Polar graph art project ideas - No prior knowledge of polar graphs is assumed. Students will explore circles, roses, and limacons and try to determine how each portion of the equation affects the graph. Polar Functions Exploration • Activity Builder by Desmos Classroom

 
Precalculus Polar Graphing Project PBworks. Anybody know any cool looking polar equations Yahoo. 101 Project Ideas Key Curriculum. Polar Graphs University of Georgia. Free Download Here pdfsdocuments2 com. Ti 84 Polar Equations Project Yahoo Answers. The Polar Express Teaching Theme amp Lesson Plan Ideas. …. Kellie pickler net worth

Polar Graph Art Project 1. Completed project is due ___1 week_____ 2. Completed design should be graphed on the large polar graph given to you during class. 3. Students should create a design using at least 3 polar equations. 4. Students must complete a θ-r chart for each equation used in the design. R values should be rounded to the nearestThe Polar Express Activity #1 - Polar Express Writing. In the story, a little boy takes a magical train ride on the Polar Express. With this Polar Express activitystudents will imagine what it would be like if they rode the Polar Express. There are a couple different writing pages, a writing foldable, and a word list included. Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Polar graph project - 2016 - ART | DesmosPolar Graph Project Ideas Downloaded from ftp.dartgo.org by guest ANNA MATA Synoptic Meteorology as Practiced by the National Meteorological Center. (the NAWAC Manual). Indiana University Press Describes what students should know and be able to do in science, mathematics, and technology by the ends of grades 2, 5, 8, and 12.Math Art in 3D. Desmos 3D adds another dimension for creativity. Many of the same strategies used in 2D, such as inequalities, restrictions, custom colors and more can be applied in 3D. A great starting place for art in 3D is utilizing the built in function ‘sphere.’. You can try out this function and start creating with the Build a Snowman ...150 Guided Projects Guided Project 56: Polar art Topics and skills: Polar coordinates, graphing, calculator In this project we give a glimpse of the explorations that are possible when graphing equations in polar coordinates and the spectacular pictures that result. Roses Recall that the equations r-a cos n and r a sin ηθ describe an n-leafed ...In today’s fast-paced and interconnected world, collaboration is key to success in any industry. Whether you’re working on a small project or managing a large team, the ability to ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.United States. "Wang Zhenyi" by Chian-Shin Du. United States. "Desmos "A Broken World" by Joshua Tellez. United States. "It's a Big World Out There" by Holly Beck. United States. The Desmos Math Art Contest is open yearly to students ages 13⁠-⁠18 to showcase their graphing calculator skills, creativity, and love of math.Sep 19, 2014 - Explore Christine Holst's board "PreCalc Honors Projects", followed by 149 people on Pinterest. See more ideas about precalculus, math classroom, high school math.Art with Graphs, Grids, Numbers and Equations- We love doing math art with graph paper and grids, and using equations such as the golden ratio to make beautiful works of art. Symmetry in Art- Symmetry is such a fun way to create! Learn about some fun symmetrical art projects. Geometric Art- Bring together shapes and art and you have so much beauty!Ashley’s Architecture Project Ashley’s Statement. In a regular Honors Pre-calculus course at Concordia International School Shanghai, students are introduced to …A project that shows trigonometry principles for beginning students requires at least a basic understanding of the subject. Draw three right triangles and label the angle and two sides that apply to the sine, cosine and tangent functions respectively. Student groups can draw X-Y graphs of the sine, cosine and tangent functions from …Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Polar Graph Project. Save Copy Log InorSign Up. r = 3 a − cosθ ...We would like to show you a description here but the site won't allow us.Describe the effect each of the parameters a, n, c, and d have on the graph of the polar equation given below. Carefully select values for each parameter to emulate the flower pictured. Your graph should have the same amount of petals as the major petals of the flower, should be of the same length, and have the same rotational