SMART Notebook Maths Tools

Transcription

1 SMART Notebook Maths Tools Windows operatin systems User s uide

2 Trade-mark notice SMART Board, SMART Notebook, smarttech, the SMART loo and all SMART talines are trade-marks or reistered trade-marks of SMART Technoloies ULC in the US and/or other countries.texas Instruments, TI-Nspire and TI-SmartView are trade-marks of Texas Instruments. All other third-party product and company names may be trade-marks of their respective owners. Copyriht notice SMART Technoloies ULC. All rihts reserved. No part of this publication may be reproduced, transmitted, transcribed, stored in a retrieval system or translated into any lanuae in any form by any means without the prior written consent of SMART Technoloies ULC. Information in this manual is subject to chane without notice and does not represent a commitment on the part of SMART. One or more of the followin patents: US ; US ; US ; US ; US ; USD616462; and USD Other patents pendin. 06/2011

3 Contents Chapter 1: Introduction to SMART Notebook Maths Tools 1 Usin the Maths toolbar 1 Chapter 2: Workin with equations 3 Insertin equations 3 Writin equations 4 Solvin mathematical expressions 7 Chapter 3: Workin with shapes 9 Insertin reular polyons 9 Insertin irreular polyons 9 Displayin interior anles 10 Displayin and editin side lenths 10 Displayin and editin the vertices of a shape 11 Dividin shapes 12 Chapter 4: Workin with raphs 13 Insertin Cartesian raphs 13 Insertin quadrant raphs 14 Insertin number line raphs 15 Selectin raphs 16 Manipulatin raphs 17 Customisin raphs 18 Generatin raphs from equations 19 Generatin raphs from tables 20 Generatin tables from raphs 20 Addin shapes to raphs 21 Chapter 5: Launchin Texas Instruments emulators 23 i

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5 Chapter 1 Introduction to SMART Notebook Maths Tools Usin the Maths toolbar 1 If you install SMART Notebook Maths Tools on your computer, SMART Notebook software includes mathematical features, such as equation editin, handwritin reconition for mathematical terms, additional shape tools, raph eneration and a launcher for Texas Instruments (TI) emulators. Usin the Maths toolbar The Maths toolbar enables you to select and use a variety of maths-specific commands and tools in the SMART Notebook software window. The followin table describes the functions of each button in the Maths toolbar. Button Command Action Equations Irreular Polyons Insert equations. Insert irreular polyons. Reular Polyons Insert reular polyons. Measurement Tools Graph Tables Graphs Launch Emulator Use a ruler, protractor or compass. Insert raph tables. Insert Cartesian, quadrant or number line raphs. Launch the Texas Instruments (TI) emulator. You can add any of the buttons from the Maths toolbar to the SMART Notebook software toolbar and then hide the Maths toolbar. To hide the Maths toolbar 1. Riht-click the SMART Notebook software toolbar. The Customise Toolbar dialoue box appears. 1

6 C H A P T E R 1 Introduction to SMART Notebook Maths Tools 2. Customise the SMART Notebook software toolbar to include the maths tools that you want to use. 3. Clear the Show Secondary Toolbar tickbox. 4. Press Done. To restore the Maths toolbar, riht-click the SMART Notebook software toolbar, select the Show Secondary Toolbar tickbox, and then press Done. 2

7 Chapter 2 Workin with equations Insertin equations 3 Writin equations 4 Tips for writin equations 5 Tips for writin trionometric equations 5 Tips for writin loarithmic equations 5 Tips for solvin multiple line equations 5 Reconised mathematical symbols 6 Numbers 6 Operators 6 Roman letters 6 Greek letters 6 Other mathematical symbols 6 Reconised mathematical functions 6 Loarithmic functions 6 Trionometric functions 7 Solvin mathematical expressions 7 You can insert or write equations in.notebook file paes usin SMART Notebook Maths Tools. You can solve inserted or written mathematical expressions at any time. Insertin equations You can insert equations into a pae usin the Equation Editor. To insert equations 1. Press Equations. 2. Press where you want to place the equation. The Equation Editor and a text box appear. 3. Type the numerals that you want to add to your equation. Press the buttons in the Equation Editor for the mathematical terms that you want to add to your equation. 3

