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Guaranteed Solutions

CHAPTER 8: GRAVITATION

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⠸⠎⠕⠍⠑⠞⠊⠍⠑⠎⠀⠝⠕⠞⠀⠕⠝⠇⠽⠀⠕⠝⠀⠮⠀⠎⠑⠁⠤⠊⠉⠑⠀⠃⠥⠞⠀⠕⠝⠀⠮ ⠇⠁⠝⠙⠀⠁⠎⠀⠺⠑⠇⠇⠂⠀⠹⠑⠽⠀⠍⠁⠙⠑⠀⠞⠗⠁⠧⠑⠇⠀⠊⠍⠏⠕⠎⠎⠊⠃⠇⠑⠀⠃⠽ ⠍⠁⠅⠔⠛⠀⠊⠞⠀⠙⠁⠝⠛⠑⠗⠳⠎⠀⠞⠕⠀⠍⠕⠧⠑⠀⠁⠃⠕⠥⠞⠲⠀⠠⠕⠝⠉⠑⠀⠞⠺⠕ ⠍⠑⠝⠀⠎⠑⠞⠀⠕⠥⠞⠀⠞⠕⠀⠺⠁⠇⠅⠀⠠⠕⠝⠑⠀⠍⠊⠇⠑⠀⠞⠕⠀⠮⠀⠍⠑⠞⠑⠕⠗⠕⠤ ⠇⠕⠛⠊⠉⠁⠇⠀⠓⠥⠞⠲⠀⠠⠃⠑⠋⠕⠗⠑⠀⠹⠑⠽⠀⠓⠁⠙⠀⠛⠕⠝⠑⠀⠍⠁⠝⠽⠀⠽⠁⠗⠙⠎ ⠁⠀⠃⠇⠊⠵⠵⠁⠗⠙⠀⠉⠁⠍⠑⠀⠙⠕⠺⠝⠀⠥⠏⠕⠝⠀⠹⠑⠍⠲⠀⠠⠹⠑⠽⠀⠞⠥⠗⠝⠑⠙ ⠃⠁⠉⠅⠀⠞⠕⠀⠮⠀⠓⠥⠞⠀⠃⠥⠞⠀⠉⠕⠥⠇⠙⠀⠝⠕⠞⠀⠋⠔⠙⠀⠊⠞⠲⠀⠠⠹⠑⠽⠀⠺⠑⠗⠑ ⠇⠕⠎⠞⠀⠋⠕⠗⠀⠞⠺⠕⠀⠙⠁⠽⠎⠀⠁⠝⠙⠀⠝⠊⠣⠞⠎⠂⠀⠁⠝⠙⠀⠺⠑⠗⠑⠀⠝⠑⠁⠗⠇⠽ ⠙⠑⠁⠙⠀⠺⠰⠓⠀⠁⠀⠎⠑⠁⠗⠡⠀⠏⠁⠗⠞⠽⠀⠋⠕⠥⠝⠙⠀⠹⠑⠍⠲

⠀⠠⠕⠝⠀⠁⠝⠕⠹⠑⠗⠀⠕⠉⠉⠁⠎⠊⠕⠝⠀⠁⠀⠍⠁⠝⠀⠺⠁⠎⠀⠇⠕⠎⠞⠀⠋⠕⠗⠀⠋⠕⠥⠗ ⠙⠁⠽⠎⠀⠔⠀⠁⠀⠃⠇⠊⠵⠵⠁⠗⠙⠲⠀⠠⠓⠑⠀⠎⠁⠊⠙⠀⠞⠓⠁⠞⠀⠓⠑⠀⠺⠁⠎⠀⠝⠑⠧⠑⠗ ⠁⠋⠗⠁⠊⠙⠀⠁⠇⠹⠕⠥⠣⠀⠓⠑⠀⠓⠁⠙⠀⠝⠕⠀⠋⠕⠕⠙⠀⠕⠗⠀⠺⠁⠞⠑⠗⠲⠀⠠⠓⠑ ⠺⠁⠇⠅⠑⠙⠀⠁⠃⠕⠥⠞⠀⠺⠰⠓⠀⠮⠀⠺⠔⠙⠀⠃⠑⠓⠔⠙⠀⠓⠊⠍⠂⠀⠎⠕⠀⠹⠁⠞⠀⠓⠑ ⠺⠕⠥⠇⠙⠀⠝⠕⠞⠀⠃⠑⠀⠋⠗⠕⠵⠑⠝⠀⠞⠕⠀⠙⠑⠁⠹⠂⠀⠁⠝⠙⠀⠺⠰⠓⠀⠓⠊⠎⠀⠋⠁⠉⠑ ⠞⠥⠗⠝⠑⠙⠀⠁⠺⠁⠽⠀⠋⠗⠕⠍⠀⠮⠀⠎⠞⠕⠗⠍⠲⠀⠠⠺⠰⠓⠀⠮⠀⠇⠥⠉⠅⠀⠞⠓⠁⠞ ⠎⠕⠍⠑⠞⠊⠍⠑⠎⠀⠁⠞⠞⠑⠝⠙⠎⠀⠍⠑⠝⠀⠔⠀⠎⠥⠡⠀⠙⠁⠝⠛⠑⠗⠎⠂⠀⠓⠑⠀⠺⠁⠎ ⠎⠁⠧⠑⠙⠀⠃⠽⠀⠺⠁⠇⠅⠔⠛⠀⠔⠞⠕⠀⠮⠀⠉⠁⠍⠏⠀⠺⠰⠓⠕⠥⠞⠀⠅⠝⠪⠔⠛⠀⠺⠓⠑⠗⠑ ⠓⠑⠀⠺⠁⠎⠲

