Applications-of-GeoGebra/C3/3D-Geometry/English - Revision history

Snehalathak at 11:49, 25 October 2018

2018-10-25T11:49:12Z

Madhurig at 07:23, 25 October 2018

2018-10-25T07:23:25Z

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Madhurig at 06:52, 24 October 2018

2018-10-24T06:52:07Z

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Vidhya: Created page with "{|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this tutorial on '''3D Geometry'''. |- | | '''Slide Number 2..."

2018-10-08T06:23:18Z

Created page with "{|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this tutorial on '''3D Geometry'''. |- | | '''Slide Number 2..."

New page

{|border=1
| | '''Visual Cue'''
| | '''Narration'''

|-
| | '''Slide Number 1'''

'''Title Slide'''
| | Welcome to this tutorial on '''3D Geometry'''.
|-
| | '''Slide Number 2'''

'''Learning Objectives'''
| | In this '''tutorial''', we will learn how to use '''GeoGebra''' to view:

And construct different structures in '''3D space'''

Solids of rotation of polynomial functions

Trigonometric functions in 3D space
|-
| | '''Slide Number 3'''

'''System Requirement'''
| | Here I am using:

'''Ubuntu Linux''' OS version 16.04

'''GeoGebra''' 5.0.481.0-d
|-
| | '''Slide Number 4'''

'''Pre-requisites'''

'''www.spoken-tutorial.org'''
| | To follow this '''tutorial''', you should be familiar with:

'''GeoGebra''' interface

Geometry

For relevant '''tutorials''', please visit our website.
|-
| | '''Slide Number 5'''

'''Rectangular Co-ordinate System'''

[[Image:]]
| | This image shows the '''rectangular coordinate system'''.

It is made up of mutually perpendicular axes and planes formed by them.

The axes are '''x''' (in red), '''y''' (in green) and '''z''' (in blue).

All points in '''3D''' space are denoted by their '''x y z coordinates'''.

The point of intersection of the three axes is the '''origin O 0 comma 0 comma 0'''.

The gray rectangle in the image depicts the '''XY''' plane.

The planes divide space into 8 octants.

Point '''A''' is in the '''XOYZ''' octant and has the '''coordinates 4 comma 4 comma 2'''.
|-
| | Show the '''GeoGebra''' window.
| | Let us draw a '''3D''' pyramid in '''GeoGebra'''.

I have already opened a new window in '''GeoGebra'''.

This time, we work with '''Algebra, 2D Graphics''' and '''3D Graphics''' views.
|-
| | Under '''View''', select '''3D Graphics'''.
| | Under '''View''', select '''3D Graphics'''.
|-
| | Click in '''2D Graphics View''' to draw in '''2D'''.
| | Click in '''2D Graphics View''' to draw in '''2D'''.
|-
| | Drag the boundary to see '''2D Graphics''' properly.
| | Drag the boundary to see '''2D Graphics''' properly.
|-
| | Click in '''2D Graphics'''.
| | Click in '''2D Graphics'''.
|-
| | In '''2D Graphics''' view, click on '''Polygon''' tool and click on '''origin (0,0)'''.

Point to '''A'''.
| | In '''2D Graphics''' view, click on the '''Polygon''' tool and click on origin 0 comma 0.

This creates point '''A''' at the origin.
|-
| | Then click on '''(2,0)''' to create point '''B'''.
| | Then click on 2 comma 0 to create point '''B'''.
|-
| | Click on '''(2,2)''' for point '''C''', and on '''(0,2)''' to draw point '''D'''.
| | Click on 2 comma 2 for '''C''' and on 0 comma 2 to draw '''D'''.
|-
| | Click again on point '''A'''.
| | Finally, click again on '''A'''.
|-
| | Point to quadrilateral '''q1''' in '''2D''' and '''3D Graphics''' views.
| | Note that a quadrilateral '''q1''' is seen in '''2D''' and '''3D Graphics''' views.

The length of each side is 2 units.
|-
| | Click on '''Move''' tool.
| | Click on the '''Move''' tool.
|-
| | Click in '''2D Graphics''' and drag the background.
| | Click in '''2D Graphics''' and drag the background.
|-
| | Drag the boundary to see '''3D Graphics''' properly.
| | Drag the boundary to see '''3D Graphics''' properly.
|-
| | Click in '''3D Graphics''' and under '''Pyramid''', on the '''Extrude to Pyramid or Cone''' tool.

