a marble is rolled down a ramp. The distance it travels is described by the formula d=490T^2 where d is the distance in centimeters that the marble rolls in t seconds. If the marble is released at the top of a ramp that is 3,920 cm long for what time period will the marble be more than halfway down the ramp?

Question

Mathematics

Big Mac

27 November, 22:10

a marble is rolled down a ramp. The distance it travels is described by the formula d=490T^2 where d is the distance in centimeters that the marble rolls in t seconds. If the marble is released at the top of a ramp that is 3,920 cm long for what time period will the marble be more than halfway down the ramp?

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MomBod · Answer 1

The period when its more than halfway

= 2 < t ≤ 2.83 seconds (to nearest hundredth).

Step-by-step explanation:

When is is halfway down the ramp d = 3920/2 = 1960 cm, so:

1960 = 490 t^2

t^2 = 1960/490 = 4

t = 2 seconds.

When it reaches the bottom d = 3920:

t^2 = 3920/490 = 8

t = 2.83 seconds.