Find the vertical asymptotes (if any) of the graph of the function.(Enter your answers as a comma-separated list.If an answer does not exist, enter DNE ) h(t)=(t^2-5t)/(t^4)-625

To find the vertical asymptotes of the function $h(t)=\frac {t^{2}-5t}{t^{4}-625}$, we need to find the values of $t$ for which the denominator is equal to zero, as these are the points where the function is undefined.<br /><br />The denominator of the function is $t^{4}-625$. To find the values of $t$ for which this expression is equal to zero, we can set it equal to zero and solve for $t$:<br /><br />$t^{4}-625=0$<br /><br />This can be factored as:<br /><br />$(t^{2}-25)(t^{2}+25)=0$<br /><br />Setting each factor equal to zero gives us:<br /><br />$t^{2}-25=0$ or $t^{2}+25=0$<br /><br />Solving these equations gives us:<br /><br />$t=\pm 5$ or $t=\pm 5i$<br /><br />Since we are looking for real values of $t$, we can ignore the complex solutions. Therefore, the vertical asymptotes of the function $h(t)$ are at $t=5$ and $t=-5$.<br /><br />Answer: The vertical asymptotes of the function $h(t)$ are at $t=5$ and $t=-5$.