8 C H A P T E R 2 Workin with equations 4. Once you have finished creatin your equation, press outside of the text object. If you insert a mathematical expression, you can solve the expression (see Solvin mathematical expressions on pae 7). You can also enerate a raph based on this equation (see Generatin raphs from equations on pae 19). Writin equations You can write equations on the pae usin pen tray pens (on interactive whiteboards) or a tethered pen and pen tool buttons (on interactive pen displays). You can also insert equations usin the Equation Editor (see Insertin equations on the previous pae). To write equations 1. Press Pens and then select an available line type. Don t select a creative pen. 2. Write the equation on the interactive screen usin the tips in the followin sections. 3. Press the equation s menu arrow, and then select Reconise Maths Ink. The equation appears surrounded by a blue border. A reen circle appear below the equation. and a red circle 4. If the equation appears correctly, press the reen circle. S o o o SMART Notebook Maths Tools reconises many characters, includin numbers, operators, Roman letters, Greek letters and other mathematical symbols (see Reconised mathematical symbols on pae 6). SMART Notebook Maths Tools also reconises many mathematical functions (see Reconised mathematical functions on pae 6). If you write a mathematical expression, you can solve it (see Solvin mathematical expressions on pae 7). You can also enerate a raph based on this equation (see Generatin raphs from equations on pae 19). If your equation appears incorrectly, press the red circle aain. Don t attempt to write over your oriinal equation., erase the equation and write it 4

9 C H A P T E R 2 Workin with equations Tips for writin equations Consider the followin when you write equations: Write each symbol clearly and don t overlap symbols. Leave space between the characters, symbols, formulae and equations that you write. Draw a multiplication symbol as a six-pointed asterisk, for example,. If your equation involves multiple lines, such as fractions, leave space between these lines. However, don t separate a sinle line equation over multiple lines. Alin superscripts, such as exponents, to the riht of and above the adjacent character or symbol. Don t allow a character and a superscript to overlap. Write problems sequentially from left to riht and from top to bottom. Tap to make a decimal point. Don t draw a tiny ball or scribble a mark. Don t use j as a variable unless you re writin a trionometric expression or a complex expression. Don t use i or o as variables unless you re writin a trionometric expression. Don t use e as a variable unless you re writin an exponential expression. Enclose exponents in parentheses. Tips for writin trionometric equations Consider the followin when you write trionometric equations: Enclose variables in parentheses, for example, sin (x). Separate multiple trionometric expressions usin a multiplication sin, for example, sin(a)*cos(a). Tips for writin loarithmic equations Consider the followin when you write exponents, loarithms and eometric series: SMART Notebook Maths Tools reconises lo (N) as lo 10 N. SMART Notebook Maths Tools reconises lom as lom or lom (natural lo). SMART Notebook Maths Tools supports lo 2 M and lo 10 M only. Write the natural loarithm ( ln) as lo. Write lo 2 as lo2. Write lo 10 as lo10.smart Notebook Maths Tools doesn t support subscripts. Tips for solvin multiple line equations SMART Notebook Maths Tools can solve some multiple-lined equations if you select all the equations, press the equation s menu arrow and then select Reconise Maths Ink. 5

10 C H A P T E R 2 Workin with equations Reconised mathematical symbols SMART Notebook Maths Tools reconises the mathematical symbols and functions in your equation and converts them into typed text.smart Notebook Maths Tools reconises many symbols, includin numbers, operators, Roman letters, Greek letters and other mathematical symbols. Numbers Operators Roman letters Greek letters Other mathematical symbols Reconised mathematical functions SMART Notebook Maths Tools reconises the mathematical symbols and functions in your equation and converts them into typed text.smart Notebook Maths Tools reconises mathematical functions in the followin cateories: Loarithmic functions Trionometric functions Loarithmic functions lo (a) lo10 (a) lo2 (a) natural loarithm base 10 loarithm base 2 loarithm 6

