Uma pessoa obesa, pesando num certo momento 156 kg, recolhe-se a um SPA onde se anunciam perda de peso de até 2,5 kg por semana. Suponhamos que isso realmente ocorra. Nessas condições: Calcule o número mínimo de semanas completas que a pessoa deverá permanecer no SPA para sair de lá com menos de 120 kg de peso.
Respostas
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Boa tarde Paula!
Solução!
![1\º~~Semana~~156-2,5=135,5Kg\\\\\\\
2\º~~Semana~~135,5-2,5=151Kg\\\\\\
3\º~~Semana~~151-2,5=148,5Kg\\\\\\
4\º~~Semana~~148,5-2,5=146Kg](https://tex.z-dn.net/?f=1%5C%C2%BA%7E%7ESemana%7E%7E156-2%2C5%3D135%2C5Kg%5C%5C%5C%5C%5C%5C%5C%0A2%5C%C2%BA%7E%7ESemana%7E%7E135%2C5-2%2C5%3D151Kg%5C%5C%5C%5C%5C%5C%0A3%5C%C2%BA%7E%7ESemana%7E%7E151-2%2C5%3D148%2C5Kg%5C%5C%5C%5C%5C%5C%0A4%5C%C2%BA%7E%7ESemana%7E%7E148%2C5-2%2C5%3D146Kg "1\º~~Semana~~156-2,5=135,5Kg\\\\\\\
2\º~~Semana~~135,5-2,5=151Kg\\\\\\
3\º~~Semana~~151-2,5=148,5Kg\\\\\\
4\º~~Semana~~148,5-2,5=146Kg")
Baseado nesse padrão de peso,podemos determinar o número de semanas usando uma progressão aritmética.
![an=156\\\\\\\
a1=120\\\\\\\
n=numeros~~de~~semanas\\\\\\\
r=2,5](https://tex.z-dn.net/?f=an%3D156%5C%5C%5C%5C%5C%5C%5C%0Aa1%3D120%5C%5C%5C%5C%5C%5C%5C%0An%3Dnumeros%7E%7Ede%7E%7Esemanas%5C%5C%5C%5C%5C%5C%5C%0Ar%3D2%2C5 "an=156\\\\\\\
a1=120\\\\\\\
n=numeros~~de~~semanas\\\\\\\
r=2,5")
![an=a1+(n-1).r\\\\\\\
156=120+(n-1).2,5\\\\\\\
156=120+2,5n-2,5\\\\\\
156=120-2,5+2,5n\\\\\\
156=117,5+2,5n\\\\\\\
156-117,5+2,5n\\\\\\
38,5=2,5n\\\\\\
n= \dfrac{38,5}{2,5}\\\\\\
\boxed{n=15,4}](https://tex.z-dn.net/?f=an%3Da1%2B%28n-1%29.r%5C%5C%5C%5C%5C%5C%5C%0A156%3D120%2B%28n-1%29.2%2C5%5C%5C%5C%5C%5C%5C%5C%0A156%3D120%2B2%2C5n-2%2C5%5C%5C%5C%5C%5C%5C%0A156%3D120-2%2C5%2B2%2C5n%5C%5C%5C%5C%5C%5C%0A156%3D117%2C5%2B2%2C5n%5C%5C%5C%5C%5C%5C%5C%0A156-117%2C5%2B2%2C5n%5C%5C%5C%5C%5C%5C%0A38%2C5%3D2%2C5n%5C%5C%5C%5C%5C%5C%0An%3D+%5Cdfrac%7B38%2C5%7D%7B2%2C5%7D%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bn%3D15%2C4%7D+ "an=a1+(n-1).r\\\\\\\
156=120+(n-1).2,5\\\\\\\
156=120+2,5n-2,5\\\\\\
156=120-2,5+2,5n\\\\\\
156=117,5+2,5n\\\\\\\
156-117,5+2,5n\\\\\\
38,5=2,5n\\\\\\
n= \dfrac{38,5}{2,5}\\\\\\
\boxed{n=15,4}")
Boa tarde!
Bons estudos!
Solução!
Baseado nesse padrão de peso,podemos determinar o número de semanas usando uma progressão aritmética.
Boa tarde!
Bons estudos!
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