location of those ...The Bagel Award-Winning Polar Graph Lesson. This week my PreAP Precal classes delved into polar coordinates and graphs. Last year, we did some converting back and forth between polar and rectangular equations and then spent a day on graphing polar equations using t-tables. While I did enjoy seeing where the petals and loops came from, we only ...Dec 18, 2014 - Explore Denise Schley's board "polar graphing", followed by 116 people on Pinterest. See more ideas about graphing, polar, precalculus.Papertem Printable Paper Ideas on Papertem Related For Polar Graph Paper Radians Art Projects With Paper. Polargraph Drawing Machine Technology Art by Euphy Follow 451 871 so is perfect for this project for me it is showing polar graph is not connected why Polar Graphing Art Equations Art with polar equations project ideas pinterest these graphPlease enjoy this short tutorial with no sound on how to create a polar coloring page in desmos.Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Learn: Polar Graphing. Save Copy. Log InorSign Up. One at a time, click the circles on the left to turn on the graphs. Open the folders to explore their contents. 1. Basic. 2. Intermediate. 5. Advanced. 12. 14. powered by. powered by "x" x "y" y ... This activity explores graphing on a polar grid. The graph of an equation in polar coordinates is the set of points which satisfy the equation. That is, a point P(r, θ) is on the graph of an equation if and only if there is a representation of P, say (r′, θ′), such that r′ and θ′ satisfy the equation. Our first example focuses on some of the more structurally simple polar equations.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Loading... Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. ... Polar Graph. Save Copy. Log InorSign Up. r = sin θ + 2. 1. r = 3 ...Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Loading... Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. ... Polar Graph Design. Save Copy. Log InorSign Up. r = 2 0 cos 4 ...Paper Circus Tent. Paper Teepee. Pet Diorama. Polar Habitat Diorama. Rainforest Diorama. Salt Dough Snowman. Standing Paper Animals. Standing Paper Dinosaurs. Tiny Top Hat.I used the polar graphs of sine and cosine to make the flowers. I used theta to create spirals. I set 'r' equal to a coefficient to create the circles. I made the spirals opposite of each other. I used sliders and recorded it to create an animation. The different coefficients that are in the sliders, make the design and size of the graph.to save your graphs! Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.How to create Graph Art (or Data Art) These are the basic steps we followed: Think of a topic that you want to illustrate. Research the available data, and see if you can find data that can be easily graphed as a single line graph. Conceptualise how you could use the shape of the line graph to create an illustration that is relevant to the topic.An example could be to first have a students plot a couple points like (5, 4), (3, 6), or (-4, 2) on the board. Then transition them from Cartesian to polar coordinates by using the floor graph and have them …Shopping for art supplies online can be a daunting task. With so many options available, it can be hard to know where to start. To help you find the perfect supplies for your next ...Students will explore circles, roses, and limacons and try to determine how each portion of the equation affects the graph. No prior knowledge of polar graphs is assumed. Polar Graph Exploration • Activity Builder by Desmos ClassroomPolar functions are equations written in the form r = f (θ), where r is the radial distance from the origin and θ is the angle. Their graphs consist of input-output pairs of values where the input values are angle measures and the output values are radial distances. In the Cartesian coordinate plane, the equation y = x creates a line that ...Please enjoy this short tutorial with no sound on how to create a polar coloring page in desmos. Polar Graph Project Ideas Downloaded from ftp.dartgo.org by guest ANNA MATA Synoptic Meteorology as Practiced by the National Meteorological Center. (the NAWAC Manual). Indiana University Press Describes what students should know and be able to do in science, mathematics, and technology by the ends of grades 2, 5, 8, and 12. Solution: Identify the type of polar equation The polar equation is in the form of a limaçon, r = a - b cos θ. Since the equation passes the