Click on the square in '''3D Graphics''' view.
| | Click in '''3D Graphics''' and under '''Pyramid''', on the '''Extrude to Pyramid or Cone''' tool.

In '''3D Graphics''' view, click on the square.
|-
| | An '''Altitude''' text box opens up, type 3 and click '''OK'''.
| | In the '''Altitude''' text-box that opens, type 3 and click '''OK'''.
|-
| | Point to pyramid '''e''' in '''3D Graphics''' view.

Point to base.

Point to '''E (1,1,3)'''.

Show altitude.
| | A pyramid '''e''' appears in '''3D Graphics''' view.

Its base is the quadrilateral '''q1'''.

Its apex is '''E''' 1 comma 1 comma 3.

Its altitude or height is 3 units.
|-
| | '''Slide Number 6'''

'''Rotation of a Polynomial'''

Let us rotate '''f(x)= ¬2x4-x3+3x2'''

Part in second '''quadrant''' ('''XY''' plane) about '''x-axis'''
| | '''Rotation of a Polynomial'''

Let us rotate '''f of x''' equals minus '''2 x raised to 4''' minus '''x cubed''' plus '''3 x squared'''.

We will rotate the part that lies in the second '''quadrant''', in '''XY''' plane, about the '''x-axis'''.
|-
| | Show the '''GeoGebra''' window.

| | I have already opened a new window in '''GeoGebra'''.

We will initially work with '''Algebra''' and '''2D Graphics''' views and open '''3D Graphics''' view later.
|-
| | In '''input bar''', type the following line and press '''Enter'''.

'''f(x) = -2 x^4 -x^3+3 x^2'''
| | In the '''input bar''', type the following line.

To type the '''caret symbol''', hold '''Shift''' key down and press 6.

'''f x''' in parentheses equals minus 2 space '''x caret''' 4 minus '''x caret''' 3 plus 3 space '''x caret''' 2

Spaces here denote multiplication.

Press '''Enter'''.
|-
| | Under '''Perpendicular Line''', click on '''Parallel line''' and on the '''y-axis'''.
| | Under '''Perpendicular Line''', click on '''Parallel line''' and on the '''y-axis'''.
|-
| | Keeping the '''cursor''' on the '''x-axis'''.
| | Keep the '''cursor''' on the '''x-axis'''.
|-
| | Drag it along until you reach the intersection of '''f''' and '''x-axis'''.

Point to the label '''function f, x-axis''' that appears.
| | Drag it along until you see '''function f, x-axis''' at the intersection of '''f''' and '''x-axis'''.
|-
| | Click on this intersection point.
| | Click on this intersection point.
|-
| | Point to '''A'''.
| | Point '''A''' appears.
|-
| | Click on '''Slider''' and in '''Graphics''' view.
| | Click on '''Slider''' and in '''Graphics''' view.
|-
| | A '''Slider''' dialog box opens.
| | A '''Slider''' dialog-box opens.
|-
| | Leave '''a''' as the '''Name'''.
| | Leave '''a''' as the '''Name'''.
|-
| | Change '''Min''' value to -1.5, '''Max''' value to 0 and '''Increment''' to 0.05.
| | Change '''Min''' value to '''minus''' 1.5, '''Max''' value to 0 and '''Increment''' to 0.05.
|-
| | Click '''OK'''.
| | Click '''OK'''.
|-
| | Point to '''slider a'''.

Point to the part of '''function''' and '''x-axis''' in the second '''quadrant'''.
| | This creates '''slider a''', which changes the value of '''a''' from -1.5 to 0.

It will focus on the part of the graph in the second '''quadrant'''.
|-
| | In the '''input bar''', type '''(a,f(a))'''.

Press '''Enter'''.
| | In the '''input bar''', type the following in parentheses.

'''a''' comma '''f a''' in parentheses.

Press '''Enter'''.
|-
| | Point to '''B'''.
| | This creates point '''B''' whose '''x coordinate''' is the value of '''a'''.

