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A drop of oil makes a circular ring in a water puddle. The radius of the oil ring expands at 1.5 cm per second. If r(t)=1.5t and a(r)=лr^2, what composition of function describes the area of the oil ring in terms of time?

Sagot :

MrRoyal

Answer:

[tex]a(t) =n(0.25t^2)[/tex]

Step-by-step explanation:

Given

[tex]r(t) = 0.5t[/tex]

[tex]a(r) = nr^2[/tex]

Required

Determine the area in terms of time

From the question, we have:

[tex]r(t) = 0.5t[/tex] -> radius per time

and

[tex]a(r) = nr^2[/tex] --> area from radius

The interpretation of the question is to find the composite function: a(t)

If [tex]a(r) = nr^2[/tex], and [tex]r(t) = 0.5t[/tex], the

Substitute 0.5t for r

[tex]a(t) =n(0.5t)^2[/tex]

[tex]a(t) =n*0.25t^2[/tex]

[tex]a(t) =n(0.25t^2)[/tex]

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