(4 Points) An algorithm takes 0.5 ms for input size 100. How long will it take for input size 500 if the running time is the following (assume low-order terms are negligible)? a. linear, b. O(N logN), c. quadratic, d. cubic
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- Q.1. Make the algorithm and flowchart : a. To find solution of any quadratic equation(Statics) An annulus is a cylindrical rod with a hollow center, as shown in Figure 6.7. Its second moment of inertia is given by this formula: I4(r24r14) I is the second moment of inertia (m4). r2 is the outer radius (m). r1 is the inner radius (m). a. Using this formula, write a function called annulusMoment ( ) that accepts two double-precision numbers as parameters (one for the outer radius and one for the inner radius), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 5a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.6. Let a, b, c, and n be integers. Prove that if and, then. 7. Find the remainder of when divided by a. 2. b. 5. с. 7. d. 9. 8. Solve the following congruences (describe the general solution). a.. b.. с.. d.. 9. I'm thinking of a number. If you multiply my number by 7. 5, and divide the result by 11, you will be left with a rema of 2. What remainder would you get if you divided my or number by 11? 10. Solve the following linear Diophantine equations, using modular arithmetic (describe the general solutions). a.. b. . с..
- (a) Consider the following algorithm. Input: Integers n and a such that n >0 and a > 1. (1) If 0 < n < a, stop. Otherwise, go to (2). (2) Replace n by n – a and go back to (1). How many times does this algorithm enter step (2)? Explain your answer. (Hint: the answer depends on both n and a, i.e. you should calculate the number of times that the algorithm enters step (2) as a function of n and a.)I should use input()Q1) Write a computer program that uses Newton's method to find the root of a given function, and apply this program to find the root of the following functions, using co as given. Stop the iteration when the error as estimated by n+1 - Enl is less than 10-6. Compare to your results for bisection. (a) f(x) = 1-2xe-/2, xo = 0; (b) f(x)=5-x-¹, x = ¹; (c) f(x)= x³ - 2x - 5, xo = 2; (d) f(x)=e-2, xo = 1; (e) f(x)=x-e, xo = 1; (f) f(x)=x-x-1, xo = 1; (g) f(x)=x²-sinx, xo =/; (h) f(x)= x³-2,0 = 1; (i) f(x) = x + tan x, zo = 3; (j) f(x)=2x-¹ In x, xo = 3.
- Algorithm using constants and variableswrite a code using different algorithmExplain this Algorithm and Flowchart. Thank you Manual Solution: Fibonacci series: if you ask the Nth term of Fibonacci series then it would be the sum of (N-1)th and (N-2)th term of Fibonacci series. Tn= Tn-1 + Tn-2 It is fixed that 1st term of Fibonacci is 0. 2nd term is 1 3rd term is T3= T2 + T1 T3 = 1 + 0 = 1 4th term = T4 = T3 + T2 = 1 + 1 = 2. Fibonacci series = 0 1 1 2 3 5 8 13 21 . . . . . . . . . . . . . . . . . . . Algorithm of Fibonacci Series: Start Declare the variables n, t1,t2, nextTerm Initialize the variables, t1=0, t2=1, and nextTerm =0 Enter the number of terms of the Fibonacci series Print First two terms of series Use loop for the following steps-> nextTerm =t1+t2-> t1=t2-> t2=nextTerm -> increase the value of n each time by 1-> print the value of nextTerm End This is the flowchart below