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Answer:
t = 8.017 or 0.608 (nearest hundredth)
Step-by-step explanation:
[tex]h = 138t-16t^2[/tex]
when h = 78:
[tex]\implies 138t-16t^2=78[/tex]
[tex]\implies 16t^2-138t+78=0[/tex]
Using quadratic formula:
[tex]t=\dfrac{138 \pm\sqrt{(-138)^2-(4 \cdot 16 \cdot 78)} }{2 \cdot 16}[/tex]
[tex]\implies t=\dfrac{138 \pm\sqrt{14052} }{32}[/tex]
[tex]\implies t=8.017, t = 0.608[/tex]