test for symmetry to the polar axis, we only need to evaluate the equation over the interval [0, π] and then reflect the graph about the polar axis. What are the types of polar graphs?The Bagel Award-Winning Polar Graph Lesson. This week my PreAP Precal classes delved into polar coordinates and graphs. Last year, we did some converting back and forth between polar and rectangular equations and then spent a day on graphing polar equations using t-tables. While I did enjoy seeing where the petals and loops came from, we only ...Research how slope is used in art. On graph paper, draw 7-10 lines that extend at various angles from one side of the paper to the other. ... Polar Graph Project Ideas; Ch 8. Types of Numbers ...Making Art with Polar Equations. Emma Feng · Follow. Published in. Beauty in Mathematics · 3 min read · Feb 9--Listen. Share. Honors Precalculus Project C. ... Polar Graphs of the Mangosteen.Students needed to create the coolest polar graph with one equation. And students needed to create the coolest polar art using multiple equations. However, …Trigonometric Art Project Ideas. Grace attended James Madison University has a bachelor's degree in history and a master's degree in teaching. She previously taught 2 years of high school social ...Graph theory is a mathematical discipline that studies the relationships between interconnected elements through the use of nodes and edges. In essence, it explores the connections and patterns that can be represented graphically. Nodes depict entities, and edges signify the relationships or links between them.Research how slope is used in art. On graph paper, draw 7-10 lines that extend at various angles from one side of the paper to the other. ... Polar Graph Project Ideas; Ch 8. Types of Numbers ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Create stunning polar graph art with this set of Quickgraph tools. Explore the beauty of coordinates art and unleash your creativity with lotus flower mandalas and geometric designs.In our teaching programs, we all learned about the different sides of the brain and different learning types. But with the recession, many schools lost the programs that helped reach all learning types - especially art. Art is more than just creating beautiful pieces, many of the great master painters used math concepts to make their pieces even more appealing.Cartesian and polar grids, show or hide axes or grid lines, adjust the window of the graph, and select radian or degree scales for trigonometric function graphing (see fig. 4). In addition, the Projector Mode option makes the graph and axis lines thicker and all the expressions larger. This is a great option for using Desmos as partPolar Graph Project Ideas 1 Polar Graph Project Ideas When somebody should go to the book stores, search inauguration by shop, shelf by shelf, it is in reality problematic. This is why we provide the book compilations in this website. It will enormously ease you to look guide Polar Graph Project Ideas as you such as.Sep 19, 2014 - Explore Christine Holst's board "PreCalc Honors Projects", followed by 149 people on Pinterest. See more ideas about precalculus, math classroom, high school math.Cool Colors Polar Bear Watercolor Lesson. A fun project that focuses on cool colors and watercolor techniques. You could also use oil pastels or chalk pastels without the glue. You can use black glue for a more dimensional look, or outline with Sharpies. Black Glue makes it easier for your students to keep the colors within the areas and it ...IDEAS, but end up in detrimental downloads. Thanks for retrieving Polar Graph Project Ideas. If you effort to acquire and deploy the Polar Graph Project Ideas, it is thoroughly plain then, at present we extend the associate to buy and create bargains to retrieve and deploy polar graph project ideas therefore straightforward!.Bubble Wrap Jellyfish Craft for Kids | Combine bubble wrap, googly eyes, and pipe cleaners for this fun craft. Paper Roll Octopus | This fun fellow will spark your kids' imagination and lead to some fun pretend play. Cereal Box Aquarium | Save this one for a long rainy afternoon. It's sure to keep kids occupied for a while creating and ...There is an alternative way to represent points in space, called polar coordinates. The idea is suggested in the following picture. Figure \(\PageIndex{1}\) Consider the point above, which would be specified as \((x,y)\) in Cartesian coordinates. We can also specify this point