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Answer:
a) add a dummy stroke to make the problem as an assignment problem of adding 5 strokes to 5 swimmers. see first attachment.
b) applying the Hungarian method.
4.8 0 0.9 4.1 2.5
10.3 0 9.1 1.6 8.7
4.8 0 10.4 1.9 5.1
2.8 0 3.2 2.1 4.7
0 0 0 0 0
Deduct the smallest element in each column from the other elements of the column.
2 0 0 2.5 0
7.5 0 8.2 0 6.2
2 0 9.5 0.3 2.6
0 0 2.3 0.5 2.2
0 0 0 0 0
Which implies:
2 8.2 2.5 6.2
7.5 9.5 0.3 2.6
2 2.3 0.5 2.2
33.8 + 34.7 + 28.5 + 29.2 = 126.2
David = Back Stroke
tony = Breast Stroke
Chris = Butterfly
Carl = Free Style
We know that
see the attached figure to better understand the problem
sin x°=opposite ÷ <span>hypotenuse
cos x</span>°=adjacent ÷ hypotenuse
cosec x°=1/ sin x°-------> hypotenuse ÷ opposite
sec x°=1/ cos x°-------> hypotenuse ÷ adjacent
therefore
case A) <span>sec x° = opposite ÷ adjacent------------> is not correct
case B) </span>cosec x° = opposite ÷ adjacent ------------> is not correct
case C) cosec x° = hypotenuse ÷ opposite ------------> is correct
case D) sec x° = adjacent ÷ hypotenuse------------> is not correct
the answer is
the equation cosec x° = hypotenuse ÷ opposite is correct
see the attached figure to better understand the problem
sin x°=opposite ÷ <span>hypotenuse
cos x</span>°=adjacent ÷ hypotenuse
cosec x°=1/ sin x°-------> hypotenuse ÷ opposite
sec x°=1/ cos x°-------> hypotenuse ÷ adjacent
therefore
case A) <span>sec x° = opposite ÷ adjacent------------> is not correct
case B) </span>cosec x° = opposite ÷ adjacent ------------> is not correct
case C) cosec x° = hypotenuse ÷ opposite ------------> is correct
case D) sec x° = adjacent ÷ hypotenuse------------> is not correct
the answer is
the equation cosec x° = hypotenuse ÷ opposite is correct