julius yego is an olympic medalist from kenya who learned to throw a javelin largely by watching training…

julius yego is an olympic medalist from kenya who learned to throw a javelin largely by watching training videos on the internet. chris is inspired by yego and is working to improve his throw. the quadratic equation shown represents the height, h, in feet, of the javelin t seconds after chris throws it. use the quadratic formula to find the exact value of t when h = 0 in this context. h = -16t² + 58.4t + 6 type the number in the box. seconds

julius yego is an olympic medalist from kenya who learned to throw a javelin largely by watching training videos on the internet. chris is inspired by yego and is working to improve his throw. the quadratic equation shown represents the height, h, in feet, of the javelin t seconds after chris throws it. use the quadratic formula to find the exact value of t when h = 0 in this context. h = -16t² + 58.4t + 6 type the number in the box. seconds

Answer

Explanation:

Step1: Identify coefficients

For the quadratic equation $-16t^{2}+58.4t + 6=0$, we have $a=-16$, $b = 58.4$, $c = 6$.

Step2: Write quadratic formula

The quadratic formula is $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Substitute values

$t=\frac{-58.4\pm\sqrt{(58.4)^{2}-4\times(-16)\times6}}{2\times(-16)}$. First, calculate $(58.4)^{2}=3410.56$ and $4\times(-16)\times6=-384$. Then $b^{2}-4ac=3410.56+384 = 3794.56$. $\sqrt{3794.56}\approx61.6$. $t=\frac{-58.4\pm61.6}{-32}$.

Step4: Calculate two values of t

For the plus - sign: $t=\frac{-58.4 + 61.6}{-32}=\frac{3.2}{-32}=- 0.1$. For the minus - sign: $t=\frac{-58.4-61.6}{-32}=\frac{-120}{-32}=\frac{15}{4}=3.75$. Since time $t\geq0$, we discard the negative value.

Answer:

$3.75$