??????????6Problem 2. Prove that ?? ≤ (5/3) ? , where n is a positive integer and ?? is the nth Fibonacci number.
- 1. Prove the following formulas log X < X for all X > 0For each of the following Prove them formally and identify constants c and n0 if not then disprove a)f(n) = n 2 + 9n 3 2 is O(n 2 ) b)f(n) = 8n + 5 is O(n)4. Look up the Pythagorean theorem if you are not already familiar with it. Use the following formula to solve for c in the formula: c = √a2 + b2. Use the proper functions from the cmath header file. Be sure to output the result..
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- 2. A certain company gives commission to each of their salesmen based from the type of appliance sold andthe price of the appliance. Below are the given rates that will be used in computing for the salesman’scommission:If type is Commission is2, 5, 6 15% of the price4, 8, 10 20% of the price3, 1, 9,7 25% of the priceInput salesman’s name, type of appliance sold, and price of the appliance. Compute and print thesalesman’s commission.In RSA:a. Given n = 221 and e = 5, find d.b. Given n =3937 and e =17, find d.c. Given p = 19, q = 23, and e = 3, find n, φ(n), and dTo find final possible values of X Need correct answer otherwise dislikes