Respuesta :
For the length of the punt, we equate the expression to zero f(x) = 0.
Given f(x) is the height (in feet) and x is the horizontal distance (in feet) from the point at which the ball is punted.
What is the horizontal distance?
Horizontal distance means the distance between two points measured at a zero percent slope.
(-16/1225)x^2 + (7/5)x + 2.5 = 0
[tex]\left(\frac{-16}{1225}\right)x^2+\left(\frac{7}{5}\right)x+2.5=0[/tex]
[tex]\frac{-16}{1225}x^2\cdot \:10+\frac{7}{5}x\cdot \:10+2.5\cdot \:10=0\cdot \:10[/tex]
[tex]-\frac{32}{245}x^2+14x+25=0[/tex]
[tex]-\frac{32}{245}x^2\cdot \:245+14x\cdot \:245+25\cdot \:245=0\cdot \:245[/tex]
[tex]-32x^2+3430x+6125=0[/tex]
[tex]x_{1,\:2}=\frac{-3430\pm \sqrt{3430^2-4\left(-32\right)\cdot \:6125}}{2\left(-32\right)}[/tex]
[tex]x_{1,\:2}=\frac{-3430\pm \:70\sqrt{2561}}{2\left(-32\right)}[/tex]
[tex]x_1=\frac{-3430+70\sqrt{2561}}{2\left(-32\right)},\:x_2=\frac{-3430-70\sqrt{2561}}{2\left(-32\right)}[/tex]
[tex]x=-\frac{35\left(\sqrt{2561}-49\right)}{32},\:x=\frac{35\left(49+\sqrt{2561}\right)}{32}[/tex]
x=-1.7569 and x=108.94
On solving for x we get, x = 108 ft.
To learn more about the horizontal distance visit:
https://brainly.com/question/8496665
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