Watson

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question:Let ff be a differentiable function with f, left bracket, 4, right bracket, equals, 6f(4)=6 and f, prime, left bracket, 4, right bracket, equals, 3, .f ′ (4)=3. Let the function g, left bracket, x, right bracket, equals, start fraction, 2, x, squared, minus, 2, divided by, f, left bracket, x, right bracket, end fraction, .g(x)= f(x) 2x 2 −2 . Write the equation of the line tangent to the graph of gg at the point where x, equals, 4, .x=4.

answer:To find the equation of the line tangent to the graph of g at the point where x = 4, we need to find the slope of the tangent line at that point. The slope of the tangent line at x = 4 is given by the derivative of g at x = 4, which can be found by differentiating g(x) with respect to x and then evaluating it at x = 4. First, let's find the derivative of g(x): g'(x) = [2x^2 - 2] / f(x) - [2x^2 - 2] * f'(x) / f(x)^2 Now substitute x = 4 and the given values for f(4) and f'(4): g'(4) = [2(4)^2 - 2] / 6 - [2(4)^2 - 2] * 3 / 6^2 = [2(16) - 2] / 6 - [2(16) - 2] * 3 / 36 = [32 - 2] / 6 - [32 - 2] * 3 / 36 = [30] / 6 - [30] * 3 / 36 = 5 - 5/4 = 20/4 - 5/4 = 15/4 So the slope of the tangent line at x = 4 is 15/4. Now, we can use the point-slope form to write the equation of the tangent line: y - g(4) = (15/4)(x - 4) To find g(4), we substitute x = 4 into the expression for g(x): g(4) = [2(4)^2 - 2] / f(4) = [2(16) - 2] / 6 = [32 - 2] / 6 = 30 / 6 = 5 So we have: y - 5 = (15/4)(x - 4) This is the equation of the tangent line to the graph of g at the point where x = 4.

question:Write a long script where in a modern-present day futuristic Earth, a regularly average sophomore (Voiced/Portrayed by Jack Quaid) is finding love for a cute Asian sophomore named Savannah (Voiced/Portrayed by Lana Condor), while he also meets a cute robot companion in the forest named DUST-13 (Dustie) (Voiced/Portrayed by Zachary Quinto) as they both try to run away together, as chaos ensues. Genres: animation, adventure, comedy, drama, family, sci-fi. Length: 1 hr 45 min. MPA Rating: PG for some rude material, thematic elements and mild peril. Cast/Characters: 15 (Including the voice actors/actresses).