Its '''y-coordinate''' lies along the curve described by the '''function f''' between '''x''' equals 1.5 and 0.
|-
| | Right-click on '''slider a''' and check '''Animation On'''.
| | Right-click on '''slider a''' and check '''Animation On'''.
|-
| | Point to '''B''' and '''slider a'''.
| | Point '''B''' travels along '''function f''' as '''a''' changes.
|-
| | Right-click on '''slider a''' and uncheck '''Animation On'''.
| | Right-click on '''slider a''' and uncheck '''Animation On'''.
|-
| | In the '''input bar''', type '''(a,0)''' and press '''Enter'''.
| | In the '''input bar''', type '''a''' comma 0 in parentheses and press '''Enter'''.
|-
| | Point to '''C''' and '''slider a'''.
| | This creates point '''C'''.

As its '''x co-ordinate a''' changes, '''C''' moves below point '''B''' along the '''x-axis'''.
|-
| | Under '''Line''', click on '''Segment''' and click on '''B''' and '''C''' to join them.
| | Under '''Line''', click on '''Segment''' and click on '''B''' and '''C''' to join them.
|-
| | Click on '''Move Graphics View''' and drag background to the left.
| | Click on '''Move Graphics View''' and drag the background to the left.
|-
| | Click on '''View''' and check '''3D Graphics''' to see the '''3D Graphics''' view.
| | Click on '''View''' and check '''3D Graphics''' to see the '''3D Graphics''' view.
|-
| | Point to '''2D Graphics''' and '''3D Graphics''' views.
| | Note that what is drawn in '''2D Graphics''' appears in the '''XY''' plane, in '''3D Graphics'''.
|-
| | Click in '''3D Graphics''' view and on '''Rotate 3D Graphics View'''.

Rotate the '''3D Graphics''' view to see the curve properly.
| | Click in '''3D Graphics''' view and on '''Rotate 3D Graphics View'''.

Rotate '''3D Graphics''' to see the curve properly.
|-
| | Place '''cursor''' on '''y-axis''' (in green).

Click to see an arrow aligned with the '''y-axis'''.
| | Place the '''cursor''' on the '''y-axis''' (in green).

Click to see an arrow aligned with the '''y-axis'''.
|-
| | Then, drag along the '''y axis''' to see the curve properly.
| | Drag to pull the '''y-axis''' in or outwards to see the curve.
|-
| | Type '''Circle[C,f(a),xAxis]''' in the '''input bar''' and press '''Enter'''.
| | In the '''input bar''', type the following line

'''Circle''' open square brackets '''capital C '''comma '''f a''' in parentheses comma '''x Axis''' with '''capital A'''.

Close square brackets.
|-
| | Point to circle '''c''' with center at point '''C'''.
| | This creates circle '''c''' with center at point '''C'''.

Its radius is equal to '''f of a''' corresponding to the value of '''a''' on '''slider a'''.

Its rotation is around the '''x-axis'''.

Press '''Enter'''.
|-
| | Right-click on circle '''c''' in '''Algebra''' view and check '''Trace On''' option.
| | In '''Algebra''' view, right-click on circle '''c''' and check '''Trace On''' option.
|-
| | Right-click on '''slider a''' and select '''Animation On''' option.
| | Right-click on '''slider a''' and select '''Animation On''' option.
|-
| | Point to the solid traced as '''a''' changes.
| | Observe the solid traced as '''a''' changes.
|-
| | Point to '''2D''' and '''3D Graphics''' views.
| | Watch both '''2D''' and '''3D Graphics''' views.
|-
| | Point to Segment '''BC''', '''x-axis''' and '''function f'''.
| | Segment '''BC''' moves between the '''x-axis''' and '''function f'''.
|-
| | Point to the part of '''f''' in the second '''quadrant'''.
| | The part of '''function f''' that is in the second '''quadrant''' in '''2D,''' rotates around the '''x-axis'''.
|-
| | Drag '''3D Graphics''' to see it from another angle.
| | Drag '''3D Graphics''' to see it from another angle.
|-
| | Show the '''GeoGebra''' window.
| | Finally, let us look at '''trigonometric functions''' in '''3D.'''

I have already opened a new window in '''GeoGebra'''.
|-
| | Click on '''3D Graphics''' tool under '''View'''.
| | Under '''View''', click on '''3D Graphics'''.
|-
| | Drag the boundary to see '''2D Graphics''' properly.
| | Drag the boundary to see '''2D Graphics''' properly.
|-
| | Click in '''2D Graphics''', then on the '''Slider''' tool and in '''Graphics''' view.
| | Click in '''2D Graphics''', then on the '''Slider''' tool and in '''Graphics''' view.
|-
| | Point to the '''slider''' dialog box and '''Number''' radio button selection.

