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question:1.下表是水的表面张力对温度的函数数据: T(℃) 0 20 40 60 80 σ×103(N/m) 78.2 73.4 70.2 66.7 63.2 利用牛顿插值法求出穿过上述数据点的多项式,给出多项式即可
answer:首先列出差商表： | T | σ | Δ₁σ | Δ₂σ | Δ₃σ | Δ₄σ | |:---:|:-----:|:------:|:----:|:-----:|:----:| | 0 | 78.2 | | | | | | 20 | 73.4 | -4.8 | | | | | 40 | 70.2 | -3.2 | -0.8 | | | | 60 | 66.7 | -3.5 | -0.15| 0.1 | | | 80 | 63.2 | -3.5 | 0.0 | 0.05 | 0.01 | 则多项式为： P(x)=78.2-4.8x-3.2x(x-20)-0.15x(x-20)(x-40)+0.01x(x-20)(x-40)(x-60) 其中，x为温度（℃）。 注：为方便表述，Delta_i表示差商表中的第i阶差商。
question:import random artists_listeners = { 'NOT': 7781046, '21 Savage': 60358167, '9lokknine': 1680245, 'A Boogie Wit Da Hoodie': 18379137, 'Ayo & Teo': 1818645, 'Bhad Bhabie': 1915352, 'Blueface': 4890312, 'Bobby Shmurda': 2523069, 'Cardi B': 30319082, 'Central Cee': 22520846, 'Chief Keef': 9541580, 'Coi Leray': 28619269, 'DaBaby': 30353214, 'DDG': 4422588, 'Denzel Curry': 7555420, 'Desiigner': 5586908, 'Don Toliver': 27055150, 'Dusty Locane': 3213566, 'Est Gee': 5916299, 'Famous Dex': 2768895, 'Fivio Foreign': 9378678, 'Fredo Bang': 1311960, 'Future': 47165975, 'Gazo': 5342471, 'GloRilla': 6273110, 'Gunna': 23998763, 'Hotboii': 1816019, 'Iann Dior': 14092651, 'J. Cole': 36626203, 'JayDaYoungan': 1415050, 'Juice WRLD': 31818659, 'Key Glock': 10397097, 'King Von': 7608559, 'Kodak Black': 24267064, 'Latto': 10943008, 'Lil Baby': 30600740, 'Lil Durk': 20244848, 'Lil Keed': 2288807, 'Lil Loaded': 2130890, 'Lil Mabu': 2886517, 'Lil Mosey': 8260285, 'Lil Peep': 15028635, 'Lil Pump': 7530070, 'Lil Skies': 4895628, 'Lil Tecca': 13070702, 'Lil Tjay': 19119581, 'Lil Uzi Vert': 3538351, 'Lil Wayne': 32506473, 'Lil Xan': 2590180, 'Lil Yachty': 11932163, 'Machine Gun Kelly': 13883363, 'Megan Thee Stallion': 23815306, 'Moneybagg Yo': 11361158, 'NLE Choppa': 17472472, 'NoCap': 1030289, 'Offset': 15069868, 'Playboi Carti': 16406109, 'PnB Rock': 5127907, 'Polo G': 24374576, 'Pooh Shiesty': 4833055, 'Pop Smoke': 24438919, 'Quando Rondo': 1511549, 'Quavo': 15944317, 'Rod Wave': 8037875, 'Roddy Ricch': 22317355, 'Russ Millions': 6089378, 'Ski Mask The Slump God': 9417485, 'Sleepy Hallow': 8794484, 'Smokepurpp': 2377384, 'Soulja Boy': 10269586, 'SpottemGottem': 1421927, 'Takeoff': 9756119, 'Tay-K': 4449331, 'Tee Grizzley': 4052375, 'Travis Scott': 46625716, 'Trippie Redd': 19120728, 'Waka Flocka Flame': 5679474, 'XXXTENTACION': 35627974, 'YBN Nahmir': 4361289, 'YK Osiris': 1686619, 'YNW Melly': 8782917, 'YounBoy Never Broke Again': 18212921, 'Young M.A': 2274306, 'Young Nudy': 7553116, 'Young Thug': 28887553, 'Yungeen Ace': 1294188, } keys = list(artists_listeners.keys()) score = 0 while True: first_artist = random.choice(keys) second_artist = random.choice(keys) while first_artist == second_artist: second_artist = random.choice(keys) while True: guess = input(f"nWhich artist has more monthly Spotify listeners - 1. {first_artist.title()} or 2. {second_artist.title()}? ") guess_lower = guess.strip().lower() if guess_lower == 'quit': print("Thanks for playing!") quit() elif guess_lower not in ['1', '2', first_artist.lower(), second_artist.lower()]: print("Invalid input. Please enter the name of one of the two artists, type 'quit' to end the game or enter 1 or 2 to make a guess.") elif guess_lower == first_artist.lower() or guess_lower == '1' and artists_listeners[first_artist] > artists_listeners[second_artist]: print(f"You guessed correctly! {first_artist.title()} had {artists_listeners[first_artist] / 1e6:.1f}M monthly Spotify listeners and {second_artist.title()} has {artists_listeners[second_artist] / 1e6:.1f}M monthly Spotify listeners.") score += 1 break elif guess_lower == second_artist.lower() or guess_lower == '2' and artists_listeners[second_artist] > artists_listeners[first_artist]: print(f"You guessed correctly! {second_artist.title()} had {artists_listeners[second_artist] / 1e6:.1f}M monthly Spotify listeners and {first_artist.title()} has {artists_listeners[first_artist] / 1e6:.1f}M monthly Spotify listeners.") score += 1 break else: print(f"nSorry, you guessed incorrectly. {first_artist.title()} had {artists_listeners[first_artist] / 1e6:.1f}M monthly Spotify listeners and {second_artist.title()} has {artists_listeners[second_artist] / 1e6:.1f}M monthly Spotify listeners.n") score = 0 play_again = input("Would you like to play again? (y/n/Ent) ") if play_again.lower() == 'n': print("Thanks for playing!") quit() print(f"nYour score is {score}.") how can i change the code so images appear of the two rappers that are being compared
answer:To have images appear of the two rappers being compared, one way to approach it is to use a package like `Pillow` or `OpenCV` to display the images. Here's an example of how you could modify the code to display the images: ```python from PIL import Image # Define an images dictionary with the file paths of each rapper's image # Change the file paths to the location of the images on your machine images = { 'Lil Baby': 'lil_baby.jpg', 'Lil Durk': 'lil_durk.jpg', 'Lil Keed': 'lil_keed.jpg', # etc. } # Modify the while loop to display the images of the two rappers being compared while True: first_artist = random.choice(keys) second_artist = random.choice(keys) while first_artist == second_artist: second_artist = random.choice(keys) # Load the images of the artists first_image = Image.open(images[first_artist]) second_image = Image.open(images[second_artist]) # Display the images first_image.show() second_image.show() # Prompt the user to make a guess guess = input(f"nWhich artist has more monthly Spotify listeners - 1. {first_artist.title()} or 2. {second_artist.title()}? ") # Close the images of the artists first_image.close() second_image.close() # The rest of the code remains the same ``` In this example, we defined an `images` dictionary that maps each artist to the corresponding image file path. Inside the while loop, we load the images of the two artists using `Pillow`'s `Image.open()` method and display them using the `show()` method. After the user makes a guess, we close the images using the `close()` method. Note that you'll need to have the images saved locally and adjust the file paths in the `images` dictionary to match the location of the images on your machine. Additionally, you may want to resize the images to a consistent size for display purposes.
question:is does PIL need to be installed first like for example pip
answer:Yes, you will need to have `Pillow` installed in order to use the `Image` module. You can install it using `pip` by running: ``` pip install pillow ``` After installation, you can import the `Image` module as shown in the code example I provided.
question:so this should be added in the beginning?
answer:Yes, you can add the following line at the beginning of your code to import the `Image` module from `Pillow`: ```python from PIL import Image ``` Then, you can use the `Image` module to open and display the images in the way described in the previous answer. Don't forget to install `Pillow` first by running `pip install pillow` in your terminal or command prompt.