a system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the…

a system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. which constraint could be part of the scenario? the pool is 1 meter deep. the pool is 2 meters deep. the toy falls at a rate of at least a $\frac{1}{2}$ meter per second. the toy sinks at a rate of no more than a $\frac{1}{2}$ meter per second.

a system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. which constraint could be part of the scenario? the pool is 1 meter deep. the pool is 2 meters deep. the toy falls at a rate of at least a $\frac{1}{2}$ meter per second. the toy sinks at a rate of no more than a $\frac{1}{2}$ meter per second.

Answer

Answer:

The toy falls at a rate of at least a $\frac{1}{2}$ meter per second.

Explanation:

Step1: Analizar la pendiente

La pendiente de la recta en la gráfica de la desigualdad representa la tasa de cambio de la profundidad con respecto al tiempo.

Step2: Observar la dirección

La región sombreada y la pendiente de la recta frontera indican que la profundidad aumenta con el tiempo. Una pendiente positiva significa que la tasa a la que el juguete cae es positiva.

Step3: Calcular la pendiente

Si consideramos dos puntos en la recta frontera, por ejemplo, $(0,0)$ y $(2,1)$, la pendiente $m=\frac{\Delta y}{\Delta x}=\frac{1 - 0}{2-0}=\frac{1}{2}$. Esto significa que el juguete cae a una tasa de $\frac{1}{2}$ metro por segundo como mínimo, ya que la región sombreada está por encima de la recta, lo que implica que la desigualdad es de tipo mayor o igual en términos de la tasa de caída.