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During a fireworks show, a rocket is fired vertically upward with an initial velocity of 200 meters per second. The height in meters, s, of the rocket in t seconds may be approximated by s = 200t – 5t2. The rocket must be at least 1,500 meters in the air to safely explode. In which time interval may it safely be exploded 30 ≤ t ≤ 40 seconds 0 ≤ t ≤ 10 seconds 10 ≤ t ≤ 40 seconds 10 ≤ t ≤ 30 seconds

Respuesta :

elcharly64

Answer:

[tex]10\leq t\leq 30[/tex]

Step-by-step explanation:

Inequalities

The height s (in meters) of a rocket fired vertically in t seconds may be approximated by  

[tex]s = 200t-5t^2[/tex]

The rocket needs to reach a minimum height of 1,500 m, thus

[tex]200t-5t^2\geq 1,500[/tex]

Simplifying by 5

[tex]40t-t^2\geq 300[/tex]

Rearranging (recall the direction of the inequality changes when multiplying by negative numbers)

[tex]t^2-40t+300\leq 0[/tex]

Factoring

[tex](t-10)(t-30)\leq 0[/tex]

The solution of this inequality is t ranging from 10 to 30, thus

[tex]\boxed{10\leq t\leq 30}[/tex]

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