⠀⠠⠺⠰⠓⠀⠎⠥⠡⠀⠺⠔⠙⠎⠀⠁⠝⠙⠀⠞⠑⠍⠏⠑⠗⠁⠞⠥⠗⠑⠎⠀⠊⠞⠀⠊⠎⠀⠝⠕⠞⠀⠎⠥⠗⠤ ⠏⠗⠊⠎⠔⠛⠀⠞⠓⠁⠞⠀⠞⠗⠁⠧⠑⠇⠀⠺⠁⠎⠀⠎⠕⠀⠙⠊⠋⠋⠊⠉⠥⠇⠞⠲⠀⠠⠃⠥⠞⠀⠍⠁⠝⠽ ⠚⠕⠥⠗⠝⠑⠽⠎⠀⠺⠑⠗⠑⠀⠍⠁⠙⠑⠀⠔⠀⠎⠏⠊⠞⠑⠀⠕⠋⠀⠮⠀⠺⠑⠁⠹⠑⠗⠲⠀⠠⠍⠑⠝ ⠺⠁⠇⠅⠑⠙⠀⠞⠕⠀⠁⠝⠙⠀⠋⠗⠕⠀⠕⠝⠀⠮⠀⠎⠑⠁⠤⠊⠉⠑⠂⠀⠎⠕⠍⠑⠞⠊⠍⠑⠎⠀⠎⠇⠑⠙⠛⠤ ⠔⠛⠀⠁⠝⠙⠀⠎⠕⠍⠑⠞⠊⠍⠑⠎⠀⠉⠁⠗⠗⠽⠔⠛⠀⠹⠑⠊⠗⠀⠇⠕⠁⠙⠎⠀⠕⠝⠀⠹⠑⠊⠗ ⠃⠁⠉⠅⠎⠲

⠀⠠⠞⠓⠊⠎ ⠊⠎ ⠠⠃⠗⠁⠊⠇⠇⠑ ⠞⠑⠭⠞⠇⠔⠑ ⠕⠝⠑ ⠀⠠⠃⠗⠁⠊⠇⠇⠑ ⠞⠑⠭⠞ ⠎⠑⠉⠕⠝⠙ ⠇⠔⠑

⠀⠁⠃⠉⠙⠑⠋⠛⠠⠤⠥⠇⠍⠝⠕⠏⠟⠗⠎⠞⠥⠧⠺⠭⠽⠯ [?]

⠎⠕⠍⠑⠞⠊⠍⠑⠎ ⠊⠞ ⠊⠎ ⠝⠑⠉⠑⠎⠎⠁⠗⠽ ⠞⠕ [?] ⠁⠝⠙ ⠞⠓⠁⠞ ⠎⠕⠍⠑ ⠃⠗⠁⠊⠇⠇⠑ ⠞⠑⠭⠞ ⠊⠎ ⠓⠑⠗⠑ [?]

⠼⠑⠲ ⠠⠺⠓⠊⠡ ⠞⠺⠕ ⠎⠑⠝⠞⠑⠝⠉⠑⠎ ⠎⠓⠕⠺ ⠞⠓⠁⠞ ⠞⠓⠑ ⠎⠝⠁⠊⠇ ⠁⠝⠙ ⠺⠓⠁⠇⠑ ⠞⠗⠁⠧⠑⠇⠑⠙ ⠞⠕ ⠍⠁⠝⠽ ⠙⠊⠋⠋⠑⠗⠑⠝⠞ ⠏⠇⠁⠉⠑⠎⠦

⠠⠁⠲ ⠦⠠⠞⠓⠊⠎ ⠊⠎ ⠞⠓⠑ ⠎⠑⠁ ⠎⠕ ⠺⠊⠇⠙ ⠁⠝⠙ ⠋⠗⠑⠑⠂ ⠞⠓⠁⠞ ⠞⠕⠕⠅ ⠞⠓⠑ ⠞⠊⠝⠽ ⠎⠝⠁⠊⠇ ⠕⠝ ⠞⠓⠑ ⠞⠁⠊⠇ ⠕⠋ ⠞⠓⠑ ⠺⠓⠁⠇⠑ ⠞⠕ ⠞⠕⠺⠑⠗⠊⠝⠛ ⠊⠉⠑⠃⠑⠗⠛⠎ ⠁⠝⠙ ⠋⠁⠗⠤⠕⠋⠋ ⠇⠁⠝⠙⠎⠲⠴ ⠐⠣⠏⠁⠗⠁⠛⠗⠁⠏⠓ ⠼⠁⠐⠜

⠠⠃⠲ ⠦⠠⠞⠓⠑⠎⠑ ⠁⠗⠑ ⠞⠓⠑ ⠺⠁⠧⠑⠎ ⠞⠓⠁⠞ ⠁⠗⠉⠓ ⠁⠝⠙ ⠉⠗⠁⠩⠂ ⠞⠓⠁⠞ ⠋⠕⠁⠍ ⠁⠝⠙ ⠋⠗⠕⠞⠓ ⠁⠝⠙ ⠙⠑⠏⠞⠓ ⠁⠝⠙ ⠎⠏⠗⠁⠽⠂ ⠁⠝⠙ ⠎⠏⠗⠁⠽ ⠞⠓⠑ ⠞⠊⠝⠽ ⠎⠝⠁⠊⠇ ⠕⠝ ⠞⠓⠑ ⠞⠁⠊⠇ ⠕⠋ ⠞⠓⠑ ⠺⠓⠁⠇⠑⠲⠴ ⠐⠣⠏⠁⠗⠁⠛⠗⠁⠏⠓ ⠼⠃⠐⠜

⠠⠉⠲ ⠦⠠⠞⠓⠑⠎⠑ ⠁⠗⠑ ⠞⠓⠑ ⠉⠁⠧⠑⠎ ⠃⠑⠝⠑⠁⠞⠓ ⠞⠓⠑ ⠺⠁⠧⠑⠎⠂ ⠺⠓⠑⠗⠑ ⠎⠞⠗⠊⠏⠽ ⠋⠊⠩ ⠺⠊⠞⠓ ⠋⠑⠁⠞⠓⠑⠗⠽ ⠋⠊⠝⠎ ⠁⠝⠙ ⠎⠓⠁⠗⠅⠎ ⠺⠊⠞⠓ ⠓⠊⠙⠑⠕⠥⠎ ⠛⠗⠊⠝⠎ ⠎⠺⠁⠍ ⠁⠗⠕⠥⠝⠙ ⠞⠓⠑ ⠺⠓⠁⠇⠑ ⠁⠝⠙ ⠞⠓⠑ ⠎⠝⠁⠊⠇ ⠕⠝ ⠓⠊⠎ ⠞⠁⠊⠇⠲⠴ ⠐⠣⠏⠁⠗⠁⠛⠗⠁⠏⠓ ⠼⠉⠐⠜