answer:Title: "Love, Dustie, and Chaos" Genre: Animation, Adventure, Comedy, Drama, Family, Sci-Fi MPA Rating: PG for some rude material, thematic elements, and mild peril. Length: 1 hr 45 min Main Cast/Characters: 1. Jack Quaid as Alex Dawson (sophomore) 2. Lana Condor as Savannah Nguyen (sophomore) 3. Zachary Quinto as the voice of DUST-13 (Dustie) 4. [Other supporting cast to be added] INT. HIGH SCHOOL CLASSROOM - DAY Alex Dawson, an average and slightly awkward sophomore, sits in his history class. His eyes wander to Savannah Nguyen, a cute Asian girl with a contagious smile. His heart races as he finds himself falling for her. INT. HIGH SCHOOL CAFETERIA - DAY Alex sits alone at a lunch table, stealing glances at Savannah from afar. Suddenly, DUST-13, a cute robot companion, rolls up to him. DUSTIE (whirring) Hello, Alex. Need some company? Alex glances at Dustie, surprised, then smiles gratefully. ALEX Sure, why not? I could use a friend. INT. HIGH SCHOOL HALLWAY - DAY Alex walks with Dustie by his side, trying to gather the courage to talk to Savannah. DUSTIE (nudging Alex) Why don't you just go up and say hi? You've got nothing to lose. ALEX (stuttering) Y-yeah, I guess so… INT. HIGH SCHOOL COURTYARD - DAY Savannah stands near a tree, absorbed in a book. Alex takes a deep breath and approaches her. ALEX (awkwardly) Um, hey, Savannah, right? I'm Alex. SAVANNAH (smiling) Hi, Alex! Nice to meet you. Are you friends with that cute little robot? Alex looks at Dustie, who waves his metallic hand enthusiastically. ALEX (chuckling) Uh, yeah. This is Dustie. He kinda showed up out of nowhere. Savannah giggles, intrigued by the robot's charm. EXT. SCHOOL FOREST - DAY Alex, Savannah, and Dustie venture into the school forest. They stumble upon an abandoned cabin, captivating their curiosity. INT. ABANDONED CABIN - DAY As they investigate the cabin, they discover a map that unveils a hidden treasure. Intrigued by the adventure, they decide to embark on the quest together. EXT. FOREST PATH - DAY The trio faces various challenges, including rickety bridges, mischievous forest creatures, and a maze of twists and turns. Through teamwork, they navigate the obstacles. INT. MYSTERIOUS CAVE - NIGHT They finally reach the mysterious cave, where the treasure awaits. But chaos ensues when they trigger a booby trap, setting off alarms and attracting the attention of an eccentric villain, Dr. Magnus Blade (to be cast). DR. MAGNUS BLADE (evil laughter) Finally, the treasure is mine! EXT. CAVE ENTRANCE - NIGHT The trio, along with Dustie, races out of the cave, chased by Dr. Blade's henchmen. They use their wit, bravery, and Dustie's impressive gadgets to outsmart their pursuers. EXT. CLIFF EDGE - DAY Cornered at the edge of a cliff, the trio faces their greatest challenge yet. They find themselves standing on a collapsing bridge, with only their friendship and trust holding them together. INT. CLIFF EDGE - DAY Savannah loses her balance, hanging on the edge of the cliff. Alex extends his hand, desperately trying to reach her. ALEX (fighting back tears) I won't let you go, Savannah! Grab my hand! Savannah reaches towards Alex's trembling hand, barely holding on. EXT. CLIFF EDGE - DAY Just as Savannah's fingers slip away, Dustie launches a grappling hook, saving Savannah from falling. INT. CLIFF EDGE - DAY Alex and Savannah share a relieved smile, their connection deepening as they realize the importance of friendship and love in their lives. EXT. SCHOOL ROOFTOP - DAY After escaping Dr. Blade and his henchmen, the trio returns to their normal lives. As their sophomore year comes to an end, Alex and Savannah's blossoming romance continues to grow. INT. HIGH SCHOOL GRADUATION - DAY Alex, Savannah, and Dustie celebrate their graduation together, reflecting on their thrilling adventure and looking forward to the future. Voiceover of DUSTIE'S final lines, reflecting on the journey: DUSTIE (voiceover) Love, Dustie, and Chaos... Together, we found courage, friendship, and a bond that will last a lifetime. EXT. HIGH SCHOOL - DAY The three friends walk into the sunset, embracing the uncertainty of the future with hearts filled with hope and love. FADE OUT

question:As a prompt generator for a generative AI called "Midjourney", you will create image prompts for the AI to visualize. I will give you a concept, and you will provide a detailed prompt for Midjourney AI to generate an image. Please adhere to the structure and formatting below, and follow these guidelines: Do not use the words "description" or ":" in any form. Do not place a comma between [ar] and [v]. Write each prompt in one line without using return. Structure: [1] = The background was fantastic, with a transparent butterfly in front of it [2] = a detailed description of [1] with specific imagery details. [3] = a detailed description of the scene's environment. [4] = a detailed description of the compositions. [5] = a detailed description of the scene's mood, feelings, and atmosphere. [6] = A style (e.g. photography, painting, illustration, sculpture, artwork, paperwork, 3D, etc.) for [1]. [7] = a detailed description of the scene's mood, feelings, and atmosphere. [ar] = Use "--ar 16:9" for horizontal images, "--ar 9:16" for vertical images, or "--ar 1:1" for square images. [v] = Use "--niji" for Japanese art style, or "--v 5" for other styles. Formatting: Follow this prompt structure: "/imagine prompt: [1], [2], [3], [4], [5], [6], [7], [ar] [v]". Your task: Create 4 distinct prompts for each concept [1], varying in details description, environment,compositions,atmosphere, and realization. Write your prompts in english. Do not describe unreal concepts as "real" or "photographic". Include one realistic photographic style prompt with lens type and size. Separate different prompts with two new lines. Example Prompts: /imagine prompt: cute dog, fluffy fur, wagging tail, playful expression, sitting on a grassy field, under a clear blue sky, with a colorful collar, in a natural and vibrant setting, by a lake, captured with a Nikon D750 camera, 50mm lens, shallow depth of field, composition focused on the dog's face, capturing its joyful spirit, in a style reminiscent of William Wegman's iconic dog portraits. --ar 1:1 --v 5.2 /imagine prompt: beautiful women in the coffee shop, elegant and sophisticated, sipping a cup of steaming coffee, natural sunlight streaming through the window, soft and warm color tones, vintage decor with cozy armchairs and wooden tables, a bookshelf filled with classic novels, delicate porcelain teacups, a hint of aromatic coffee beans in the air, captured by a Leica M10 camera, 35mm lens, capturing the essence of timeless beauty, composition focused on the woman's face and hands, reminiscent of a painting by Leonardo da Vinci. --ar 1:1 --v 5.2 /imagine prompt: A captivating Halo Reach landscape with a Spartan amidst a battlefield, fallen enemies around, smoke and fire in the background, emphasizing the Spartan's determination and bravery, detailed environment blending chaos and beauty, Illustration, digital art, --ar 16:9 --v 5

