Answered

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The equation g(t)=2+23.7t−4.9t2 models the height, in meters, of a pumpkin t seconds after it has been launched from a catapult. Is the pumpkin still in the air 8 seconds later? Explain or show how you know.

Sagot :

boffeemadrid

Answer:

The pumpkin is not in the air

Step-by-step explanation:

The equation is

[tex]g(t)=2+23.7t-4.9t^2[/tex]

Let us find when the pumpkin will reach the ground

[tex]0=2+23.7t-4.9t^2\\\Rightarrow -49t^2+237t+20=0\\\Rightarrow t=\frac{-237\pm \sqrt{237^2-4\left(-49\right)\times 20}}{2\left(-49\right)}\\\Rightarrow t=-0.08,4.91[/tex]

So, the pumpkin will reach the ground at 4.91 seconds. Hence, at 8 seconds the pumpkin will reach the ground.

OR

At [tex]t=8\ \text{s}[/tex]

[tex]g(8)=2+23.7\times 8-4.9\times 8^2\\\Rightarrow g(8)=-122\ \text{m}[/tex]

The height of the pumpkin is negative 122 m. This means it is lower than the ground. So, the pumpkin is not in the air 8 seconds later.

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