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timofeeve [1]
3 years ago
14

an achers arrow follows a parabolic patch. the height of the arrow, f(x), in feet, can modeled by the function f(x)=-0.07x^2+1.5

x+6.7, where x is the arrows horizontal distance, in feet. what is the maximum height of the arrow?
Mathematics
1 answer:
padilas [110]3 years ago
7 0

Answer:

The maximum height of the arrow is 14.73 m.  

Step-by-step explanation:

The height of the arrow follows a parabolic path. Its height can be modeled by the function,

f(x)=-0.07x^2+1.5x+6.7 ......(1)

It is required to find the maximum height of the arrow

For maximum height, f'(x)=0

i.e.

\dfrac{d(-0.07x^2+1.5x+6.7)}{dx}=0\\\\-0.14x+1.5=0\\\\0.14x=1.5\\\\x=\dfrac{1.5}{0.14}\\\\x=10.71\ m

Put x = 10.71 m in equation (1). So,

f(x)=-0.07(10.71)^2+1.5(10.71)+6.7\\\\f(x)=14.73\ m

So, the maximum height of the arrow is 14.73 m.

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