iteration to guess an explicit formula
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Use iteration to guess an explicit formula for the sequence: tk = tk−1 + 5k2 + 7k + 3, for all integers k ≥ 1, where t0 = 0 (using formulas from the Summation Properties Formulae to simplify your answers whenever possible).
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- Overview One of the oldest methods for computing the square root e of a number is the Babylonian Method e. The Babylonian Method uses an iterative algorithm to make successively more accurate estimates of a number's square root. The algorithm stops iterating when the estimate shows no further sign of improvement, or when the estimate is within some acceptable margin of error. The acceptable margin of error is often called an epsilon. Assuming that you need to solve for the square root of x, the algorithm works as follows. 1. Choose an epsilon value that determines how close your solution should be to the actual square root value before you decide it is "good enough." Because this assignment asks you to solve for the square root to three decimal places, we can safely set the epsilon value to 0.0001 (four decimal places). This guarantees that our solution will be accurate to the precision we need to display to the screen. 2. Choose an initial estimate e for the square root of x. An easy…Solve the following recurrence equations by expanding the formulas (also called the 'iteration method' on slides). Specifically, you should get T(n) = O(f(n)) for a function f(n). You may assume that T(n) = O(1) for n = O(1). You should not use the Master Theorem. (a) T(n) = 2T (n/3) + 1. (b) T(n) = 7T(n/7) + n. (c) T(n) = T(n − 1) + 2.Correct answer will be upvoted else downvoted. Computer science. Polycarp recalled the 2020-th year, and he is content with the appearance of the new 2021-th year. To recall such a great second, Polycarp needs to address the number n as the amount of a specific number of 2020 and a specific number of 2021. For instance, if: n=4041, then, at that point, the number n can be addressed as the total 2020+2021; n=4042, then, at that point, the number n can be addressed as the total 2021+2021; n=8081, then, at that point, the number n can be addressed as the total 2020+2020+2020+2021; n=8079, then, at that point, the number n can't be addressed as the amount of the numbers 2020 and 2021. Assist Polycarp with seeing if the number n can be addressed as the amount of a specific number of numbers 2020 and a specific number of numbers 2021. Input The primary line contains one integer t (1≤t≤104) — the number of experiments. Then, at that point, t experiments follow.…
- Design an algorithm to find the kth number such that the only prime factors are 3, 5, and 7. Note that 3, 5, and 7 do not have to be factors, but it should not have any other prime factors. For example, the first several multiples would be (in order) 1, 3, 5, 7, 9, 15, 21.The square root of any number N>0 can be opproximated by repeated calculation using the formula N = squared_value NG = 0.5 (FG + N/FG) where NG stands for next guess and FG stands for first guess. The value of NG and FG are compared. If the two values are comparably close, then NG is the final answer. If the two values are off, NG becomes FG and the formula is used again to compute FG. After so many iterations, NG and FG will merge. a. Write a function that calculates the square root of a number using this method. The initial guess wilI be the starting value of FG (FG = 1). The function will compute a value for NG using the formula given and returns that value. (Change the name of the functions to something more meaningful) double fun_1 (double FG, double N); b. Write a function that prompts the user for any number N > 0, and returns that value back. The prototype is like follows: double fun_2 ( void ); Now inside the main function, check the difference between NG and FG to see whether…The square root of any number N>0 can be opproximated by repeated calculation using the formula N = squared_value NG = 0.5 (FG + N/FG) where NG stands for next guess and FG stands for first guess. The value of NG and FG are compared. If the two values are comparably close, then NG is the final answer. If the two values are off, NG becomes FG and the formula is used again to compute FG. After so many iterations, NG and FG will merge. a. Write a function that calculates the square root of a number using this method. The initial guess will be the starting value of FG (FG = 1). The function will compute a value for NG using the formula given and returns that value. (Change the name of the functions to something more meaningful) double fun_1 (double FG, double N); b. Write a function that prompts the user for any number N > 0, and returns that value back. The prototype is like follows: double fun_2 ( void ); c. Now inside the main function, check the difference between NG and FG to see…
- Correct answer will be upvoted else Multiple Downvoted. Computer science. You are given an arrangement an of length n comprising of integers from 1 to n. The grouping may contain duplicates (for example a few components can be equal). Track down the number of tuples of m=3 components with the end goal that the maximum number in the tuple varies from the base by close to k=2. Formally, you want to view as the number of triples of lists i<j<z with the end goal that max(ai,aj,az)−min(ai,aj,az)≤2. For example, on the off chance that n=4 and a=[1,2,4,3], there are two such triples (i=1,j=2,z=4 and i=2,j=3,z=4). In the event that n=4 and a=[1,1,1,1], all four potential triples are suitable. Input The principal line contains a solitary integer t (1≤t≤2⋅105) — the number of experiments. Then, at that point, t experiments follow. The principal line of each experiment contains an integer n (1≤n≤2⋅105) — the length of the succession a. The following line contains n…Given f(x)=x2+6x and g(x)=1−x2, find f+g, f−g, fg, and fg. Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).There are two isotopes of an unknown element, X-19 and X-21. The abundance of X-19 is 14.29%. A weighted average uses the percentages of each isotope to scale their contribution to the total mass. Each isotope's contribution is the percentage (in decimal form) multiplied by the mass of the isotope. What is the contribution (in amu) to the weighted average from the X-19 isotope, which has a mass of 19.00 amu?
- Please help with question: Determine the running time of the following algorithms. Write summations to represent loops and simplify. Show all work. If bounding is used, the upper and lower bounds must only differ by a constant. Note: This is not the line-by-line analysis method. Loops are inclusive.Given: NFA 1 q4 q3 q2 Using State Elimination Method, construct the regular expression equivalent to the given NFA. Add new start state q0 and new final state q1. Eliminate state q2 first, then state q3, then state q4, and state q5 last. Upon elimination of the four (4) states, the regular expression RE equivalent to the given NFA is Sample Answer: 10*(10)* NOTE: In your answer just use the exact number of parenthesis. That is, do not use extra parenthesis in your answer.The size of a colony of blue bacteria growing in a petri dish is modeled by the equation where t is time in days. The size of a colony of green bacteria is modeled by the equation where t is again time in days. Both colony sizes are measured in square centimeters. Part A: Graph the growth of both colonies on the same plot over the course of 6 days in one hour increments. One way to get one hour increments is to use a step size of 1/24. Another way is to use linspace and specify that it should create 6days x 24hours evenly spaced values. In either case, make sure you start at 0 days, not 1 day. Make the color of the curve match the color of the bacteria it represents. Give your graph a title and axis labels. Part B: How large is the green bacteria colony when the blue colony reaches its maximum size. You must answer this question using Matlab calculations, not manually entering the answer. To check your work, the blue colony’s maximum size is 270.56 and when it reaches that…