Question

try it! use approximate solutions

1. at the next tee, a golf ball was hit and modeled by $-16x^{2}+11x+6=0$.

when will the golf ball hit the ground?

Explanation:

Step1: Identify quadratic equation

The given equation is $-16x^2 + 11x + 6 = 0$. Multiply by -1 to simplify:
$16x^2 - 11x - 6 = 0$

Step2: Apply quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=16$, $b=-11$, $c=-6$.
First calculate discriminant:
$\Delta = (-11)^2 - 4(16)(-6) = 121 + 384 = 505$
Then solve for $x$:
$x=\frac{11\pm\sqrt{505}}{32}$

Step3: Select positive solution

$\sqrt{505}\approx22.47$, so:
$x_1=\frac{11+22.47}{32}\approx\frac{33.47}{32}\approx1.05$
$x_2=\frac{11-22.47}{32}\approx\frac{-11.47}{32}\approx-0.36$
Time cannot be negative, so discard $x_2$.

Answer:

The golf ball will hit the ground after approximately 1.05 units of time.