⠠⠙⠲ ⠦⠠⠞⠓⠊⠎ ⠊⠎ ⠞⠓⠑ ⠎⠅⠽ ⠎⠕ ⠧⠁⠎⠞ ⠁⠝⠙ ⠓⠊⠛⠓⠂ ⠎⠕⠍⠑⠞⠊⠍⠑⠎ ⠎⠥⠝⠝⠽ ⠁⠝⠙ ⠃⠇⠥⠑ ⠁⠝⠙ ⠺⠁⠗⠍⠂ ⠎⠕⠍⠑⠞⠊⠍⠑⠎ ⠋⠊⠇⠇⠑⠙ ⠺⠊⠞⠓ ⠁ ⠞⠓⠥⠝⠙⠑⠗⠎⠞⠕⠗⠍⠲⠴ ⠐⠣⠏⠁⠗⠁⠛⠗⠁⠏⠓ ⠼⠙⠐⠜

⠠⠑⠲ ⠦⠠⠁⠝⠙ ⠎⠓⠑ ⠛⠁⠵⠑⠙ ⠁⠞ ⠞⠓⠑ ⠎⠅⠽⠂ ⠞⠓⠑ ⠎⠑⠁⠂ ⠞⠓⠑ ⠇⠁⠝⠙⠂ ⠞⠓⠑ ⠺⠁⠧⠑⠎ ⠁⠝⠙ ⠞⠓⠑ ⠉⠁⠧⠑⠎ ⠁⠝⠙ ⠞⠓⠑ ⠛⠕⠇⠙⠑⠝ ⠎⠁⠝⠙⠂ ⠎⠓⠑ ⠛⠁⠵⠑⠙ ⠁⠝⠙ ⠛⠁⠵⠑⠙⠂ ⠙⠊⠎⠍⠁⠽⠑⠙ ⠃⠽ ⠊⠞ ⠁⠇⠇⠂ ⠁⠝⠙ ⠎⠓⠑ ⠎⠁⠊⠙ ⠞⠕ ⠞⠓⠑ ⠺⠓⠁⠇⠑⠂ ⠄⠠⠊ ⠋⠑⠑⠇ ⠎⠕ ⠎⠍⠁⠇⠇⠲⠄⠴ ⠐⠣⠏⠁⠗⠁⠛⠗⠁⠏⠓ ⠼⠑⠐⠜ ⠠⠞⠓⠊⠎ ⠎⠏⠑⠉⠊⠁⠇ ⠃⠕⠕⠅ ⠚⠕⠥⠗⠝⠑⠽ ⠎⠞⠁⠗⠞⠎ ⠓⠑⠗⠑...

⠠⠕⠝⠀⠑⠁⠡⠀⠕⠋⠀⠮⠀⠋⠕⠇⠇⠕⠺⠬⠀⠎⠇⠔⠑⠎⠀⠽⠀⠺⠔⠇⠀⠋⠔⠙⠀⠁
⠧⠻⠎⠑⠀⠋⠗⠕⠍⠀⠮⠀⠠⠃⠊⠃⠇⠑⠲⠀⠠⠊⠝⠀⠮⠀⠃⠇⠁⠝⠅⠀⠁⠞⠀⠮⠀⠑⠝⠙
⠕⠋⠀⠑⠁⠡⠀⠇⠔⠑⠀⠺⠗⠊⠞⠑⠀⠮⠀⠝⠁⠍⠑⠀⠕⠋⠀⠮⠀⠠⠃⠊⠃⠇⠑
⠏⠻⠎⠕⠝⠀⠺⠓⠕⠀⠎⠁⠊⠙⠀⠮⠀⠺⠕⠗⠙⠎⠲

