Linda shoots an arrow at a target in an archery competition. The arc of the arrow can be modeled by the equation y= -0.02x to the power of 2 + 0.65+4 where x is the horizontal distance (in meters) from Linda and y is the height (in meters) of the arrow. How far from Linda does the arrow hit the ground? Round to the nearest tenth.

37.8metres

Step-by-step explanation:

The arc of the arrow can be modeled by the equation:

y=-0.02x²+0.65x+4

Where x is the horizontal distance (in meters) from Linda and y is the height (in meters) of the arrow.

The arrow hits the ground when its height (y) is zero.

Therefore, we determine the value(s) of x for which:

y=-0.02x²+0.65x+4=0

Using a calculator to solve the quadratic equation:

x=37.79 or -5.29

Since the distance cannot be a negative value, we ignore -5.29.

The distance from Linda when the arrow hits the ground is 37.8metres (to the nearest tenth)

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