$\"\"$

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The projectile equation is $\"\"$ .

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(a) Graph:

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Graph the equation $\"\"$ .

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$\"\"$

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$\"\"$

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(b)

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Determine the range of the projectile.

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Find the range of the projectile by equating $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The range of the projectile is $\"\"$ .

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$\"\"$

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(c)

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Find the distance that projectile travels.

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Arc length of the curve $\"\"$ in the interval $\"\"$ is $\"\"$ .

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The projectile equation is $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The range of the projectile is $\"\"$ to $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Apply formula: $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The projectile travels the distance is $\"\"$ .

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$\"\"$

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(a)

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Graph:

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Graph the equation $\"\"$ .

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$\"\"$

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(b) The range of the projectile is $\"\"$ .

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(c) The projectile travels the distance is $\"\"$ .