⠼⠁⠲⠀⠦⠠⠊⠎⠀⠁⠝⠽⠹⠬⠀⠞⠕⠕⠀⠓⠁⠗⠙⠀⠿⠀⠮⠀⠠⠇⠕⠗⠙⠢ ⠠⠛⠑⠝⠑⠎⠊⠎⠀⠼⠁⠓⠒⠁⠙⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠼⠃⠲⠀⠦⠠⠋⠑⠁⠗⠀⠝⠕⠞⠂⠀⠎⠞⠁⠝⠙⠀⠎⠞⠔⠇⠂⠀⠯⠀⠎⠑⠑⠀⠮
⠎⠁⠇⠧⠁⠞⠊⠕⠝⠀⠕⠋⠀⠮⠀⠠⠇⠕⠗⠙⠲⠴⠀⠠⠑⠭⠕⠙⠥⠎⠀⠼⠁⠙⠒⠁⠉
⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠼⠉⠲⠀⠦⠠⠺⠓⠁⠞⠀⠍⠑⠁⠝⠑⠹⠀⠮⠀⠃⠇⠑⠁⠞⠬⠀⠕⠋⠀⠮⠀⠩⠑⠑⠏
⠔⠀⠍⠔⠑⠀⠑⠁⠗⠎⠂⠀⠯⠀⠮⠀⠇⠕⠺⠬⠀⠕⠋⠀⠮⠀⠕⠭⠑⠝
⠺⠓⠊⠡⠀⠠⠊⠀⠓⠑⠁⠗⠢⠴⠀⠼⠁⠀⠠⠎⠁⠍⠥⠑⠇⠀⠼⠁⠑⠒⠁⠙
⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠼⠙⠲⠀⠦⠠⠍⠽⠀⠓⠑⠇⠏⠀⠉⠕⠍⠑⠹⠀⠋⠗⠕⠍⠀⠮⠀⠠⠇⠕⠗⠙⠂⠀⠺⠓⠊⠡
⠍⠁⠙⠑⠀⠓⠑⠁⠧⠑⠝⠀⠯⠀⠑⠁⠗⠹⠲⠴⠀⠠⠏⠎⠁⠇⠍⠀⠼⠁⠃⠁⠒⠃
⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠼⠑⠲⠀⠦⠠⠏⠥⠞⠀⠝⠕⠞⠀⠽⠗⠀⠞⠗⠥⠎⠞⠀⠔⠀⠏⠗⠔⠉⠑⠎⠂⠀⠝⠕⠗⠀⠔⠀⠮
⠎⠕⠝⠀⠕⠋⠀⠍⠁⠝⠂⠀⠔⠀⠺⠓⠕⠍⠀⠹⠀⠊⠎⠀⠝⠕⠀⠓⠑⠇⠏⠲⠴
⠠⠏⠎⠁⠇⠍⠀⠼⠁⠙⠋⠒⠉⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠼⠋⠲⠀⠦⠠⠽⠑⠀⠜⠑⠀⠍⠽⠀⠺⠊⠞⠝⠑⠎⠎⠑⠎⠂⠀⠎⠁⠊⠹⠀⠮⠀⠠⠇⠕⠗⠙⠂
⠯⠀⠍⠽⠀⠎⠻⠧⠁⠝⠞⠀⠺⠓⠕⠍⠀⠠⠊⠀⠓⠁⠧⠑⠀⠡⠕⠎⠑⠝⠲⠴
⠠⠊⠎⠁⠊⠁⠓⠀⠼⠙⠉⠒⠁⠚⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠼⠛⠲⠀⠦⠠⠓⠑⠁⠗⠂⠀⠠⠊⠀⠏⠗⠁⠽⠀⠽⠕⠥⠂⠀⠁⠇⠇⠀⠏⠑⠕⠏⠇⠑⠂⠀⠯
⠃⠑⠓⠕⠇⠙⠀⠍⠽⠀⠎⠕⠗⠗⠕⠺⠲⠴⠀⠠⠇⠁⠍⠑⠝⠞⠁⠞⠊⠕⠝⠎
⠼⠁⠒⠁⠃⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠼⠓⠲⠀⠦⠠⠺⠓⠁⠞⠀⠙⠕⠞⠓⠀⠮⠀⠠⠇⠕⠗⠙⠀⠗⠑⠟⠥⠊⠗⠑⠀⠕⠋⠀⠮⠑⠑⠂⠀⠃⠥⠞ ⠞⠕⠀⠙⠕⠀⠚⠥⠎⠞⠇⠽⠂⠀⠯⠀⠞⠕⠀⠇⠕⠧⠑⠀⠍⠻⠉⠽⠂⠀⠯⠀⠞⠕⠀⠺⠁⠇⠅ ⠓⠥⠍⠃⠇⠽⠀⠾⠀⠹⠽⠀⠠⠛⠕⠙⠢⠴⠀⠠⠍⠊⠉⠁⠓⠀⠼⠋⠒⠓ ⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠼⠊⠲⠀⠦⠠⠊⠀⠺⠔⠇⠀⠗⠑⠚⠕⠊⠉⠑⠀⠔⠀⠮⠀⠠⠇⠕⠗⠙⠂⠀⠠⠊⠀⠺⠔⠇⠀⠚⠕⠽ ⠔⠀⠮⠀⠠⠛⠕⠙⠀⠕⠋⠀⠍⠽⠀⠎⠁⠇⠧⠁⠞⠊⠕⠝⠲⠴⠀⠠⠓⠁⠃⠁⠅⠅⠥⠅ ⠼⠉⠒⠁⠓⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠸⠕⠧⠑⠗⠍⠁⠝ ⠐⠕⠋ ⠞⠓⠑ ⠸⠏⠁⠗⠊⠎ ⠸⠉⠕⠍⠍⠥⠝⠑

⠸⠞⠓⠑ ⠐⠛⠗⠑⠁⠞ ⠞⠗⠁⠛⠑⠙⠽ ⠷ ⠞⠓⠑ ⠸⠏⠁⠗⠊⠎ ⠸⠉⠕⠍⠍⠥⠝⠑ ⠠⠶⠊⠝ ⠺⠓⠊⠉⠓ ⠎⠕⠍⠑ ⠼⠃⠚⠂⠚⠚⠚ ⠺⠕⠗⠅⠑⠗⠎ ⠺⠑⠗⠑ ⠍⠥⠗⠙⠑⠗⠑⠙ ⠃⠽ ⠞⠓⠑ ⠺⠓⠊⠞⠑ ⠞⠑⠗⠗⠕⠗ ⠷ ⠞⠓⠑ ⠃⠕⠥⠗⠛⠑⠕⠊⠎⠊⠑ ⠁⠝⠙ ⠎⠕⠍⠑ ⠼⠉⠓⠂⠚⠚⠚ ⠺⠑⠗⠑ ⠊⠍⠏⠗⠊⠎⠕⠝⠑⠙ ⠕⠗ ⠑⠭⠊⠇⠑⠙⠠⠄ ⠸⠎⠕⠍⠑ ⠷ ⠞⠓⠑ ⠇⠁⠞⠞⠑⠗ ⠑⠧⠑⠝⠞⠥⠁⠇⠇⠽ ⠍⠁⠙⠑ ⠞⠓⠑⠊⠗ ⠺⠁⠽ ⠞⠕ ⠸⠝⠑⠺ ⠸⠉⠁⠇⠑⠙⠕⠝⠊⠁⠠⠄ ⠁ ⠸⠋⠗⠑⠝⠉⠓ ⠉⠕⠇⠕⠝⠽ ⠊⠝ ⠞⠓⠑ ⠸⠎⠕⠥⠞⠓ ⠸⠏⠁⠉⠊⠋⠊⠉⠠⠄ ⠺⠓⠑⠗⠑ ⠞⠓⠑⠽ ⠺⠑⠗⠑ ⠥⠎⠑⠙ ⠁⠎ ⠋⠕⠗⠉⠑⠙ ⠇⠁⠃⠕⠥⠗ ⠞⠕ ⠎⠥⠏⠏⠗⠑⠎⠎ ⠞⠓⠑ ⠊⠝⠙⠊⠛⠑⠝⠕⠥⠎ ⠸⠅⠁⠝⠁⠅ ⠏⠑⠕⠏⠇⠑ ⠁⠝⠙ ⠞⠕ ⠺⠕⠗⠅ ⠊⠝ ⠞⠓⠑ ⠝⠊⠉⠅⠑⠇ ⠍⠊⠝⠑⠎⠠⠶ ⠺⠁⠎ ⠝⠕⠞ ⠇⠕⠎⠞ ⠕⠝ ⠸⠍⠁⠗⠭ ⠕⠗ ⠸⠇⠑⠝⠊⠝⠠⠄ ⠃⠕⠞⠓ ⠷ ⠺⠓⠕⠍ ⠙⠑⠧⠕⠞⠑⠙ ⠉⠕⠝⠎⠊⠙⠑⠗⠁⠃⠇⠑ ⠞⠊⠍⠑ ⠞⠕ ⠁⠝⠁⠇⠽⠎⠊⠝⠛ ⠞⠓⠑ ⠝⠁⠞⠥⠗⠑ ⠷ ⠞⠓⠑ ⠸⠉⠕⠍⠍⠥⠝⠑ ⠁⠝⠙ ⠊⠞⠎ ⠇⠊⠍⠊⠞⠁⠞⠊⠕⠝⠎⠠⠄