Type '''t''' in the '''Name''' field.
| | A '''slider''' dialog-box opens.

By default, the '''Number''' radio-button is selected.

In the '''Name''' field, type '''t'''.
|-
| | Set '''Min''' to -6, '''Max''' to 16 and '''increment''' of 0.1.

Click '''OK'''.
| | Set '''Min''' to minus 6, '''Max''' to 16 and '''increment''' of 0.1.

Click '''OK'''.
|-
| | Point to '''slider t'''.
| | This creates a '''slider t''' which will change '''t''' from minus 6 to 16.
|-
| | In the '''input bar''', type '''f(t)=cos(t)''' and press '''Enter'''.
| | In the '''input bar''', type '''f t''' in parentheses equals '''cos t''' in parentheses and press '''Enter'''.
|-
| | Click in '''2D Graphics'''.
| | Click in '''2D Graphics'''.
|-
| | Under '''Move Graphics View''', click on '''Zoom Out''' and click in '''2D Graphics'''.
| | Under '''Move Graphics View''', click on '''Zoom Out''' and click in '''2D Graphics'''.
|-
| | Click on '''Move Graphics View''' and drag the background.
| | Click on '''Move Graphics View''' and drag the background.
|-
| | Point to the '''cosine function''' of '''f(t)''' in '''2D''' and '''3D Graphics''' views.
| | You can see the graph of the '''cosine function''' of '''f of t''', in '''2D''' and '''3D Graphics''' views.
|-
| | Similarly, type '''g(t)=sin(t)''' in the '''input bar''' and press '''Enter'''.
| | Similarly, in the '''input bar''', type '''g t''' in parentheses equals '''sin t''' in parentheses.

Press '''Enter'''.
|-
| | Point to '''sine function''' graph ('''g(t)''').
| | '''Sine function''' graph of '''g of t''' appears.
|-
| | Now, type '''h(t)=t/4''' in the '''input bar''' and press '''Enter'''.
| | In the '''input bar''', type '''h t''' in parentheses equals '''t''' divided by 4 and press '''Enter'''.
|-
| | Point to line ('''h(t)''').
| | Line '''h of t''' is of the form '''y''' equals '''mx''' where slope '''m''' is 1 divided by 4.
|-
| | Click in '''3D Graphics''' view.
| | Click in '''3D Graphics''' view.
|-
| | Click on '''Point''' tool and click in the gray area in '''3D Graphics''' view.

Point to point '''A'''.
| | Click on the '''Point''' tool and click in the gray area in '''3D Graphics''' view.

This creates point '''A'''.
|-
| | Drag the boundary to see its '''co-ordinates''' properly.
| | Drag the boundary to see its '''co-ordinates''' properly.
|-
| | Double click on point '''A''' in '''Algebra''' view.

Change the '''co-ordinates''' to '''(f(t),g(t),h(t))'''.

Press '''Enter'''.
| | In '''Algebra''' view, double-click on '''A'''.

Change the '''coordinates''' to the following.
|-
| | Point to '''A'''.
| | The '''x- coordinate''' of '''A''' is '''cos t'''.

The '''y-coordinate''' is '''sin t''' and '''t''' divided by '''4''' is its '''z coordinate'''.
|-
| | Right-click on '''slider t''' and click on '''Object Properties'''.
| | Right-click on '''slider t''' and click on '''Object Properties'''.
|-
| | A '''Preferences''' dialog-box opens.

Click on '''Slider''' tab.

Under '''Animation''', for '''Repeat''', choose option “'''Increasing'''” from dropdown menu.
| | A '''Preferences''' dialog-box opens.

Click on '''Slider''' tab.

Under '''Animation''', for '''Repeat''', choose option “'''Increasing'''” from the dropdown menu.
|-
| | Close the '''Preferences''' dialog box.
| | Close the '''Preferences''' dialog box.
|-
| | Right-click on point '''A''' in '''Algebra''' view and select '''Trace On'''.
| | In '''Algebra''' view, right-click on '''A''' and select '''Trace On'''.
|-
| | Right-click on '''slider t''' and check '''Animation On'''.
| | Right-click on '''slider t''' and check '''Animation On'''.
|-
| | Point to point '''A''' and the '''helix''' in '''3D Graphics''' view.