11 C H A P T E R 2 Workin with equations Trionometric functions acos (a) asin (a) atan (a) cos (a) cosh (a) cot (a) coth (a) csc (a) sec (a) sin (a) sinc (a) sinh (a) tan (a) tanh (a) inverse cos function inverse sin function inverse tan function cos function hyperbolic cos function cot function hyperbolic cot function cosecant function secant function sin function sinc function sinh function tan function tanh function Solvin mathematical expressions If you insert or write a mathematical expression on a pae, you can solve this expression and display the complete equation usin the available menu options. S You can also enerate raphs from equations (see Generatin raphs from equations on pae 19). SMART Notebook Maths Tools can solve some equations numerically but not symbolically, and it can solve some equations symbolically but not numerically. If a solution type isn t available, you re unable to select it in the menu. To solve an expression numerically 1. Select the equation. 2. Press the equation s menu arrow and then select Maths Actions > Simplify Numerically. To solve an expression symbolically 1. Select the equation. 2. Press the equation s menu arrow and then select Maths Actions > Simplify Symbolically. 7

12 C H A P T E R 2 Workin with equations To find an equation s zero value 1. Select the equation. 2. Press the equation s menu arrow and then select Maths Actions > Find Zeroes. To find an equation s minimum and maximum values 1. Select the equation. 2. Press the equation s menu arrow and then select Maths Actions > Find Extrema. 8

13 Chapter 3 Workin with shapes Insertin reular polyons 9 Insertin irreular polyons 9 Displayin interior anles 10 Displayin and editin side lenths 10 Displayin and editin the vertices of a shape 11 Dividin shapes 12 With SMART Notebook Maths Tools, you can create reular and irreular polyons and then edit these shapes interior anles, side lenths and vertices. You can also divide a circle, square or rectanle into separate pieces of equal area. Insertin reular polyons You can insert reular polyons with 3 to 15 sides usin the Reular Polyons tool. To insert a reular polyon 1. Press Reular Polyons and then select the number of sides (the number in the polyon represents the number of sides). 2. Create a shape by pressin where you want to place the shape and drain until the shape is the size that you want. Insertin irreular polyons In addition to creatin shapes usin the SMART Notebook software Shapes tool, you can insert irreular polyons usin the Irreular Polyons tool. To insert irreular polyons 1. Press Irreular Polyons. 2. Press where you want to place the shape s first vertex. The first vertex appears as a small red circle. 9

14 C H A P T E R 3 Workin with shapes 3. Press where you want to place the next vertex. A line appears between the two vertices. 4. Repeat step 3 to add more vertices. 5. Press the first vertex s red circle to stop addin vertices and complete the shape. Once you have created an irreular polyon, you can display its interior anles and display its side lenths (see Displayin interior anles below and Displayin and editin side lenths below). Displayin interior anles You can display the interior anles of a shape. S If you display these anles and then edit the vertices of the shape (see Displayin and editin the vertices of a shape on the next pae), SMART Notebook Maths Tools updates the labels and displays the new interior anles. You can also display side lenths (see Displayin and editin side lenths below). To display interior anles 1. Select the shape. 2. Press the shape s menu arrow and then select Show/Hide Interior Anles. To hide interior anles, press the shape s menu arrow and then select Show/Hide Interior Anles aain. Displayin and editin side lenths You can display the side lenths of a shape. If you edit the displayed lenth, SMART Notebook Maths Tools recalculates and displays the lenths of the other sides. S If you display these lenths and then edit the vertices of the shape (see Displayin and editin the vertices of a shape on the next pae), SMART Notebook Maths Tools updates the labels and displays the new side lenths. You can also display interior anles (see Displayin interior anles above). 10

15 C H A P T E R 3 Workin with shapes To display side lenths 1. Select the shape. 2. Press the shape s menu arrow and then select Show/Hide Side Lenths. SMART Notebook Maths Tools calculates the lenths based on the ruler s default units. To hide side lenths, press the shape s menu arrow and then select Show/Hide Side Lenths aain. To edit side lenths 1. If you haven t done so already, display the side lenths. 2. Double-click the side lenth that you want to chane. 3. Type the new lenth. 4. Press somewhere else on the pae. SMART Notebook Maths Tools recalculates and displays the lenths of the other sides. Displayin and editin the vertices of a shape You can edit the position of a shape s vertices. If you re displayin the shape s interior anles or side lenths, SMART Notebook Maths Tools updates the labels and displays the new interior anles or side lenths automatically. To display the vertices of a shape 1. Select the shape. 2. Press the shape s menu arrow and then select Show/Hide Vertices. A red circle replaces each of the shape s vertices. To edit the vertices of a shape 1. If you haven t done so already, display the shape s vertices. 2. Dra a red circle to move that vertex. 3. When you finish editin the shape s vertices, press anywhere else on the pae. To hide the vertices of a shape 1. Select the shape. 2. Press the shape s menu arrow and then select Show/Hide Vertices aain. 11

