answer:Certainly! Here's a Python solution that uses the built-in `sorted()` function and list comprehension: ```python def sort_nums(lst, order): # Separate the list into multiples of 3 and others multiples_of_3 = [num for num in lst if num % 3 == 0] others = [num for num in lst if num % 3 != 0] # Sort the 'others' list in ascending or descending order if order == 'asc': others = sorted(others) else: # 'desc' others = sorted(others, reverse=True) # Append the 'multiples_of_3' list to the 'others' list result = others + multiples_of_3 return result # Test the function with example inputs lst = [3, 5, 2, 6, 8, 1] order = 'asc' print(sort_nums(lst, order)) # Output: [1, 2, 5, 8, 3, 6] lst = [3, 5, 2, 6, 8, 1] order = 'desc' print(sort_nums(lst, order)) # Output: [8, 5, 2, 1, 3, 6] ``` This solution first separates the original list into two lists: `multiples_of_3`, which contains integers that are multiples of 3, and `others`, which contains the remaining integers. It then sorts the `others` list in the specified order (ascending or descending), using the `sorted()` function. The `sorted()` function returns a new sorted list without modifying the original list. Finally, the solution concatenates the sorted `others` list with the `multiples_of_3` list using the `+` operator, resulting in the desired sorted list with the multiples of 3 grouped and sorted at the rightmost side. The order of the elements in `multiples_of_3` remains the same as in the original list, as required by the problem statement.

answer:1. **Identify the given elements and the goal:** - We have a triangle (ABC) with sides (AB = 10), (BC = 17), and (CA = 21). - Point (P) lies on the circle with diameter (AB). - We need to find the greatest possible area of triangle (APC). 2. **Understand the properties of the circle:** - Since (P) lies on the circle with diameter (AB), the circle is a semicircle with (AB) as the diameter. - Any angle subtended by the diameter of a circle is a right angle (Thales' theorem). Therefore, (angle APB = 90^circ). 3. **Use the right triangle property:** - Since (angle APB = 90^circ), triangle (APB) is a right triangle. - The area of triangle (APB) can be calculated using the formula for the area of a right triangle: (text{Area} = frac{1}{2} times text{base} times text{height}). 4. **Maximize the area of triangle (APC):** - To maximize the area of triangle (APC), we need to maximize the height from (C) to (AB). - Extend line (CA) to a point (D) such that (O) (the midpoint of (AB)) gets projected to (D) on line (AC). - The distance (DO) is the projection of (O) on (AC), and (OP = 5) (since (O) is the midpoint of (AB) and (AB = 10)). 5. **Calculate the maximum height (DP):** - The maximum height (DP) is the sum of (DO) and (OP). - Given (DO = 4) (since (O) is the midpoint of (AB) and the projection of (O) on (AC) is (4)), and (OP = 5), we have: [ DP = DO + OP = 4 + 5 = 9 ] 6. **Calculate the area of triangle (APC):** - The area of triangle (APC) is given by: [ text{Area} = frac{1}{2} times text{base} times text{height} = frac{1}{2} times 21 times 9 = frac{189}{2} ] (blacksquare) The final answer is ( boxed{ frac{189}{2} } )

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answer:Title: Drug Gang Members Sentenced for Supplying Cocaine from Liverpool to Wales Introduction: A UK court has sentenced members of a notorious drugs gang for their involvement in the distribution of cocaine from Liverpool to west and south Wales. The criminal organization, responsible for a substantial drug supply chain, has finally met its downfall as its members face jail time. Step 1: Describe the drug gang and their operations The drugs gang, known for its widespread network, was involved in the supply of substantial quantities of cocaine from Liverpool to various locations in west and south Wales. The organization played a significant role in expanding the illicit drug trade in these regions and profiting from the addiction and misery of countless individuals. Step 2: Discuss the police investigation and arrests A thorough and extensive investigation by the police led to the arrests of several members of the gang, uncovering their extensive network and operations. The officers' relentless pursuit of justice brought down this criminal empire, significantly disrupting the drug trade in the regions it operated. The investigation also highlighted the tactics used by the gang, such as exploiting vulnerable individuals and infiltrating communities to expand their reach. Step 3: Detail the court proceedings and sentencing Following the arrests of the involved individuals, the case went to court, where the prosecution meticulously laid out the evidence against the gang members. The court heard arguments from both the prosecution and defense, delving into the extent of the gang's activities, their supply chain, and the impact of their actions on the communities they infiltrated. Ultimately, the judge handed down jail terms to the gang members for their involvement in the supply of cocaine. The sentences varied in length, reflecting the varying degrees of involvement and influence within the organization. Step 4: Highlight the impact of the sentencing on affected communities The jailing of these individuals has brought a sense of relief and vindication to the communities affected by their illicit operations. With a significant drug supply chain dismantled, it is hoped that this will discourage other potential criminals from entering the drug trade and help reduce drug-related crime in the regions. Step 5: Discuss the importance of continued efforts against drug-related crime While the sentencing of this drugs gang is indeed a victory against drug-related crime, it is crucial to recognize that the fight against drug trafficking and distribution continues. Authorities must maintain vigilance and implement effective preventative measures to further crack down on drug-related crime and protect the public from the harm caused by these substances. Conclusion: The sentencing of the drug gang members marks a significant milestone in the battle against drug trafficking and distribution in the UK. The jailing of these individuals serves as a stark reminder of the consequences of engaging in criminal activities. It is crucial for authorities to continue their efforts to dismantle similar drug networks and safeguard communities from the destructive impact of illicit substances, ensuring a safer and healthier society for all.