answer:Here's the complete Python code for simple interest calculations: ```python def calculate_simple_interest(principal, rate, time): simple_interest = (principal * rate * time) / 100 return simple_interest def calculate_total_amount(principal, rate, time): simple_interest = calculate_simple_interest(principal, rate, time) total_amount = principal + simple_interest return total_amount def calculate_rate_of_interest(principal, total_amount, time): simple_interest = total_amount - principal rate = (simple_interest * 100) / (principal * time) return rate def calculate_time_period(principal, total_amount, rate): simple_interest = total_amount - principal time = (simple_interest * 100) / (principal * rate) return time def simple_interest_calculations(): while True: print(nSimple Interest Calculations Menu:) print(1. Calculate Simple Interest) print(2. Calculate Total Amount) print(3. Calculate Rate of Interest) print(4. Calculate Time Period) print(5. Quit) choice = int(input(Enter your choice: )) if choice == 1: principal = float(input(Enter the principal amount: )) rate = float(input(Enter the rate of interest (in %): )) time = float(input(Enter the time period (in years): )) simple_interest = calculate_simple_interest(principal, rate, time) print(fSimple Interest: Rs {simple_interest}) elif choice == 2: principal = float(input(Enter the principal amount: )) rate = float(input(Enter the rate of interest (in %): )) time = float(input(Enter the time period (in years): )) total_amount = calculate_total_amount(principal, rate, time) print(fTotal Amount to be paid after {time} years: Rs {total_amount}) elif choice == 3: principal = float(input(Enter the principal amount: )) total_amount = float(input(Enter the total amount: )) time = float(input(Enter the time period (in years): )) rate_of_interest = calculate_rate_of_interest(principal, total_amount, time) print(fRate of Interest: {rate_of_interest}%) elif choice == 4: principal = float(input(Enter the principal amount: )) total_amount = float(input(Enter the total amount: )) rate = float(input(Enter the rate of interest (in %): )) time_period = calculate_time_period(principal, total_amount, rate) print(fTime Period: {time_period} years) elif choice == 5: print(Exiting program. Goodbye!) break else: print(Invalid choice. Please try again.) if __name__ == __main__: simple_interest_calculations() ``` This code presents a menu to the user for different simple interest calculations. It then takes input from the user based on their choice and displays the result. The user can continue to perform different calculations until they choose to quit.

answer:Here's the complete Python code for solving quadratic equations with interactive menu and input validation: ```python import math def solve_quadratic_equation(a, b, c): # Calculate the determinant determinant = b**2 - 4*a*c print(fDeterminant: {determinant}) if determinant > 0: print(The equation has two distinct solutions.) root1 = (-b + math.sqrt(determinant)) / (2*a) root2 = (-b - math.sqrt(determinant)) / (2*a) print(fThe solutions are: {root1} and {root2}) elif determinant == 0: print(The equation has one repeated solution.) root = -b / (2*a) print(fThe solution is: {root}) else: print(The equation has two complex solutions.) real_part = -b / (2*a) imaginary_part = math.sqrt(-determinant) / (2*a) print(fThe solutions are: {real_part} + {imaginary_part}i and {real_part} - {imaginary_part}i) def main(): while True: print(nQuadratic Equation Solver Menu:) print(1. Solve Quadratic Equation) print(2. Quit) choice = int(input(Enter your choice: )) if choice == 1: # Get coefficients from the user while True: try: a = float(input(Enter the coefficient a (cannot be zero): )) if a == 0: print(Coefficient a cannot be zero. Please try again.) else: break except ValueError: print(Invalid input. Please enter a number.) b = float(input(Enter the coefficient b: )) c = float(input(Enter the coefficient c: )) # Solve the quadratic equation solve_quadratic_equation(a, b, c) elif choice == 2: print(Exiting program. Goodbye!) break else: print(Invalid choice. Please try again.) if __name__ == __main__: main() ``` This code presents a menu to the user for solving quadratic equations. It then takes input from the user for the coefficients a, b, and c, ensuring that a is not zero. It calculates the determinant and displays the solutions based on the determinant's value. The user can continue to solve quadratic equations until they choose to quit.

