!["Maryland Retail Center Sold for $10M by CRC Brokers" # 2006 AMC 12B Problems/Problem 6. (Redirected from 2006 AMC 12B Problem 6) ## Problem. A circle of radius $r$ is inscribed in a semicircle. The semicircle is then inscribed in a square. What is the ratio of the area of the circle to the area of the square? $text {(A) } frac{pi}{8}qquad text {(B) } frac{pi}{6}qquad text {(C) } frac{pi}{4}qquad text {(D) } frac{pi}{3}qquad text {(E) } frac{pi}{2}$ ## Solution. [asy] unitsize(1cm); defaultpen(0.8); real r=1; pair A=(-1,0), B=(1,0), C=(0,1), D=(0,-1), O=(0,0); draw(A--B--C--cycle); draw(arc(O,r,0,180)); draw(O--(0.707,0.707)); label](https://cremarketbeat.com/wp-content/uploads/2025/01/CRC_Govenors.jpg)
“Maryland Retail Center Sold for $10M by CRC Brokers” # 2006 AMC 12B Problems/Problem 6. (Redirected from 2006 AMC 12B Problem 6) ## Problem. A circle of radius $r$ is inscribed in a semicircle. The semicircle is then inscribed in a square. What is the ratio of the area of the circle to the area of the square? $\text {(A) } \frac{\pi}{8}\qquad \text {(B) } \frac{\pi}{6}\qquad \text {(C) } \frac{\pi}{4}\qquad \text {(D) } \frac{\pi}{3}\qquad \text {(E) } \frac{\pi}{2}$ ## Solution. [asy] unitsize(1cm); defaultpen(0.8); real r=1; pair A=(-1,0), B=(1,0), C=(0,1), D=(0,-1), O=(0,0); draw(A–B–C–cycle); draw(arc(O,r,0,180)); draw(O–(0.707,0.707)); label
Continental Realty Corporation (CRC) has successfully sold Governors Commons, a popular shopping center located in Glen Burnie, Maryland. The property
January 24, 2025
!["Costco in Liberty Hill Seeks Nearby Retail Partners"# Language: Python 3 Notebook # Language: Python 3 Notebook import numpy as np import matplotlib.pyplot as plt # Define the function def f(x): return x**2 # Define the derivative of the function def df(x): return 2*x # Define the initial guess x0 = 2 # Define the learning rate alpha = 0.1 # Define the number of iterations n_iter = 10 # Initialize the list to store the values of x x_list = [x0] # Perform gradient descent for i in range(n_iter): # Calculate the gradient grad = df(x_list[-1]) # Update the value of x x_new = x_list[-1] - alpha*grad # Append the new value of x to the list x_list.append(x_new) # Convert the list to a numpy array x_list = np.array(x_list) # Plot the function and the gradient descent path x = np.linspace(-2, 2, 100) plt.plot(x, f(x)) plt.plot(x_list, f(x_list)](https://cremarketbeat.com/wp-content/uploads/2025/01/Costco-2.jpg)