using polar coordinates, which we write as \(\left( r, \theta \right)\).Dec 5, 2017 - Explore Tasha Treat's board "Polar express crafts!!!", followed by 191 people on Pinterest. See more ideas about crafts, kids christmas, preschool christmas.Graph theory is a mathematical discipline that studies the relationships between interconnected elements through the use of nodes and edges. In essence, it explores the connections and patterns that can be represented graphically. Nodes depict entities, and edges signify the relationships or links between them.Moved Permanently. Redirecting to /browse/Search:polar%20graphing%20projectA polar curve is a shape constructed using the polar coordinate system. Polar curves are defined by points that are a variable distance from the origin (the pole) depending on the angle measured off the positive \ (x\)-axis. Polar curves can describe familiar Cartesian shapes such as ellipses as well as some unfamiliar shapes such as cardioids ...Easy Polar Bear Drawing and Winter Art Project Our easy polar bear drawing tutorial is perfect for kids to follow; providing a step-by-step visual how to draw a polar bear guide, a video demo and various polar bear coloring pages and drawing prompts to accommodate every age and ability level!Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.This folder houses the polar graph partner projects for period 1. Content. The Crescent Moon Lotus. by Lourie Chiang . Blossom. by minji kim . Superhero by: Austin Kim. by Hyung Ju . Polar Graph: The Elliplemrose by Brenda Beckham. by Brenda Beckham . Polar Project: Polarized Nature. by Zahrah Kabbara and Neha Fatima . Helen Vuong and Cattleya ...Sep 19, 2014 - Explore Christine Holst's board "PreCalc Honors Projects", followed by 149 people on Pinterest. See more ideas about precalculus, math classroom, high school math. Why I am passionate about this issue: Water pollution is the contamination of water sources by substances that make the water unusable for drinking, cooking, cleaning, swimming, and other activities. This is obviously worrying because humans depend on water for everything, and it's vital for human survival and the world. Polar Bear Craft. Cut out a paper polar bear and decorate it with cotton balls, packing noodles, or tissue paper. Suitable for the primary grades. Polar Bear Puppet. Make a polar bear puppet from simple materials. Penguins. Penguin Paper Craft. Paper penguin created with a template. Suitable for primary students.The process requires graph paper. It is a paper that is divided into a matrix of 1cm cells. Initially, the students use regular graph paper. Later on, when they need to present values in terms of degrees, radians, or angles, they employ polar graph papers. A polar graph paper is a circular graph paper used to project polar coordinates.Create stunning polar graph art using the Quick Graph app on your iPhone. Explore the beauty of fractals and let your artistic visions come to life. Perfect for those interested in occult, graphing, and dreamweaver. Unleash your creativity today!Craft & DIY Art Project Ideas. 35. Bottle Cap Mosaics: Create colorful mosaics using different bottle caps.. 36. Paper Plate Masks: Unleash creativity by making animal masks using paper plates and paint.. 37. Rock Pets: Paint and adopt cute pet rocks, giving them character and charm.. 38. Old Newspaper Collage: Upcycle old newspapers to create unique collages.It is easier to graph polar equations if we can test the equations for symmetry with respect to the line \(\theta=\dfrac{\pi}{2}\), the polar axis, or the pole. There are three symmetry tests that indicate whether the graph of a polar equation will exhibit symmetry. If an equation fails a symmetry test, the graph may or may not exhibit symmetry.Spirograph Art. Spirograph Design. Spirograph. Grafik. Geometric Drawing. Math Art. Scans from How to Draw with Spirograph; 1967 ... Polar Graph / Easter Egg [R-D] Nature. Mathematics. Geometry Art. ... Similar ideas popular now. Photography ...Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Precalculus Graphing Project. Save Copy. Log InorSign Up. x = 1 0 0 < y < 2 4. 1. y = 1 2 0 < x < 2 0. 2. y = − 3 x + 5 4 1 0 < x < 1 3. 