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(Geometry: great circle distance) The great circle distance is the distance between two points on the surface of a sphere. Let
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- (Algebra: solve 2 x 2 linear equations) You can use Cramer's rule to solve the following 2 x 2 system of linear equation: ax + by = e ed – bf af- ec ad - bc cx + dy = f ad – bc y = Write a program that prompts the user to enter a and f and display the result. If ad - bc is 0 b, c, d , e, , report that The equation has no solution.arrow_forwardHeat capacity of a solid: Debye's theory of solids gives the heat capacity of a solid at temperature T to be 3 T rOp/T Cy = 9VpkB (e* – 1)2 dx, - where V is the volume of the solid, p is the number density of atoms, kg is Boltzmann's constant, and 0D is the so-called Debye temperature, a property of solids that depends on their density and speed of sound. Develop a computer code to evaluate Cy (T) for a given value of the temperature, for a sample consisting of 1000 cubic centimeters of solid aluminum, which has a number density of p = 6.022 x 1028m-3 and a Debye temperature of 0p = 428K. The Boltzmann's constant kg = 1.380649 x 10-23 J · K-1. Please evaluate the integral with the following methods: (a) MATLAB adaptive Simpson quadrature, [Q.FCNT] = QUAD(FUN,A,B,TOL) with TOL =le-10.arrow_forwardQ1) 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.arrow_forward
- b) What is the difference between (x+H), (x+-), and (--x). c) Write the purpose for the use of the following: =, |I, //arrow_forward(Physics: acceleration) Average acceleration is defined as the change of velocity divided by the time taken to make the change, as shown in the following formula: a = (v1 - v0) / t Here, v0 is the starting velocity in meters per second, v1 is the ending velocity in meters per second, and t is the time span in seconds. Assume v0 is 5.6, v1 is 10.5, and t is 0.5, and write the code to display the average acceleration. Class Name: Exercise01_02Extraarrow_forward(Algebra: solve 2 X 2 linear equations) You can use Cramer's rule to solve the following 2 x 2 system of linear equations: ed – bf af – ec y bc ax + by = e X = cx + dy = f ad ad – bc Write a function with the following header: void solveEquation(double a, double b, double c, double d, double e, double f, double& x, double& y, bool& isSolvable) If ad – bc is 0, the equation has no solution and isSolvable should be false. Write a program that prompts the user to enter a, b, c, d, e, and f and displays the result. If ad – bc is 0, report that "The equation has no solution." See Program- ming Exercise 3.3 for sample runs.arrow_forward
- Find the error in the following codearrow_forward## MP (Machine Problem) Details The bulls and cows game is a code-breaking game designed for two or more players. Each player chooses a secret code of 4 digits from 0 – 9. The digits must be all different. The goal of the game is for each player to guess the other player's secret code. The players in turn present their guesses to the opponents. The opponents respond by telling the players: 1. The number of bulls, i.e. the number of matching digits in their right positions, and 2. The number of cows, i.e. the number of matching digits but in different positions. ### Requirements The main goal of this assignment is to develop the bulls and cows game that allows a single player to play interactively against the computer. The game stores two secret codes, one from the player and one from the computer. The player and the computer will try to guess each other’s secret code. Both the player and the computer only have seven attempts for guessing the secret code. If the player enters invalid…arrow_forwardPYTHON (Uee While Loop) only Write a python program that calculates the populations of foxes and rabbits who live within a certain area of land, as that number changes from year to year. It will take the initial populations as inputs, and then proceed to calculate the year-by-year changes. The following is derived from the “Lotka-Volterra equations”, which you may look up if you desire. Essentially, we will model the foxes and rabbits with 4 constants, and 2 data structures of year-by-year values. They are defined as follows: r[y] # of rabbits in year y f[y] # of foxes in year y α or alpha - birth rate of rabbits β or beta - death rate of rabbits, dependent on # of foxes γ or gamma - birth rate of foxes, dependent on # of rabbits δ or delta - death rate of foxes, caused naturally The formulas we will use are: r[y]=r[y−1]+(r[y−1]×α)−(r[y−1]×f[y−1]×β)r[y]=r[y−1]+(r[y−1]×α)−(r[y−1]×f[y−1]×β) f[y]=f[y−1]+(f[y−1]×r[y−1]×γ)−(f[y−1]×δ)f[y]=f[y−1]+(f[y−1]×r[y−1]×γ)−(f[y−1]×δ) However,…arrow_forward
- Computer Science Please help You went camping overnight but forgot to take with you a heater and need to make one using a dc battery of V0 and spare electrical wires of different lengths and resistivity. The battery has lead with the resistance of Rw. Please obtain the formula for the joule heat power and plot it as a function of RH ( in MATLAB) and in comparison to the resistance of the connecting leads, Rw. (Note: express RH = x Rw, where x is the effective ratio; vary x and plot Pmax vs. x). and Find the heating power if the heater is made out of superconducting metal. Will this heater work and why?! What is to happen on the molecular ( i.e. electron) level ?!arrow_forwardUse Newton’s method to: (a) Create a program that computes for the power am/n given a real number a. You are not allowed to use roots, or raise numbers to fractional powers in the formula. [Hint: This value is the solution of xn − am = 0.] (b) Create a program that computes for arcsin(x) of a given number x ∈ [0, 1]. You are not allowed to use inverse trigonometric functions in the formula but trigonometric functions such as sin, cos, tan are allowed.arrow_forward6.Coding-----""Euler's totient function, also known as phi-function ϕ(n),counts the number of integers between 1 and n inclusive,which are coprime to n.(Two numbers are coprime if their greatest common divisor (GCD) equals 1)."""def euler_totient(n): """Euler's totient function or Phi function. Time Complexity: O(sqrt(n)).""" result = n for i in range(2, int(n ** 0.5) + 1): if n % i == 0: while n % i == 0: n //= i.arrow_forward
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