Answer
(a) $ t = 2.786$ and $ t = -4.785$
(b) $ t = -0.359$ and $ t = -4.640$
Work Step by Step
(a)
Expression given:
$ \frac{10}{t+5}+6t = 18$
Multiply both sides by $t+5$:
$ 10+6t\times(t+5) = 18\times(t+5)$
Expand:
$ 10+6t^{2}+30t = 18t + 90$
Rearrange:
$ 6t^{2}+12t - 80= 0$
Solve using calculator or quadratic formula to find:
$ t \approx 2.786$ and $ t \approx -4.785$
(b)
Expression given:
$ \frac{10}{t+5}+6t = 0$
Multiply both sides by $t+5$:
$ 10+6t\times(t+5) = 0\times(t+5)$
Expand:
$ 10+6t^{2}+30t = 0$
Rearrange:
$ 6t^{2}+30t+10= 0$
Solve using calculator or quadratic formula to find:
$ t \approx -0.359$ and $ t \approx -4.640$
