Question: A long jumper leaves the ground at an angle of 17^(@) above the horizontal, at a speed of 9m//s. The height of the jumper can be modeled by h(x)=-0.053x^(2)+0.363 x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch.(a) At what horizontal distance from the point of launch does the maximum height occur?

A long jumper leaves the ground at an angle of $17^($@$)$ above the horizontal, at a speed of $9$m$//$s$.$ The height of the jumper can be modeled by h$($x$)=-0\mathrm{.}053$x$^(2)+0\mathrm{.}363$ x$,$ where h is the jumper's height in meters and x is the horizontal distance from the point of launch.

$($a$)$ At what horizontal distance from the point of launch does the maximum height occur? Round to $2$ decimal places.

The long jumper reaches a maximum height when the horizontal distance from the point of launch is approximately meters.

$($b$)$ What is the maximum height of the long jumper? Round to $2$ decimal places.

The maximum height of the long jumper is approximately meters.

$($c$)$ What is the length of the jump? Round to $1$ decimal place.

The length of the jump is approximately meters.