Point to point '''A’s co-ordinates''' in '''Algebra''' view.
| | Point '''A''' traces a '''helix''' in '''3D''' space with '''coordinates''' mentioned earlier.
|-
| | Click in '''Rotate 3D Graphic View''' and rotate the background.

Rotate '''3D Graphics''' view.
| | Click in '''Rotate 3D Graphic View''' and rotate the background.

Rotate '''3D Graphics''' view so you are looking down the '''z-axis''' at the '''XY''' plane.
|-
| | Point to the traces of point '''A (cos(t), sin(t))'''.
| | Note that the traces of '''A''' are the circumference of a '''unit circle'''.

Point '''A''' moves along the circle as angle '''t''' changes.

In '''2D''', its '''coordinates''' are '''cos t''' comma '''sin t'''.
|-
| |
| | Let us summarize.
|-
| | '''Slide Number 6'''

'''Summary'''
| | In this '''tutorial''', we have learnt how to use '''GeoGebra''' to view:

And construct different structures in '''3D''' space

Solids of rotation of '''polynomial functions'''

'''Trigonometric functions''' in '''3D''' space
|-
| | '''Slide Number 7'''

'''Assignment'''

Construct a prism and a cylinder.

Draw lines to pierce the structures and find their intersection points.

Graph the '''polynomial, f(x)=x5-7x4+9x3+23x2-50x+24'''.

Show the solid formed due to rotation of peak in first '''quadrant''' in '''XY''' plane.
| | As an assignment:

Construct a prism and a cylinder anywhere in '''3D''' space.

Draw lines to pierce the structures and find their intersection points.

Graph the given '''polynomial'''.

Show the solid formed due to rotation of the peak, in the first '''quadrant''', in the '''XY''' plane.
|-
| | '''Slide Number 8'''

'''Assignment'''

You tried to fly a kite off a cliff. The kite got dumped into the lake below

You gave out 325 feet of string

The angle of declination from where you stand at the cliff’s edge to the kite is 15 degrees

How high is the cliff?
| | As another assignment,

You tried to fly a kite off a cliff. The kite got dumped into the lake below.

You gave out 325 feet of string.

The angle of declination from where you stand at the cliff’s edge to the kite is 15 degrees.

How high is the cliff?
|-
| | '''Slide Number 8'''

'''About Spoken Tutorial Project'''
| | The video at the following link summarizes the '''Spoken Tutorial''' project.

Please download and watch it.
|-
| | '''Slide Number 9'''

'''Spoken Tutorial workshops'''
| | The '''Spoken Tutorial '''project''' '''team:

<nowiki* conducts workshops using spoken tutorials and</nowiki>

<nowiki>* gives certificates on passing online tests.</nowiki>

For more details, please write to us.
|-
| | '''Slide Number 10'''

'''Forum for specific questions:'''

Do you have questions in THIS Spoken Tutorial?

Please visit this site

Choose the minute and second where you have the question

Explain your question briefly

Someone from our team will answer them
| | Please post your timed queries on this forum.
|-
| | '''Slide Number 11'''

'''Acknowledgement'''
| | '''Spoken Tutorial''' project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.
|-
| |
| | This is '''Vidhya Iyer''' from '''IIT Bombay,''' signing off.