3. y = 3 x − 6 ... Polar: Logarithmic Spiral. example. Polar: Limacon. example. Polar: Conic Sections ...The equation has failed the symmetry test, but that does not mean that it is not symmetric with respect to the pole.Passing one or more of the symmetry tests verifies that symmetry will be exhibited in a graph. However, failing the symmetry tests does not necessarily indicate that a graph will not be symmetric about the line [latex]\theta =\frac{\pi }{2}[/latex], the polar axis, or the pole.y = sin s cos s x cos m · s · cos s ≤ x ≤ 0. powered by. or. to save your graphs! New Blank Graph. Examples. Lines: Slope Intercept Form. example. Lines: Point Slope Form.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. DESMOS Graphing Art Project | DesmosJan 7, 2024 · AMIGO Polar Panic – Quick, Make-a-Match Kids…. $7.85. Buy on Amazon. Polar Adventure – A Family Board Game to Teach…. $29.99. Buy on Amazon. Combining hands-on art projects with engaging literature is a wonderful approach to entertain and educate your little ones about polar bears and their Arctic habitat. Arctic Art Projects for Kids. These art projects and activities are a wonderful accompaniment to your lessons on the Arctic and polar regions. You could easily tie this unit in with our Inuit (Eskimo) craft projects to add in cultural studies as well. While the focus of these art projects is the Arctic, we've included penguins and other polar ...Day 1: Graphing Linear Equations. On the first day of the project, students selected 10 equations to graph on their paper as a rough draft of their design. Once they submitted their drafts for evaluation, they began the process of problem solving and reasoning with tasks aligned to both slope-intercept form (in the context of pricing their ...Polar Graph Art (9-12) This activity allows students to explore ways to be creative by designing and making a pieces of art with polar graphs. Students explore polar graphs to make connections between equations, parameters, and graphs. This activity leads to wonderful pieces of art to display around the classroom or school.No prior knowledge of polar graphs is assumed. Students will explore circles, roses, and limacons and try to determine how each portion of the equation affects the graph. Polar Graph Exploration • Activity Builder by Desmos Classroom2.) Dream Home Design Project. Grade Levels: Grades 1-8+ Description: For this fun math art project, students are tasked with designing the floor plans for their dream homes and backyards by applying math skills including measurement, scale, area, and perimeter. Students can use graph paper and markers or digital tools like Google Sketchup to create their home's blueprints, calculate the ...Some common polar equations are used to create symmetrical art on a polar graph. The following projects help high school math students learn about graphing equations on a …Coordinate Project Rubric PDF Download ablinfo org. Art with polar equations Project Ideas Pinterest. Free Download Here pdfsdocuments2 com. Graphing Calculator Art How to Make a Face Sciencing. Picture Of A Tick buysms de. minion conics project YouTube. Polar Coordinates Art Project Desmos Graphing Calculator.Cartesian and polar grids, show or hide axes or grid lines, adjust the window of the graph, and select radian or degree scales for trigonometric function graphing (see fig. 4). In addition, the Projector Mode option makes the graph and axis lines thicker and all the expressions larger. This is a great option for using Desmos as part

Description. Practice graphing with polar coordinates by having your students embark on a date in this love themed project! The cardiod (heart), lemniscate (bow), rose curve (flower), circle and more are explored! There is a calculator portion where students reveal a butterfly and a portion where they can create their own graph as well. INCLUDED:. Directions to lululemon outlet

polar graph art project ideas

Are you an art enthusiast looking for a new project? Perhaps you’re a craft lover in search of unique supplies. Whatever your creative needs may be, finding the best arts and craft...Desmos Polar Graphs. In this project, I explored polar graphs by using Desmos to create fun, visually-appealing graphs. This was the first piece of art I created. Rose graphs can be created using the r=asinbtheta. I utilized this equation along with the slider function on Desmos to create this pretty flower design. The best part?Spirograph Art. Spirograph Design. Spirograph. Grafik. Geometric Drawing. Math Art. Scans from How to Draw with Spirograph; 1967 ... Polar Graph / Easter Egg [R-D] Nature. Mathematics. Geometry Art. ... Similar ideas popular now. Photography ...In this project, students investigate transformations of polar equations by manipulating the parameters of the equations and analyzing the resulting graphs. ...Directions: 1. Create a design depicting a recognizable object (as opposed to an abstract design). 