Answer: d = 1/5t
Step-by-step explanation:
[tex]\\[/tex]Since it is a direct variation , Let d represent the distance and t represent the time ,then
[tex]\\[/tex]d ∝ t
[tex]\\[/tex]introducing the proportionality constant, we have
[tex]\\[/tex]d = kt
[tex]\\[/tex]Substituting t = 10 and d = 2 , we have
[tex]\\[/tex]2 = 10k
[tex]\\[/tex]k = 1/5
[tex]\\[/tex]substitute k = 1/5 into the original equation , we have
[tex]\\[/tex]d = 1/5t
A direct variation equation for the relationship between time and distance is [tex]\rm d= \dfrac{1}{5} t[/tex].
Given
Your distance from lightning varies directly with the time it takes you to hear thunder you hear thunder 10 seconds after you see the lightning, you are about 2 miles from the lightning.
A direct variation, also called direct proportion is a relationship between two variables.
Let d is the distance and t is the time.
The distance varies directly with the time which means distance is directly proportional to time.
Distance ∝ Time
d ∝ t
When the proportionality sign removes;
[tex]\rm d = kt[/tex]
Where k is the proportionality constant.
The value of d is 2 and t is 10 substitute in the equation.
[tex]\rm d = kt\\\\2 = k(10)\\\\10k=2\\\\k = \dfrac{2}{10}\\\\k = \dfrac{1}{5}[/tex]
Therefore,
A direct variation equation for the relationship between time and distance is;
[tex]\rm d= \dfrac{1}{5} t[/tex]
Hence, a direct variation equation for the relationship between time and distance is [tex]\rm d= \dfrac{1}{5} t[/tex].
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