16 C H A P T E R 3 Workin with shapes Dividin shapes You can divide a circle, square or rectanle into separate pieces of equal area. You can then edit and manipulate these pieces as individual objects. You re unable to divide other shape types in this way. To divide a shape 1. Select the shape. 2. Press the shape s menu arrow and then select Shape Division. The Shape Division dialoue box appears. 3. Select the number of pieces that you want to divide the shape into from the Divide shape into drop-down list. 4. PressOK. The shape divides into separate objects. 12

17 Chapter 4 Workin with raphs Insertin Cartesian raphs 13 Insertin quadrant raphs 14 Insertin number line raphs 15 Selectin raphs 16 Manipulatin raphs 17 Customisin raphs 18 Generatin raphs from equations 19 Generatin raphs from tables 20 Generatin tables from raphs 20 Addin shapes to raphs 21 With SMART Notebook Maths Tools, you can create Cartesian, quadrant and number line raphs, as well as enerate raphs from equations and tables and tables from raphs. Insertin Cartesian raphs You can insert a Cartesian raph into a pae. You can include the default Cartesian raph or create a raph with customised axes and insert this instead. Once you have inserted the raph, you can add points to it. Once you have inserted the raph, you can also manipulate its position, size and rotation, as well as customise its title, axes and labels (see Manipulatin raphs on pae 17 and Customisin raphs on pae 18). To insert the default Cartesian raph Press Graphs and then press Cartesian. A Cartesian raph appears. To insert a customised Cartesian raph 1. Press Graphs and then press Wizard. The Insert Graph dialoue box appears. 13

18 C H A P T E R 4 Workin with raphs 2. Select Cartesian and then press Next. The customisation fields appear. 3. If you want to chane the increments of the numbers alon either of the raph s axes, type a different Step value or increase it usin the up and down arrows. 4. Type numbers to define the Start and End points of the x (horizontal) axis and y (vertical) axis or chane these numbers usin the up and down arrows. 5. To display a raph without horizontal lines, clear the Horizontal Lines tickbox. 6. To display a raph without vertical lines, clear the Vertical Lines tickbox. 7. To display a raph without numbers on the axes, clear the Show Numbers tickbox. 8. Press Finish. To insert points in the raph 1. Double-click the position in the raph where you want to place a point. 2. Repeat step 1 until you ve placed all the points you want to add to the raph. You can enerate a table of values based on your raph (see Generatin tables from raphs on pae 20). To remove points from the raph 1. Double-click the point that you want to remove. 2. Repeat step 1 until you ve removed all the points that you want to remove from the raph. Insertin quadrant raphs You can insert a quadrant raph into a pae. You can include the default quadrant raph or create a raph with customised axes and insert this instead. After you ve inserted the raph, you can add points to it. Once you have inserted the raph, you can also manipulate its position, size and rotation, as well as customise its title, axes and labels (see Manipulatin raphs on pae 17 and Customisin raphs on pae 18). To insert the default quadrant raph Press Graphs and then press Quadrant. A quadrant raph appears. 14

19 C H A P T E R 4 Workin with raphs To insert a customised quadrant raph 1. Press Graphs and then press Wizard. The Insert Graph dialoue box appears. 2. Select Quadrant and then press Next. The customisation fields appear. 3. If you want to chane the increments of the numbers alon either of the raph s axes, type a different Step value or increase it usin the up and down arrows. 4. Type numbers to define the Start and End points of the x (horizontal) axis and y (vertical) axis or chane these numbers usin the up and down arrows. 5. To display a raph without horizontal lines, clear the Horizontal Lines tickbox. 6. To display a raph without vertical lines, clear the Vertical Lines tickbox. 7. To display a raph without numbers on the axes, clear the Show Numbers tickbox. 8. Press Finish. To insert points in the raph 1. Double-click the position in the raph where you want to place a point. 2. Repeat step 1 until you ve placed all the points you want to add to the raph. You can enerate a table of values based on your raph (see Generatin tables from raphs on pae 20). To remove points from the raph 1. Double-click the point that you want to remove. 2. Repeat step 1 until you ve removed all the points that you want to remove from the raph. Insertin number line raphs You can insert a number line raph into a pae. You can include the default number line or create a customised axis and insert this instead. Once you have inserted the raph, you can also manipulate its position, size and rotation, as well as customise its title, axes and labels (see Manipulatin raphs on pae 17 and Customisin raphs on pae 18). 15