2. Choose a creative title for your design. 3. Use a single polar equation as the basis for your design. You may choose to embellish the background with other shapes, but the polar graph must be the focal point of the design.Students will explore circles, roses, and limacons and try to determine how each portion of the equation affects the graph. No prior knowledge of polar graphs is assumed. Polar Graph Exploration • Activity Builder by Desmos ClassroomExplore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Solution: Identify the type of polar equation The polar equation is in the form of a limaçon, r = a - b cos θ. Since the equation passes the test for symmetry to the polar axis, we only need to evaluate the equation over the interval [0, π] and then reflect the graph about the polar axis. What are the types of polar graphs?Download a free Polar Graph Paper Divisions Each 10 Degrees to make your document professional and perfect. Find other professionally designed templates in TidyForm. Charlene Bartholow. Polar Grid In Degrees With Radius 7. Illustration of a polar graph/grid that is marked, but not labeled, in 30° increments and units marked to 7.Employ this polar graphically paper for plating, school projects, mathematic classes, science projects, project courses, and art projects. The printable polar grid paper includes full-sized and quarter circles, inches 10 degree, 15 degrees, both 30 degrees. Polar Coordinates Diagram Paper: Circular Grid Notebook Using Radians. by ...Oct 31, 2022 - This winter craft use sponges, cardboard, and erasers to paint polar bears at night as they create a polar bear art project for kids. Oct 31, 2022 - This winter craft use sponges, cardboard, and erasers to paint polar bears at night as they create a polar bear art project for kids. ... Similar ideas popular now.Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Precalculus Graphing Project. Save Copy. Log InorSign Up. x = 1 0 0 < y < 2 4. 1. y = 1 2 0 < x < 2 0. 2. y = − 3 x + 5 4 1 0 < x < 1 3. 3. y = 3 x − 6 ... Polar: Logarithmic Spiral. example. Polar: Limacon. example. Polar: Conic Sections ...Polar Graph Art (9-12) This activity allows students to explore ways to be creative by designing and making a pieces of art with polar graphs. Students explore polar graphs to make connections between equations, parameters, and graphs. This activity leads to wonderful pieces of art to display around the classroom or school. A subreddit dedicated to sharing graphs created using the Desmos graphing calculator. Rubric: 10 points - at least four polar different polar graphs on the same polar coordinate system. In the spirit of Halloween 2020, were using math to draw a pumpkin on desmos If youre not into halloween, this is also a full desmos art project tutorial. It ... Where To Download Polar Graph Project Ideas Pdf Free Copy Cross Stitch Designs Graph Paper: Cross Stitch Project Ideas Janice VanCleave's Great Science Project Ideas from Real Kids Neo4j - A Graph ... Projects Or Crafts 4x4 Inches120 Pages Great Graph Art Composition Book / Magical Dragon Scales Design / 5x5Jun 22, 2020 - 6+ Polar Graph Paper Templates - PDF | Free & Premium Templates. Jun 22, 2020 - 6+ Polar Graph Paper Templates - PDF | Free & Premium Templates ... Ideas. Doodles. Crafts. Zentangle Patterns. Design. Printable Graph Paper ... Graphing. Graph Paper Art. Download Polar Graph Paper Divisions Each 10 Degrees for Free. Download a free ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Spiraling Outward. You see spirals in the ocean's shells and the far-reaches of space. And you can create them from polar functions. The general form for a spiral is r = aθ, where θ is the angle measure in radians and a is a number multiplier. In the graph of r = 1/3 θ. The 1/3 multiplier makes the spiral tighter around the pole.Second Hour Pre-Calculus. Fifth Hour Pre-Calculus. Sixth Hour Pre-Calculus. C.A.R.E Projects. Functions. Functions (Cress and Little) Functions Prerequisites. Functions 1. Functions 2.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.polar graph. Have a question about using Wolfram|Alpha? Contact Pro Premium Expert Support ». Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. 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