Write script and report on findings. Piecewise functions are sometimes useful when the relationship between a dependent and independentvariable cannot be adequately represented by a single equation.velocity of a rocketbe described by10t² - 5t624 - 3tv(t)=36t+12(t-16)²2136.e-0.1(1-26)00≤t≤88 26otherwiseDevelop a Python function to compute v with an input of t. Then, add a script that uses the function togenerate a plot a v versus t for t = -5 to 50.

Rocket velocity is a crucial parameter in aerospace engineering, depicting the speed of a rocket at…

Answered: Python function

Engineering

Computer Science

Python function

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Write a python code that implements the Forward Euler method to solve thedifferential equation. The slope function depends on the unknown solution y(t). Define your slope function so that the model parameters, b, PM, h areinput variables in your function definition. Complete your code by writing a loop that calculates the solution foreach time point and can plot your final approximate solution.
import numpy as np # Define the differential equation functiondef func(t, y): return t - y**2# Define the initial conditions and parameterst0 = 0y0 = 1t_max = 2n = 10h = (t_max - t0) / n# Implement Euler's methodt = t0y = y0for i in range(n): y += h * func(t, y) t += hprint(y)print("\n")
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Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you ll in the values is the correct one.
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Prove that the coin changing problem exhibits optimal substructure. Design a recursive backtracking (brute-force) algorithm that returns the minimum number of coins needed to make change for n cents for any set of k different coin denominations. Write down the pseudocode and prove that your algorithm is correct.
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A student is interested in computing the area under the function f(x)=x over the interval [0,1] and decides to get an accurate answer using a Monte Carlo experiment (by this we are assuming the student doesn't know the answer to such an elementary mathematical question). Which of the following R codes will give such an approximate answer? M = 10^6x = runif(M)y = runif(M)mean( y <= x ) M = 10^6x = runif(M)mean( x ) M = 10^6x = rnorm(M)mean( x ) M = 10^6x = rnorm(M)y = runif(M)mean( y <= x )