Thank you for joining.
|-
|}

@@ Line 158: / Line 158: @@
 We will initially work with '''Algebra''' and '''2D Graphics''' views and open '''3D Graphics''' view later.
 |-
-||In '''input bar''', type the following line >> press '''Enter'''.
+||In '''input bar''', type the following line
 '''f(x) = -2 x^4 -x^3+3 x^2'''
@@ Line 169: / Line 171: @@
 Press '''Enter'''.
 |-
-||Under '''Perpendicular Line''', click on '''Parallel line''' >> on the '''y-axis'''.
+||Under '''Perpendicular Line''', click on '''Parallel line'''
 ||Under '''Perpendicular Line''', click on '''Parallel line''' and on the '''y-axis'''.
 |-
@@ Line 205: / Line 209: @@
 ||Point to '''slider a'''.
-Point to the part of '''function''' and '''x-axis''' in the second '''quadrant'''.
+Point to the part of '''function''',
 ||This creates '''slider a''', which changes the value of '''a''' from -1.5 to 0.
@@ Line 241: / Line 247: @@
 As its '''x co-ordinate a''' changes, '''C''' moves below point '''B''' along the '''x-axis'''.
 |-
-||Under '''Line''', click on '''Segment''' >> click on '''B''' and '''C''' to join them.
+||Under '''Line''', click on '''Segment'''
 ||Under '''Line''', click on '''Segment''' and click on '''B''' and '''C''' to join them.
 |-
@@ Line 247: / Line 255: @@
 ||Click on '''Move Graphics View''' and drag the background to the left.
 |-
-||Click on '''View''' >> check '''3D Graphics''' to see the '''3D Graphics''' view.
+||Click on '''View'''
 ||Click on '''View''' and check '''3D Graphics''' to see the '''3D Graphics''' view.
 |-
@@ Line 270: / Line 280: @@
 ||Drag to pull the '''y-axis''' in or outwards to see the curve.
 |-
-||Type '''Circle[C,f(a),xAxis]''' in the '''input bar''' >> press '''Enter'''.
+||Type '''Circle[C,f(a),xAxis]''' in the '''input bar'''
 ||In the '''input bar''', type the following line.
@@ Line 283: / Line 295: @@
 Press '''Enter'''.
 |-
-||Right-click on circle '''c''' in '''Algebra''' view and check '''Trace On''' option.
+||Right-click on circle '''c''' in '''Algebra''' view
 ||In '''Algebra''' view, right-click on circle '''c''' and check '''Trace On''' option.
 |-
@@ Line 315: / Line 329: @@
 ||Drag the boundary to see '''2D Graphics''' properly.
 |-
-||Click in '''2D Graphics'''>> '''Slider''' tool and in '''Graphics''' view.
+||Click in '''2D Graphics'''
 ||Click in '''2D Graphics''', then on the '''Slider''' tool and in '''Graphics''' view.
 |-
@@ Line 337: / Line 353: @@
 ||This creates a '''slider t''' which will change '''t''' from minus 6 to 16.
 |-
-||In the '''input bar''', type '''f(t)=cos(t)''' >> press '''Enter'''.
+||In the '''input bar''', type '''f(t)=cos(t)'''
 ||In the '''input bar''', type '''f t''' in parentheses equals '''cos t''' in parentheses and press '''Enter'''.
 |-
@@ Line 343: / Line 361: @@
 ||Click in '''2D Graphics'''.
 |-
-||Under '''Move Graphics View''', click on '''Zoom Out''' >> click in '''2D Graphics'''.
+||Under '''Move Graphics View''', click on '''Zoom Out'''
 ||Under '''Move Graphics View''', click on '''Zoom Out''' and click in '''2D Graphics'''.
 |-
@@ Line 400: / Line 420: @@
 Click on '''Slider''' tab.
-Under '''Animation''', for '''Repeat''', choose option '''Increasing''' from dropdown menu.
+Under '''Animation''', for '''Repeat''',
 || A '''Preferences''' dialog-box opens.
@@ Line 410: / Line 432: @@
 ||Close the '''Preferences''' dialog box.
 |-
-||Right-click on point '''A''' in '''Algebra''' view >> select '''Trace On'''.
+||Right-click on point '''A''' in '''Algebra''' view
 ||In '''Algebra''' view, right-click on '''A''' and select '''Trace On'''.
 |-
@@ Line 474: / Line 498: @@
 '''Assignment'''
-You tried to fly a kite off a cliff. The kite got dumped into the lake below
+You tried to fly a kite off a cliff.
 You gave out 325 feet of string
-The angle of declination from where you stand at the cliff’s edge to the kite is 15 degrees
+The angle of declination from where you stand at the cliff’s edge
 How high is the cliff?
@@ Line 503: / Line 531: @@
 ||The '''Spoken Tutorial '''project''' '''team:
-<nowiki* conducts workshops using spoken tutorials and</nowiki>
+conducts workshops using spoken tutorials and</nowiki>
-<nowiki>* gives certificates on passing online tests.</nowiki>
+gives certificates on passing online tests.</nowiki>
 For more details, please write to us.