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An accident at an oil drilling platform is causing a circular-shaped oil slick to form. The volume of the oil slick is roughly given V(r) = 0.07πr^2, where r is the radius of the slick in feet. In turn, the radius is increasing over time according to the function r(t) = 0.4t, where t is measured in minutes.

1) find (V of r)(t) and simply it

Respuesta :

calculista

Answer:

[tex]V(t)=0.0112\pi t^{2}[/tex]

Step-by-step explanation:

we have

[tex]V(r)=0.07\pi r^{2}[/tex] -----> equation A

[tex]r(t)=0.4t[/tex] -----> equation B

To find out (V of r)(t) substitute equation B in equation A

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

[tex]V(t)=0.07\pi (0.4t)^{2}[/tex]

[tex]V(t)=0.07\pi (0.16)t^{2}[/tex]

[tex]V(t)=0.0112\pi t^{2}[/tex]

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