20 C H A P T E R 4 Workin with raphs To insert the default number line raph Press Graphs and then press Number Line. A number line raph appears. To insert a customised number line raph 1. Press Graphs and then press Wizard. The Insert Graph dialoue box appears. 2. Select Number Line and then press Next. The customisation fields appear. 3. If you want to chane the increments of the numbers alon the axis, type a different Step value or increase it usin the up and down arrows. 4. Type numbers to define the Start and End points of the axis or chane these numbers usin the up and down arrows. 5. To display a raph without numbers on the axes, clear the Show Numbers tickbox. 6. Press Finish. Selectin raphs Before you can manipulate a raph or access its menu options, you must select it. Once you have selected the raph, you can: Move the raph. Customise the raph. Generate a table from the raph. To select the raph 1. Press Select. 2. Press outside but near to the upper-riht-hand corner of the raph and then dra a rectanle to the opposite corner. A selection rectanle appears around the raph. o o The white circle in the raph s lower-riht-hand corner is a resize handle. The downward arrow in the raph s upper-riht-hand corner is a menu arrow. 16

21 C H A P T E R 4 Workin with raphs Manipulatin raphs You can insert a Cartesian raph or quadrant raph into a pae or enerate a raph from an equation or a table of values. Once you have inserted the raph, you can move or chane the zoom level of this raph. You can also customise a raph s title, axes and labels (see Customisin raphs on the next pae). To move a raph 1. Select the raph. A selection rectanle appears around the raph. 2. Press somewhere inside the border but outside of the raph and then dra to a different position on the pae. To chane a raph s zoom level 1. Select the raph. A selection rectanle appears around the raph. 2. If no icons appear below the raph, press the two downward arrows in the raph s lower-riht-hand corner. Eiht icons appear below the raph. 3. Press to zoom in. OR Press to zoom out. To display a different part of a raph 1. Select the raph. A selection rectanle appears around the raph. 2. If no icons appear below the raph, press the two downward arrows in the raph s lower-riht-hand corner. Eiht icons appear below the raph. 3. Press the hand icon. 4. Dra the raph. 17

22 C H A P T E R 4 Workin with raphs 5. When SMART Notebook Maths Tools displays the part of the raph that you want to view, press the hand icon aain. Customisin raphs You can insert a Cartesian raph or quadrant raph into a pae or enerate a raph from an equation or a table of values. Once you have inserted the raph, you can customise the title of the raph and edit the start point, end point, labels and rid lines of its axes. You can also add a line of best fit based on the points in the raph. You can also manipulate a raph s position and size (see Manipulatin raphs on the previous pae). To customise a raph usin the hidden menu 1. Select the raph. A selection rectanle appears around the raph. 2. If no icons appear below the raph, press the two downward arrows in the raph s lower-riht-hand corner. 3. Use the followin icons to customise the raph: Button Command Action Show/Hide Lines Display horizontal and vertical lines on the raph Show/Hide Point Labels Show/Hide Line of Best Fit Show/Hide Numbers Show/Hide X/Y Labels and Titles Display point labels Display a line of best fit, based on the points that you add to the raph Display numbers on the axes Display labels on the axes and a title above the raph To customise a raph usin the Properties tab 1. Select the raph. 2. Press the raph s menu arrow and then select Properties. 3. If you want to include a label above the raph, type it in the Title box. 18

