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The force F​ (in pounds) required to push a sofa across a floor varies directly as the weight w​ (in pounds) of the sofa.
a. A person can push a 120​-pound sofa across a wood floor by pushing with a force of 50 pounds. Find an equation that describes the relationship between w and F.
What does F =

Respuesta :

carlosego

Answer: [tex]F=0.41w[/tex]


Step-by-step explanation:

1. You know that the force F varies directly as the weight w of the sofa. Then, you can write the following expression:

[tex]F=kw[/tex]

Where k is the constant of proportionality.

2. You know that a person can push a 120​ pound sofa with a force of 50 pounds, then you can calcualte the constant of proportionality as following:

[tex]k=\frac{F}{w}=\frac{50lb}{120lb}=0.41[/tex]

3. Then, the equation is:

[tex]F=0.41w[/tex]

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