⠸⠊⠝ ⠸⠉⠊⠧⠊⠇ ⠸⠺⠁⠗ ⠊⠝ ⠸⠋⠗⠁⠝⠉⠑⠂ ⠸⠍⠁⠗⠭ ⠕⠃⠎⠑⠗⠧⠑⠙ ⠞⠓⠁⠞ ⠦⠞⠓⠑ ⠺⠕⠗⠅⠊⠝⠛ ⠉⠇⠁⠎⠎ ⠉⠁⠝⠝⠕⠞ ⠎⠊⠍⠏⠇⠽ ⠇⠁⠽ ⠓⠕⠇⠙ ⠷ ⠞⠓⠑ ⠗⠑⠁⠙⠽⠤⠍⠁⠙⠑ ⠎⠞⠁⠞⠑ ⠍⠁⠉⠓⠊⠝⠑⠗⠽⠂ ⠁⠝⠙ ⠺⠊⠑⠇⠙ ⠊⠞ ⠋⠕⠗ ⠊⠞⠎ ⠕⠺⠝ ⠏⠥⠗⠏⠕⠎⠑⠎⠠⠄ ⠸⠞⠓⠑ ⠉⠑⠝⠞⠗⠁⠇⠊⠎⠑⠙ ⠎⠞⠁⠞⠑ ⠏⠕⠺⠑⠗⠂ ⠺⠊⠞⠓ ⠊⠞⠎ ⠥⠃⠊⠟⠥⠊⠞⠕⠥⠎ ⠕⠗⠛⠁⠝⠎ ⠷ ⠎⠞⠁⠝⠙⠊⠝⠛ ⠁⠗⠍⠽⠂ ⠏⠕⠇⠊⠉⠑⠂ ⠃⠥⠗⠑⠁⠥⠉⠗⠁⠉⠽⠂ ⠉⠇⠑⠗⠛⠽⠂ ⠁⠝⠙ ⠚⠥⠙⠊⠉⠊⠁⠗⠽⠂ ⠕⠗⠊⠛⠊⠝⠁⠞⠑⠎ ⠋⠗⠕⠍ ⠞⠓⠑ ⠙⠁⠽⠎ ⠷ ⠁⠃⠎⠕⠇⠥⠞⠑ ⠍⠕⠝⠁⠗⠉⠓⠽⠠⠄⠴ ⠸⠞⠓⠑ ⠃⠕⠥⠗⠛⠑⠕⠊⠎⠊⠑ ⠓⠁⠙ ⠞⠁⠅⠑⠝ ⠕⠧⠑⠗ ⠞⠓⠊⠎ ⠁⠏⠏⠁⠗⠁⠞⠥⠎ ⠁⠝⠙ ⠥⠎⠑⠙ ⠊⠞ ⠞⠕ ⠎⠥⠏⠏⠗⠑⠎⠎ ⠞⠓⠑ ⠺⠕⠗⠅⠊⠝⠛ ⠉⠇⠁⠎⠎⠠⠄ ⠸⠞⠓⠑ ⠸⠉⠕⠍⠍⠥⠝⠑ ⠙⠑⠍⠕⠝⠎⠞⠗⠁⠞⠑⠙ ⠞⠓⠁⠞ ⠞⠓⠑ ⠺⠕⠗⠅⠊⠝⠛ ⠉⠇⠁⠎⠎ ⠓⠁⠙ ⠞⠕ ⠎⠍⠁⠎⠓ ⠞⠓⠑ ⠕⠇⠙ ⠎⠞⠁⠞⠑ ⠍⠁⠉⠓⠊⠝⠑ ⠁⠝⠙ ⠉⠗⠑⠁⠞⠑ ⠁ ⠝⠑⠺ ⠕⠝⠑⠠⠄

