Here are the calues I have
vo=17 d=19.16 a= -1.5 t= ?
and the equation is
D=1/2(vo)t+ 1/2a(t²)
What is t and how do I solve it?
We have....
19 = (1/2)(17)t + (1/2)(-1.5)t^2 simplify by multiplying through by 2
38 = 17t - (1.5)t^2 rearrange
1.5t^2 - 17t + 38 = 0 multiply through by 2 again
3t^2 - 34t + 76 = 0 this won't factor.....using the quadratic formula and the onsite solve, we have
$${\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{34}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,\small\textbf+\,}}{\mathtt{76}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,-\,}}{\mathtt{17}}\right)}{{\mathtt{3}}}}\\
{\mathtt{t}} = {\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{17}}\right)}{{\mathtt{3}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{3.063\: \!250\: \!108\: \!031\: \!115\: \!2}}\\
{\mathtt{t}} = {\mathtt{8.270\: \!083\: \!225\: \!302\: \!218\: \!1}}\\
\end{array} \right\}$$
We have....
19 = (1/2)(17)t + (1/2)(-1.5)t^2 simplify by multiplying through by 2
38 = 17t - (1.5)t^2 rearrange
1.5t^2 - 17t + 38 = 0 multiply through by 2 again
3t^2 - 34t + 76 = 0 this won't factor.....using the quadratic formula and the onsite solve, we have
$${\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{34}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,\small\textbf+\,}}{\mathtt{76}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,-\,}}{\mathtt{17}}\right)}{{\mathtt{3}}}}\\
{\mathtt{t}} = {\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{17}}\right)}{{\mathtt{3}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{3.063\: \!250\: \!108\: \!031\: \!115\: \!2}}\\
{\mathtt{t}} = {\mathtt{8.270\: \!083\: \!225\: \!302\: \!218\: \!1}}\\
\end{array} \right\}$$