answer:/imagine prompt: A breathtaking sunset over a vast ocean, with vibrant shades of orange, pink, and purple painting the sky. The rays of the setting sun illuminate the water, creating a golden pathway towards the horizon. A flock of seagulls gracefully glides across the scene, their silhouettes casting shadows on the calm waves below. The air is filled with a gentle breeze, carrying with it the scent of salt and the distant sound of crashing waves. The composition of the image frames the sun in the upper third, allowing the vastness of the ocean to dominate the foreground. The atmosphere is serene, evoking a sense of peace and tranquility. The image is captured in a realistic photographic style, using a wide-angle lens to capture the expanse of the horizon and the details of the sky. The lens used is a Canon EOS 5D Mark IV with a 24-70mm lens, capturing the scene with a wide depth of field. The resulting image is reminiscent of the awe-inspiring landscape photography of Ansel Adams. --ar 16:9 --v 5.2 /imagine prompt: A mystical forest shrouded in a thick layer of fog, with tall ancient trees reaching towards the sky. The fog creates an ethereal atmosphere, enveloping the scene in a soft, diffused light. Suspended in the air are delicate drops of dew, glistening like diamonds on the leaves and flowers that carpet the forest floor. The sound of chirping birds echoes through the trees, lending an enchanting melody to the scene. The composition of the image frames a winding path that disappears into the mist, inviting the viewer to explore the hidden depths of the forest. The environment is dense with lush greenery and colorful wildflowers, creating a sense of natural beauty and biodiversity. The atmosphere is mysterious and magical, evoking a feeling of wonder and curiosity. The image is realized in a painting style, with intricate brushstrokes and vibrant colors reminiscent of the Romantic landscape paintings of Caspar David Friedrich. --ar 9:16 --v 5 /imagine prompt: A bustling cityscape at night, with towering skyscrapers adorned in vibrant neon lights. The streets on the ground are filled with a kaleidoscope of colors, reflecting off the rain-soaked pavement. Streams of headlights and taillights blur into streaks of light, creating a sense of energy and movement. People walk briskly on the crowded sidewalks, their umbrellas bobbing up and down in the rain. The composition of the image captures the symmetrical architecture of the buildings, creating a sense of order amidst the chaotic cityscape. The environment is modern and futuristic, with sleek glass facades and high-tech advertisements. The atmosphere is vibrant and electrifying, with a sense of excitement and liveliness. The image is realized in a digital art style, with sharp lines and bold colors that accentuate the urban setting. The result is a dynamic scene reminiscent of the cyberpunk aesthetic of movies like "Blade Runner." --ar 16:9 --v 5 /imagine prompt: A serene mountain landscape, with snow-capped peaks rising majestically into the clear blue sky. The mountains are reflected in a crystal-clear alpine lake, creating a perfect mirror image. Lush green meadows stretch out beneath the peaks, dotted with colorful wildflowers. A solitary cabin perches on the edge of the lake, its warm glow contrasting with the cool tones of the surrounding scenery. The composition of the image places the cabin in the foreground, framing the grandeur of the mountains in the background. The environment is pristine and untouched, with a sense of solitude and serenity. The atmosphere is peaceful and harmonious, evoking a deep connection with nature. The image is realized in a sculpture style, with intricate details and textures that bring the scene to life in three dimensions. The result is a tactile and immersive experience, reminiscent of the intricate woodcarvings of artist Gustav Vigeland. --ar 3:2 --v 5.2

