Let there be a sequence of numbers defined by fo=0, fi = 1, and fn=fn-1 + fn-2, for n > 1. (a) For n = 0, give a value of f3n. (b) For n > 0, give an expression for f3n in terms of f3n-2 and f3(n-1).
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- Ql: The Collatz conjecture function is defined for a positive integer m as follows. (COO1) g(m) = 3m+1 if m is odd = m/2 if m is even =1 if m=1 The repeated application of the Collatz conjecture function, as follows: g(n), g(g(n)), g(g(g(n))), ... e.g. If m=17, the sequence is 1. g(17) = 52 2. g(52) = 26 3. g(26) = 13 4. g(13) = 40 5. g(40) = 20 6. g(20) = 10 7. g(10) = 5 8. g(5) = 16 9. g(16) = 8 10. g(8) = 4 11. g(4) = 2 12. g(2) = 1 Thus if m=17, apply the function 12 times in order to reach m=1. Use Recursive Function.INTRODUCTION: Heat conduction from a cylindrical solid wall of a pipe can be determined by the follow T1-T2 q = 2nLk R2 In R. where: q is the computed heat conduction in Watts. k is the thermal conductivity of the pipe material in Watts/°C/m. L is the length of the pipe in cm. Ri is the inner radius of the pipe in cm. R2 is the outer radius of the pipe in cm. Ti is the internal temperature in °C. T2 is the external temperature in °C. ASSIGNMENT: Write a C program that will allow the user to enter the inner and outer radii of the pipe, the the internal and external temperatures. Once the user enters the input values, the programThe velocity v and the falling distance d as a function of time of a skydiver that experience the air resistance can be approximated by: and d() = " in cosh :) kg v(t) = mg tanh where k = 0.24 Kg is a constant, m is the skydiver mass, g = 9.81 " is the acceleration due to gravity, and t is the time in seconds since the skydiver starts falling. Write m MATLAB code to determine the velocity v and the falling distance d at t = 8s for a 95kg skydiver. • Note: Velocity v and distance d are each worth 50% of the total points for this problem. Script e C Reset I MATLAB Docume 1 % Define variable(s) here. 3 v = % write the equation for v here, do not change the variable name. 4 d = % write the equation for d here, do not change the variable name.
- In the example below, the sum of the fourth powers of each digit that forms the 4-digit numbers gives the number itself: 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474 = 94 + 44 + 74 + 44 And sum of these numbers is 1634 + 8208 + 9474 = 19316. Find the sum of all numbers that can be written as the sum of the fifth forces of their numbers. (P.s.: You have to done it by C++)The distance d between a point p(x, y), where x and y are the coordinates of p, and the center of a circle (a, b), where a and b are the coordinates of the center, is given by the formula: (a, b). r d = (x – a)² + (y – b)² r The point p(x, y) is considered inside the circle if d r. (x, y)' (x', y') Write a Java class called CirclePointthat: a. Reads from the user 2 integer values x and y represent the coordinates of the point p, b. Reads from the user 2 integer values a and b represent the coordinates of the center of the circle, c. Reads from the user a real value r represents the radius of the circle, d. Calculates and prints the distance d (rounded to 2 decimal places) between the point p and the center of the circle, and e. Checks and prints whether the point is inside, on or outside the circle. NOTE: if the radius value is negative, an error message should be shown. Sample Run 1: ==================== Enter the coordinates of the point: 5 7 Enter the coordinates of the center of…An approximation to the integral of a function f(x) over an interval [a, b] can be found by first approximating f(x) by the straight line that goes through the end points (a, f(a)) and (b, f(b)), and then finding the area under the straight line, which is the area of a trapezoid. Write a function trapezint(f, a, b) that returns this approximation to the integral. Test your code by integrating cos(x) and sin(x) from 0 to π.
- 3. Give the regular expression, NFA, and DFA for L, = {w: w ends in 00 or 01}, where Σ (0, 1 .Q1.What is the smallest 32-bit floating point number f such that 128 + f > 128 ? What is the smallest 32-bit floating point number g such that 1 + g > 1 ? What is the relationship between f and g? Where f and g are differentiable functions. We have found that the given functions have the same derivative. In general, if two differentiable functions differs by a constant at x, its derivatives slopes at this point are the same. Write a short C++ or Python program to support your answer (for example, show that you checked whether there is no smaller number than your f by trying 128+f/2 == 128. Q2. Explain what changes are needed to change the 4x3 memory presented on Slide 62 of Chapter 3 to a 16x6 memory.If a, b, and c are the three sides of a triangle, then its area is, Area = √[s(s-a)(s-b)(s-c)]Here, "s" is the semi-perimeter of the triangle, i.e., s = (a + b + c)/2. However to be a validtriangle “the summation of any two sides should be greater than the third side.”i) Now Design a Class Triangle with a method checkValid() that returns true if it satisfies the criteria of a valid triangle.ii) Write down a method throwException() that uses the checkValid() and throws OwnException as described below.iii) Your own Exception class OwnException will throw an Exception if the valid triangle criteria is not satisfied with the information of “Not a real triangle” with the values of three sides.iv) A triangle object can be only instantiated with the value of three sides if it is a valid triangle otherwise an exception will be thrown. Similarly changing the sides of a triangle is possible if it satisfies the above criteria otherwise an exception will be thrown.v) In the Driver Class gets the…
- Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X BIf a, b, and c are the three sides of a triangle, then its area is, Area = √[s(s-a)(s-b)(s-c)] Here, "s" is the semi-perimeter of the triangle, i.e., s = (a + b + c)/2. However to be a valid triangle “the summation of any two sides should be greater than the third side.” i) Now Design a Class Triangle with a method checkValid() that returns true if it satisfies the criteria of a valid triangle. ii) Write down a method throwException() that uses the checkValid() and throws OwnException as described below. iii) Your own Exception class OwnException will throw an Exception if the valid triangle criteria is not satisfied with the information of “Not a real triangle” with the values of three sides. iv) A triangle object can be only instantiated with the value of three sides if it is a valid triangle otherwise an exception will be thrown. Similarly changing the sides of a triangle is possible if it satisfies the above criteria otherwise an exception will be thrown. v) In the Driver Class get…Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of %3D %3D * fog is бх + 6 бх +9 бх + 7 бх + 8