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smokemicpot
05.11.2019 •
Mathematics
How many 5-digit sequences can we form from the integers 1, 2, 9 if:
a) the digits can be the same.
b) the digits cannot be the same and the order in which they appear matters.
c) the digits cannot be the same and the order in which they appear does not matter
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Ответ:
a) 59049, b) 15120, c) 126.
Step-by-step explanation:
Since we have given that
5 digit sequences from the integers 1,2,...9.
a) the digits can be the same.
Repetition is allowed.
So, Number of ways to form 5 digit sequences would be
b) the digits cannot be the same and the order in which they appear matters.
Repetition is not allowed and order is maintained, so we will use "Permutation":
c) the digits cannot be the same and the order in which they appear does not matter.
Repetition is not allowed and order is not maintained, so we will use "Combination":
Hence, a) 59049, b) 15120, c) 126.
Ответ:
La persona está a 5 kilómetros con respecto al punto de partida.
Step-by-step explanation:
Considérese que la dirección norte coincide con el semieje +y y que la dirección este coincide con el semieje +x. A continuación, obtenemos las formas vectoriales equivalentes de cada afirmación:
(i) Una persona camina 7 kilómetros hacia el norte:
(ii) Después 3 kilómetros hacia el este:
(iii) Y luego, 3 kilómetros hacia el sur:
El vector resultante de desplazamiento se construye a partir de la siguiente suma de vectores:
Asumiendo que la distancia coincide con el desplazamiento resultante, calculamos la distancia con respecto al punto de partida mediante el Teorema de Pitágoras:
La persona está a 5 kilómetros con respecto al punto de partida.