⠠⠉⠁⠗⠇⠀⠠⠛⠥⠎⠞⠁⠧⠀⠠⠚⠥⠝⠛ ⠐⠣⠼⠁⠊⠛⠑⠤⠼⠁⠊⠋⠁⠐⠜

⠠⠞⠓⠑⠀⠠⠗⠑⠙⠀⠠⠃⠕⠕⠅

⠠⠇⠊⠃⠑⠗⠀⠠⠝⠕⠧⠥⠎

⠠⠁⠀⠠⠗⠑⠁⠙⠑⠗⠄⠎⠀⠠⠑⠙⠊⠞⠊⠕⠝

⠠⠑⠙⠊⠞⠑⠙⠀⠁⠝⠙⠀⠠⠊⠝⠞⠗⠕⠙⠥⠉⠑⠙⠀⠃⠽ ⠠⠎⠕⠝⠥⠀⠠⠎⠓⠁⠍⠙⠁⠎⠁⠝⠊

⠠⠞⠗⠁⠝⠎⠇⠁⠞⠑⠙⠀⠃⠽
⠠⠍⠁⠗⠅⠀⠠⠅⠽⠃⠥⠗⠵⠂⠀⠠⠚⠕⠓⠝⠀⠠⠏⠑⠉⠅
⠁⠝⠙⠀⠠⠎⠕⠝⠥⠀⠠⠎⠓⠁⠍⠙⠁⠎⠁⠝⠊

⠠⠏⠓⠊⠇⠑⠍⠕⠝⠀⠠⠎⠑⠗⠊⠑⠎

⠠⠺⠄⠠⠺⠄⠀⠠⠝⠕⠗⠞⠕⠝⠀⠈⠯⠀⠠⠉⠕⠍⠏⠁⠝⠽ ⠠⠝⠑⠺⠀⠠⠽⠕⠗⠅⠀⠠⠇⠕⠝⠙⠕⠝

⠠⠝⠕⠀⠍⠁⠝⠀⠉⠁⠝⠀⠇⠕⠎⠑⠀⠺⠓⠁⠞⠀⠓⠑⠀⠝⠑⠧⠑⠗⠀⠓⠁⠙⠂⠀
⠝⠕⠗⠀⠉⠁⠝⠀⠁⠝⠽⠀⠕⠝⠑⠀⠉⠁⠗⠑⠀⠞⠕⠀⠇⠕⠎⠑⠀⠺⠓⠁⠞⠀
⠓⠑⠀⠙⠕⠑⠎⠀⠝⠕⠞⠀⠑⠎⠞⠑⠑⠍⠲

⠠⠇⠕⠧⠑⠀⠞⠓⠑⠀⠇⠊⠞⠞⠇⠑⠀⠞⠗⠁⠙⠑⠀⠺⠓⠊⠉⠓⠀⠞⠓⠕⠥⠀
⠓⠁⠎⠞⠀⠇⠑⠁⠗⠝⠑⠙⠂⠀⠁⠝⠙⠀⠃⠑⠀⠉⠕⠝⠞⠑⠝⠞⠀⠺⠊⠞⠓⠀
⠊⠞⠲

⠠⠝⠑⠧⠑⠗⠀⠇⠑⠞⠀⠞⠓⠑⠀⠋⠥⠞⠥⠗⠑⠀⠙⠊⠎⠞⠥⠗⠃⠀⠽⠕⠥⠲⠀
⠠⠽⠕⠥⠀⠺⠊⠇⠇⠀⠍⠑⠑⠞⠀⠊⠞⠂⠀⠊⠋⠀⠽⠕⠥⠀⠓⠁⠧⠑⠀⠞⠕⠂⠀
⠺⠊⠞⠓⠀⠞⠓⠑⠀⠎⠁⠍⠑⠀⠺⠑⠁⠏⠕⠝⠎⠀⠕⠋⠀⠗⠑⠁⠎⠕⠝⠀
⠺⠓⠊⠉⠓⠀⠞⠕⠙⠁⠽⠀⠁⠗⠍⠀⠽⠕⠥⠀⠁⠛⠁⠊⠝⠎⠞⠀⠞⠓⠑⠀
⠏⠗⠑⠎⠑⠝⠞⠲

⠠⠇⠕⠕⠅⠀⠺⠑⠇⠇⠀⠊⠝⠞⠕⠀⠞⠓⠽⠎⠑⠇⠋⠆⠀⠞⠓⠑⠗⠑⠀⠊⠎⠀
⠁⠀⠎⠕⠥⠗⠉⠑⠀⠕⠋⠀⠎⠞⠗⠑⠝⠛⠞⠓⠀⠺⠓⠊⠉⠓⠀⠺⠊⠇⠇⠀
⠁⠇⠺⠁⠽⠎⠀⠎⠏⠗⠊⠝⠛⠀⠥⠏⠀⠊⠋⠀⠞⠓⠕⠥⠀⠺⠊⠇⠞⠀
⠁⠇⠺⠁⠽⠎⠀⠇⠕⠕⠅⠲

⠠⠞⠓⠑⠀⠎⠕⠥⠇⠀⠃⠑⠉⠕⠍⠑⠎⠀⠙⠽⠑⠙⠀⠺⠊⠞⠓⠀⠞⠓⠑⠀ ⠉⠕⠇⠕⠗⠀⠕⠋⠀⠊⠞⠎⠀⠞⠓⠕⠥⠛⠓⠞⠎⠲

⠠⠺⠓⠑⠝⠀⠽⠕⠥⠀⠁⠗⠊⠎⠑⠀⠊⠝⠀⠞⠓⠑⠀⠍⠕⠗⠝⠊⠝⠛⠀
⠞⠓⠊⠝⠅⠀⠕⠋⠀⠺⠓⠁⠞⠀⠁⠀⠏⠗⠊⠧⠊⠇⠑⠛⠑⠀⠊⠞⠀⠊⠎⠀
⠞⠕⠀⠃⠑⠀⠁⠇⠊⠧⠑⠂⠀⠞⠕⠀⠞⠓⠊⠝⠅⠂⠀⠞⠕⠀⠑⠝⠚⠕⠽⠂⠀
⠞⠕⠀⠇⠕⠧⠑⠲

