Question
A cricket has lost one of its wings and wants to climb a tree. To do so, it jumps trying to reach one of the branches, but because every time it goes out it loses energy, the height of its jumps becomes smaller and smaller. The height of his first jump is 9 meters and in each subsequent jump he only manages to jump two thirds of the previous height Only in the seventh jump will the cricket reach a height of
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Answer to a math question A cricket has lost one of its wings and wants to climb a tree. To do so, it jumps trying to reach one of the branches, but because every time it goes out it loses energy, the height of its jumps becomes smaller and smaller. The height of his first jump is 9 meters and in each subsequent jump he only manages to jump two thirds of the previous height Only in the seventh jump will the cricket reach a height of
Timmothy
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Para determinar la altura que alcanzará el grillo en el séptimo salto, podemos utilizar la información proporcionada sobre la altura del primer salto (9 metros) y el patrón de que cada salto posterior sea dos tercios del salto anterior.
Calculemos la altura de cada salto:
1er salto: 9 metros
2do salto: (2/3) * 9 = 6 metros
3er salto: (2/3) * 6 = 4 metros
4to salto: (2/3) * 4 = 8/3 metros (o aproximadamente 2,67 metros)
5to salto: (2/3) * (8/3) = 16/9 metros (o aproximadamente 1,78 metros)
6to salto: (2/3) * (16/9) ≈ 1,19 metros
Ahora, para el séptimo salto, calcularemos la altura:
7mo salto: (2/3) * 1,19 ≈ 0,79 metros
Por tanto, en el séptimo salto, el grillo alcanzará una altura aproximada de 0,79 metros.
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