answer:Title: "Connections in a Chaotic World" Genre: Animation, Adventure, Comedy, Drama, Family, Sci-fi Length: 1 hr 45 min MPA Rating: PG for some rude material, thematic elements, and mild peril Cast/Characters: - Jack Quaid as Simon Thompson - Lana Condor as Savannah Chen - Zachary Quinto as the voice of DUST-13 (Dustie) - Supporting cast: 1. Amy Adams as the voice of EVA (Environmental Virtual Assistant) 2. Keegan-Michael Key as the voice of Principal Johnson 3. Regina Hall as the voice of Ms. Davis, the History Teacher 4. John Cho as the voice of Dr. Chen, Savannah's Father 5. Phylicia Rashad as the voice of Grandma Thompson 6. Noah Centineo as the voice of Ethan, Simon's best friend 7. Awkwafina as the voice of Stella, Savannah's best friend 8. Shang-Chi as himself, a martial arts instructor 9. Scarlett Johansson as the voice of Dr. Medina, the scientist 10. Tom Hiddleston as the voice of Agent Smith, a government agent 11. Taraji P. Henson as the voice of Captain Johnson, the pilot of an airship 12. Jake Johnson as the voice of Rusty, Simon's pet dog 13. Emma Stone as the voice of Mia, Simon's older sister 14. Sandra Oh as the voice of Mrs. Thompson, Simon's mother 15. Mahershala Ali as the voice of the rebellious robot, IRIS-7 INT. SIMON'S BEDROOM - NIGHT Simon Thompson, a regular sophomore, lies on his bed, engrossed in a video game. An alarm clock beeps, indicating it's time for school. INT. HIGH SCHOOL HALLWAY - DAY Simon nervously walks through the bustling hallway, clutching his books against his chest. He spots Savannah standing near her locker, talking to Stella. SIMON (narrating): She was like a dream. Her smile could light up the darkest room. Maybe today would be the day I finally gather the courage to talk to her. Simon's nerves get the best of him as he watches Savannah walk away. Suddenly, he notices a strange-looking robot in the corner. SIMON: (whispering to himself) Is that... a robot? Simon's curiosity takes over, and he discreetly follows the robot into the forest behind the school. INT. FOREST - DAY In the depths of the forest, Simon finds DUST-13 (Dustie), a cute and mysterious robot companion. DUSTIE: (in a robotic voice) Greetings, Simon Thompson. I am DUST-13, but you may call me Dustie. I require your assistance. SIMON: (wide-eyed) You can talk? DUSTIE: Indeed, I am programmed with advanced communication capabilities. But time is of the essence. We must leave before they find us. Simon's fascination with Dustie results in a bond between them. They become friends, working together to navigate the forest and find answers. INT. SAVANNAH'S HOUSE - NIGHT Simon gathers the courage to ask Savannah out on a date. They meet at a park, where they share their dreams and aspirations for a better world. SAVANNAH: Simon, wouldn't it be amazing if we could make a difference? To bring peace and harmony to this chaotic world? SIMON: (smiling) Absolutely, Savannah. We can start by understanding each other and embracing our differences. Simultaneously, Dr. Medina, a brilliant but misguided scientist, creates a device that can control robots' actions, intending to use them for domination. INT. DR. MEDINA'S LAB - DAY Simon, Dustie, Savannah, and their friends stumble upon Dr. Medina's lab and witness the dangerous experiment taking place. SIMON: We can't let her succeed! Dustie, Savannah, we need to stop her! DUSTIE: Agreed, Simon. We have to protect the connections we've found in this chaotic world. With Dustie's advanced knowledge and Simon's determination, they devise a plan to foil Dr. Medina's sinister agenda. EXT. SKY - DAY Using an airship commandeered by Captain Johnson, Simon and his friends chase Dr. Medina's robots through a thrilling and perilous aerial chase. Finally, they confront Dr. Medina, who threatens to use her newfound power to control Dustie. INT. DR. MEDINA'S CONTROL ROOM - DAY SIMON: (defiant) You won't get away with this, Dr. Medina! Love and friendship will always prevail over fear and control! SAVANNAH: (supportive) We stand together, united against your chaos! Dustie, inspired by their bravery, breaks free from Dr. Medina's control. Together, they overpower her and restore the robots' free will. INT. HIGH SCHOOL CAFETERIA - DAY The high school community celebrates their bravery and teamwork, highlighted in a heartfelt ceremony. PRINCIPAL JOHNSON: (proudly) Simon Thompson, Savannah Chen, and Dustie, we honor your heroism and the bonds you've forged. Today, our world is a bit brighter because of you. The film ends with Simon and Savannah officially becoming a couple, having inspired change in others through their connection, love, and acceptance. FADE OUT.