⠠⠗⠑⠚⠑⠉⠞⠀⠽⠕⠥⠗⠀⠎⠑⠝⠎⠑⠀⠕⠋⠀⠊⠝⠚⠥⠗⠽⠀⠁⠝⠙⠀ ⠞⠓⠑⠀⠊⠝⠚⠥⠗⠽⠀⠊⠞⠎⠑⠇⠋⠀⠙⠊⠎⠁⠏⠏⠑⠁⠗⠎⠲

⠠⠙⠕⠀⠑⠧⠑⠗⠽⠀⠁⠉⠞⠀⠕⠋⠀⠽⠕⠥⠗⠀⠇⠊⠋⠑⠀⠁⠎⠀
⠞⠓⠕⠥⠛⠓⠀⠊⠞⠀⠺⠑⠗⠑⠀⠞⠓⠑⠀⠧⠑⠗⠽⠀⠇⠁⠎⠞⠀
⠁⠉⠞⠀⠕⠋⠀⠽⠕⠥⠗⠀⠇⠊⠋⠑⠲

⠠⠊⠋⠀⠊⠞⠀⠊⠎⠀⠝⠕⠞⠀⠗⠊⠛⠓⠞⠀⠙⠕⠀⠝⠕⠞⠀⠙⠕⠀⠊⠞⠆⠀ ⠊⠋⠀⠊⠞⠀⠊⠎⠀⠝⠕⠞⠀⠞⠗⠥⠑⠀⠙⠕⠀⠝⠕⠞⠀⠎⠁⠽⠀⠊⠞⠲

⠠⠁⠉⠉⠑⠏⠞⠀⠞⠓⠑⠀⠞⠓⠊⠝⠛⠎⠀⠞⠕⠀⠺⠓⠊⠉⠓⠀⠋⠁⠞⠑⠀
⠃⠊⠝⠙⠎⠀⠽⠕⠥⠂⠀⠁⠝⠙⠀⠇⠕⠧⠑⠀⠞⠓⠑⠀⠏⠑⠕⠏⠇⠑⠀
⠺⠊⠞⠓⠀⠺⠓⠕⠍⠀⠋⠁⠞⠑⠀⠃⠗⠊⠝⠛⠎⠀⠽⠕⠥⠀⠞⠕⠛⠑⠞⠓⠑⠗⠂⠀
⠃⠥⠞⠀⠙⠕⠀⠎⠕⠀⠺⠊⠞⠓⠀⠁⠇⠇⠀⠽⠕⠥⠗⠀⠓⠑⠁⠗⠞⠲

⠀⠁⠃⠉⠙⠚⠋⠛⠌⠍⠎⠏⠐⠑⠒⠓⠔⠕⠖⠗⠘⠙⠚⠛⠜⠝⠞⠟⠠⠡⠢⠣⠤⠥⠦⠧⠨⠩⠪⠫⠬⠭⠮⠯⠰⠱⠲⠳⠴⠵⠶⠷⠸⠹⠺⠻⠼⠽⠾⠿ [?]

⠠⠁⠗⠞ ⠼⠓ ⠐⠕⠋ ⠎⠞⠁⠞⠑ ⠕⠗ ⠎⠥⠉⠓ ⠕⠞⠓⠑⠗ ⠍⠊⠝⠊⠎⠞⠑⠗ ⠁⠎ ⠍⠁⠽ ⠃⠑ ⠙⠑⠎⠊⠛⠝⠁⠞⠑⠙ ⠃⠽ ⠞⠓⠑ ⠛⠕⠧⠑⠗⠝⠍⠑⠝⠞ ⠕⠋ ⠞⠓⠁⠞ ⠎⠞⠁⠞⠑ ⠍⠁⠽ ⠁⠝⠝⠕⠥⠝⠉⠑ ⠞⠕ ⠞⠓⠑ ⠎⠑⠉⠗⠑⠞⠁⠗⠽ ⠛⠑⠝⠑⠗⠁⠇ ⠕⠋ ⠞⠓⠑ ⠠⠥⠝⠊⠞⠑⠙ ⠠⠝⠁⠞⠊⠕⠝⠎ ⠞⠓⠁⠞ ⠎⠥⠉⠓ ⠎⠞⠁⠞⠑ ⠊⠝⠞⠑⠝⠙⠎ ⠞⠕ ⠁⠏⠏⠇⠽ ⠞⠓⠑ ⠏⠗⠕⠧⠊⠎⠊⠕⠝⠎ ⠕⠋ ⠞⠓⠊⠎ ⠠⠉⠕⠝⠧⠑⠝⠞⠊⠕⠝ ⠞⠕ ⠁⠝⠽ ⠝⠕⠝⠤ ⠍⠑⠞⠗⠕⠏⠕⠇⠊⠞⠁⠝ ⠞⠑⠗⠗⠊⠞⠕⠗⠽ ⠕⠗ ⠞⠑⠗⠗⠊⠞⠕⠗⠊⠑⠎ ⠋⠕⠗ ⠺⠓⠊⠉⠓ ⠊⠞ ⠊⠎ ⠊⠝⠞⠑⠗⠤ ⠝⠁⠞⠊⠕⠝⠁⠇⠇⠽ ⠗⠑⠎⠏⠕⠝⠎⠊⠃⠇⠑ ⠁⠝⠙ ⠞⠓⠑ ⠁⠙⠍⠊⠝⠊⠎⠞⠗⠁⠞⠊⠕⠝ ⠕⠋ ⠺⠓⠊⠉⠓ ⠊⠞ ⠓⠁⠎ ⠝⠕⠞ ⠽⠑⠞ ⠁⠎⠎⠥⠍⠑⠙ ⠁⠝⠙ ⠎⠥⠉⠓ ⠁⠝⠝⠕⠥⠝⠉⠑⠍⠑⠝⠞ ⠎⠓⠁⠇⠇ ⠊⠝⠏⠥⠞ ⠞⠓⠑ ⠏⠗⠕⠧⠊⠎⠊⠕⠝⠎ ⠕⠋ ⠞⠓⠊⠎ ⠠⠉⠕⠝⠧⠑⠝⠞⠊⠕⠝ ⠞⠕ ⠞⠓⠑ ⠞⠑⠗⠗⠊⠞⠕⠗⠽ ⠕⠗ ⠞⠑⠗⠗⠊⠞⠕⠗⠊⠑⠎ ⠝⠁⠍⠑⠙ ⠞⠓⠑⠗⠑⠊⠝ ⠁⠎ ⠋⠗⠕⠍ ⠞⠓⠑ ⠙⠁⠞⠑ ⠕⠝ ⠺⠓⠊⠉⠓ ⠊⠞ ⠊⠎ ⠗⠑⠉⠑⠊⠧⠑⠙ ⠃⠽ ⠞⠓⠑ ⠎⠑⠉⠗⠑⠞⠁⠗⠽ ⠛⠑⠝⠑⠗⠁⠇ ⠕⠋ ⠞⠓⠑ ⠠⠥⠝⠊⠞⠑⠙ ⠠⠝⠁⠞⠊⠕⠝⠎ ⠕⠗ ⠁⠞ ⠎⠥⠉⠓ ⠇⠁⠞⠑⠗ ⠙⠁⠞⠑ ⠁⠎ ⠍⠁⠽ ⠃⠑ ⠎⠏⠑⠉⠊⠋⠊⠑⠙ ⠊⠝ ⠞⠓⠑ ⠁⠝⠝⠕⠥⠝⠉⠑⠍⠑⠝⠞⠲