answer:The provided Python code is already quite comprehensive, handling both Celsius to Fahrenheit and Fahrenheit to Celsius conversions, as well as invalid inputs. However, here's a slightly modified version that includes some minor improvements and additional features: ```python def celsius_to_fahrenheit(celsius): fahrenheit = (celsius * 9/5) + 32 return fahrenheit def fahrenheit_to_celsius(fahrenheit): celsius = (fahrenheit - 32) * 5/9 return celsius def get_float_input(prompt): while True: try: value = float(input(prompt)) return value except ValueError: print(Invalid input. Please enter a number.) def get_choice(): while True: try: choice = int(input(Enter your choice: )) if choice < 1 or choice > 3: print(Invalid choice. Please enter a number between 1 and 3.) else: return choice except ValueError: print(Invalid input. Please enter a number.) def print_conversion_result(original_value, original_unit, converted_value, converted_unit): print(f{original_value}°{original_unit} is equal to {converted_value}°{converted_unit}) def main(): while True: print(nTemperature Conversion Menu:) print(1. Celsius to Fahrenheit) print(2. Fahrenheit to Celsius) print(3. Quit) choice = get_choice() if choice == 1: celsius = get_float_input(Enter temperature in Celsius: ) fahrenheit = celsius_to_fahrenheit(celsius) print_conversion_result(celsius, C, fahrenheit, F) elif choice == 2: fahrenheit = get_float_input(Enter temperature in Fahrenheit: ) celsius = fahrenheit_to_celsius(fahrenheit) print_conversion_result(fahrenheit, F, celsius, C) elif choice == 3: print(Exiting program. Goodbye!) break if __name__ == __main__: main() ``` In this modified version, a new function `print_conversion_result` is introduced to handle printing the conversion results in a more structured and readable way. Additionally, the input prompts are slightly modified for clarity and consistency. Overall, the code remains well-structured and user-friendly.

answer:1. Let ( t_1, t_2, t_3, t_4 ) be the times (in hours) that you spend on the essays, respectively. Since there are 4 hours and 5 minutes until class, and you want each essay to actually give you points, the ( t_i ) are multiples of ( frac{1}{2} ), and they sum to 4 (4 hours). 2. The score for each essay is given by: [ 100 left( 1 - frac{1}{4^{t_i}} right) ] Therefore, the total score for all four essays is: [ 100 left( 1 - frac{1}{4^{t_1}} right) + 100 left( 1 - frac{1}{4^{t_2}} right) + 100 left( 1 - frac{1}{4^{t_3}} right) + 100 left( 1 - frac{1}{4^{t_4}} right) ] Simplifying, we get: [ 400 - 100 left( frac{1}{4^{t_1}} + frac{1}{4^{t_2}} + frac{1}{4^{t_3}} + frac{1}{4^{t_4}} right) ] 3. To maximize the total score, we need to minimize: [ frac{1}{4^{t_1}} + frac{1}{4^{t_2}} + frac{1}{4^{t_3}} + frac{1}{4^{t_4}} ] 4. By the Arithmetic Mean-Geometric Mean (AM-GM) Inequality, we have: [ frac{1}{4^{t_1}} + frac{1}{4^{t_2}} + frac{1}{4^{t_3}} + frac{1}{4^{t_4}} ge 4 sqrt[4]{frac{1}{4^{t_1 + t_2 + t_3 + t_4}}} ] Since ( t_1 + t_2 + t_3 + t_4 = 4 ), we get: [ 4 sqrt[4]{frac{1}{4^4}} = 4 sqrt[4]{frac{1}{256}} = 4 cdot frac{1}{4} = 1 ] 5. Equality in the AM-GM inequality holds if and only if ( t_1 = t_2 = t_3 = t_4 = 1 ). This works since each ( t_i ) is a multiple of ( frac{1}{2} ). 6. Therefore, the minimum value of ( frac{1}{4^{t_1}} + frac{1}{4^{t_2}} + frac{1}{4^{t_3}} + frac{1}{4^{t_4}} ) is 1, and the maximum total score is: [ 400 - 100 cdot 1 = 300 ] 7. The maximum possible average of your essay scores is: [ frac{300}{4} = 75 ] The final answer is (boxed{75})