23 C H A P T E R 4 Workin with raphs 4. Do the followin: o o o o o To display numbers on the axes, select Show Numbers or clear this tickbox to remove them. To display vertical lines, select Vertical Lines or clear this tickbox to remove them. To display horizontal lines, select Horizontal Lines or clear this tickbox to remove them. To display point labels, select Show Point Labels or clear this tickbox to remove them. To chane the labels on the axes, the rane of the axes or the increments of the numbers on the axes, type new values for the Label, Start, End and Step. Generatin raphs from equations If you insert or write an equation, you can enerate and display a raph based on the equation. To enerate a raph from an equation 1. Select the equation. 2. Press the equation s menu arrow and then select Maths Actions > Generate Graph. The raph appears. Once you have inserted the raph, you can also manipulate its position, size and rotation, as well as customise its title, axes and labels (see Manipulatin raphs on pae 17 and Customisin raphs on the previous pae). If you update the information in the equation, SMART Notebook Maths Tools updates the raph. To break the connection between an equation and a raph 1. Select the equation or the raph. A blue hihliht appears around both the equation and the raph. An X in a blue circle appears between them. 2. Press the X symbol. If you update the information in the equation and the connection is broken, SMART Notebook Maths Tools doesn t update the raph. To reconnect an equation and a raph 1. Select the equation. A blue hihliht appears around the table and a small blue square appears beside it. 19

24 C H A P T E R 4 Workin with raphs 2. Select the blue square and dra it over the raph. Generatin raphs from tables You can create a table of values and then enerate a raph based on these values. To enerate a raph from a table 1. Press Graph Tables. A rid appears. 2. Move the pointer over the rid to select the number of rows that you want in the table. The cells of the rid correspond to the cells of your table. The table appears on the pae. 3. Type values into the table s cells. 4. Press the table s menu arrow, and then select Maths Actions > Generate Graph. If you update the information in the table, SMART Notebook Maths Tools updates the raph and vice versa. To break the connection between a raph and a table 1. Select the table or the raph. A blue hihliht appears around both the table and the raph. An X in a blue circle appears between them. 2. Press the X symbol. If you update the information in the table and the connection is broken, SMART Notebook Maths Tools doesn t update the raph and vice versa. To reconnect a raph and a table 1. Select the table. A blue hihliht appears around the table and a small blue square appears beside it. 2. Select the blue square and dra it over the raph. Generatin tables from raphs If you insert a Cartesian or quadrant raph and then insert points into it, you can enerate a table of values based on these points. 20

25 C H A P T E R 4 Workin with raphs To enerate a table from a raph 1. Select the raph. 2. Press the raph s menu arrow and then select Maths Actions > Generate Table. If you add or remove the points in the raph, SMART Notebook Maths Tools updates the table and vice versa. To break the connection between a table and a raph 1. Select the table or the raph. A blue hihliht appears around both the table and the raph. An X in a blue circle appears between them. 2. Press the X symbol. If you update the information in the raph and the connection is broken, SMART Notebook Maths Tools doesn t update the table and vice versa. To reconnect a table and a raph 1. Select the table. A blue hihliht appears around the table and a small blue square appears alonside it. 2. Select the blue square and dra it over the raph. Addin shapes to raphs You can add a shape to a raph and then display the coordinates of its vertices. To add a shape to a raph 1. Create a shape. 2. Press the shape and dra it over the raph. To display the coordinates of the shape s vertices 1. Select the shape. 2. Press the shape s menu arrow and then select Show/Hide Vertex Points. To hide the coordinates, press the shape s menu arrow and then select Show/Hide Vertex Points aain. 21

26 C H A P T E R 4 Workin with raphs To display side lenths 1. Select the shape. 2. Press the shape s menu arrow and then select Show/Hide Side Lenths. SMART Notebook Maths Tools calculates the lenths based on the raph s units. To reflect the shape 1. Select the shape. 2. Press the shape s menu arrow and then select Reflect Shape. 3. Select Reflect over X=0, Reflect over Y=0, Reflect over Y=X or Reflect over Y=-X. A reflection of the shape appears on the raph. The oriinal shape doesn t move. 22

27 Chapter 5 Launchin Texas Instruments emulators If you install TI-Nspire, TI-SmartView 84 or TI-SmartView 73 software on your computer, you can launch it from the Maths toolbar. S A Texas Instruments (TI) emulator isn t included with SMART Notebook Maths Tools software and this feature works only if TI software is already installed on your computer. You can download software from the Internet that describes itself as a TI emulator or includes features similar to a TI emulator. However, pressin the Launch Emulator button launches only fully licensed versions of TI emulators. To launch the Texas Instruments emulator 1. Press Launch Emulator. If TI-Nspire, TI-SmartView 84 or TI-SmartView 73 software is installed on your computer, an icon appears with the name of your software. 2. Press this icon. 23

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