Final answer:
The equation 320t^2+420=2000 is rearranged to t^2 - 4.9375 = 0. By applying the quadratic formula, we find the solutions t = -2.2 and t = 2.2, corresponding to choices a) and b).
Step-by-step explanation:
To solve the equation 320t^2+420=2000 for t, we first need to rearrange the equation so that it equals zero. To do this, we subtract 2000 from both sides to get 320t^2 - 1580 = 0.
Now we divide the entire equation by 320 to simplify it further to t^2 - 4.9375 = 0.
From here, we use the quadratic formula -b ± √b² - 4ac / (2a) to solve for t. Plugging in the values, we get t = ±√(0 + 4.9375 ∙ 4 / 2), which yields two possible solutions. However, since the equation t^2 + 10t - 2000 = 0 from the given hints is incorrect (it should be t^2 - 4.9375 = 0), we recognize an error in the provided information.
By correctly solving the equation t^2 - 4.9375 = 0 we obtain two potential solutions: t = -√4.9375 and t = √4.9375, which are approximately t = -2.22 and t = 2.22.
Therefore, the correct answers are t = -2.2 and t = 2.2, matching choices a) and b) respectively.