⠠⠁⠗⠞⠊⠉⠇⠑ ⠼⠓

⠼⠁⠲ ⠠⠁⠝⠽ ⠠⠎⠞⠁⠞⠑ ⠍⠁⠽ ⠙⠑⠝⠕⠥⠝⠉⠑ ⠞⠓⠊⠎ ⠠⠉⠕⠝⠧⠑⠝⠞⠊⠕⠝ ⠃⠽ ⠺⠗⠊⠞⠞⠑⠝ ⠝⠕⠞⠊⠋⠊⠉⠁⠞⠊⠕⠝ ⠞⠕ ⠞⠓⠑ ⠠⠎⠑⠉⠗⠑⠞⠁⠗⠽ ⠠⠛⠑⠝⠑⠗⠁⠇ ⠕⠋ ⠞⠓⠑ ⠠⠥⠝⠊⠞⠑⠙ ⠠⠝⠁⠞⠊⠕⠝⠎⠲ ⠠⠎⠥⠉⠓ ⠙⠑⠝⠥⠝⠉⠊⠁⠞⠊⠕⠝ ⠎⠓⠁⠇⠇ ⠞⠁⠅⠑ ⠑⠋⠋⠑⠉⠞ ⠕⠝⠑ ⠽⠑⠁⠗ ⠋⠗⠕⠍ ⠞⠓⠑ ⠙⠁⠞⠑ ⠕⠝ ⠺⠓⠊⠉⠓ ⠊⠞ ⠊⠎ ⠗⠑⠉⠑⠊⠧⠑⠙ ⠃⠽ ⠞⠓⠑ ⠠⠎⠑⠉⠗⠑⠞⠁⠗⠽ ⠠⠛⠑⠝⠑⠗⠁⠇⠲

⠼⠃⠲ ⠠⠁⠝⠽ ⠠⠎⠞⠁⠞⠑ ⠺⠓⠊⠉⠓ ⠓⠁⠎ ⠍⠁⠙⠑ ⠁ ⠝⠕⠞⠊⠋⠊⠉⠁⠞⠊⠕⠝ ⠥⠝⠙⠑⠗ ⠏⠁⠗⠁⠤ ⠛⠗⠁⠏⠓ ⠼⠃ ⠕⠋ ⠁⠗⠞⠊⠉⠇⠑ ⠼⠛ ⠍⠁⠽ ⠁⠞ ⠁⠝⠽ ⠞⠊⠍⠑ ⠞⠓⠑⠗⠑⠁⠋⠞⠑⠗ ⠃⠽ ⠁ ⠺⠗⠊⠞⠞⠑⠝ ⠝⠕⠞⠊⠋⠊⠉⠁⠞⠊⠕⠝ ⠞⠕ ⠞⠓⠑ ⠠⠎⠑⠉⠗⠑⠞⠁⠗⠽ ⠠⠛⠑⠝⠑⠗⠁⠇ ⠕⠋ ⠞⠓⠑ ⠠⠥⠝⠊⠞⠑⠙ ⠠⠝⠁⠞⠊⠕⠝⠎ ⠙⠑⠉⠇⠁⠗⠑ ⠞⠓⠁⠞ ⠞⠓⠊⠎ ⠠⠉⠕⠝⠧⠑⠝⠞⠊⠕⠝ ⠎⠓⠁⠇⠇ ⠉⠑⠁⠎⠑ ⠞⠕ ⠑⠭⠞⠑⠝⠙ ⠞⠕ ⠞⠓⠑ ⠞⠑⠗⠗⠊⠞⠕⠗⠽ ⠞⠕ ⠺⠓⠊⠉⠓ ⠞⠓⠑ ⠝⠕⠞⠊⠋⠊⠉⠁⠞⠊⠕⠝ ⠗⠑⠋⠑⠗⠎ ⠕⠝⠑ ⠽⠑⠁⠗ ⠁⠋⠞⠑⠗ ⠞⠓⠑ ⠙⠁⠞⠑ ⠕⠝ ⠺⠓⠊⠉⠓ ⠎⠥⠉⠓ ⠝⠕⠞⠊⠋⠊⠉⠁⠞⠊⠕⠝ ⠊⠎ ⠗⠑⠉⠑⠊⠧⠑⠙ ⠃⠽ ⠞⠓⠑ ⠠⠎⠑⠉⠗⠑⠞⠁⠗⠽ ⠠⠛⠑⠝⠑⠗⠁⠇⠲

⠎⠞⠁⠗⠞⠇⠔⠛ ⠊⠝⠉⠊⠙⠑⠝⠞⠎ ⠊⠝ ⠞⠓⠑ ⠇⠊⠋⠑ ⠕⠋ ⠎⠺⠁⠍⠊ ⠧⠊⠧⠑⠅⠁⠝⠁⠝⠙⠁ ⠁⠝⠙ ⠎⠕⠍⠑ ⠕⠋ ⠓⠊⠎ ⠉⠓⠕⠊⠉⠑ ⠞⠓⠕⠌⠞⠎

⠃⠽ ⠎⠺⠁⠍⠊ ⠞⠑⠚⠁⠎⠁⠝⠁⠝⠙⠁

⠎⠗⠊ ⠗⠁⠍⠁⠅⠗⠊⠃⠝⠁ ⠍⠁⠞⠓⠁ ⠃⠑⠇⠥⠗ ⠍⠁⠞⠓

Ebook ISBN: 979-8-88572-899-7

HELEN KELLER INSTITUTE FOR DEAF & DEAFBLIND MUMBAI, ACKNOWLEDGES WITH DEEP GRATITUDE AND LOVE TO NITHYANANDA SWAMIJI DHYANPEETAM NITHYANANDA FOUNDATION, FOR PERMISSION TO CREATE THE PRINT BRAILLE VERSION OF 'GUARANTEED SOLUTIONS'.