Therefore, the value of \(a_4\) is:
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- \(a_2 = 2a_1 + 3 = 2(1) + 3 = 2 + 3 = 5\)
- \(a_3 = 2a_2 + 3 = 2(5) + 3 = 10 + 3 = 13\)
- \(a_4 = 2a_3 + 3 = 2(13) + 3 = 26 + 3 = 29\)
- Question:** In a futuristic navigation system, the position of a spacecraft is given by the expressions \(x(t) = 5t^2 + 3t + 2\) and \(y(t) = 2t^2 + 7t + 1\). Find the value of \(t\) when the spacecraft is at the point where \(x(t) = y(t)\).
- To find when \(x(t) = y(t)\), set the expressions equal:
- 5t^2 + 3t + 2 = 2t^2 + 7t + 1
