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stealth61 [152]
3 years ago
8

The area A(r)(in square meters) of a circular algae colony with radius r meters is given by A(r)=pir^2. Basically that's A(r)= p

i r square.The radius M(t)(in meters) after t minutes is given by M(t)= 10/3 t.Write a formula for the areaZ(t)(in square meters) of the algae colony colony after t minutes.You don't have to simplify. Thanks.
Mathematics
1 answer:
Taya2010 [7]3 years ago
7 0

Answer:

The expression provided by the area (square meters) is given by:  A(t) = pi \frac{100t^{2} }{9}.

Step-by-step explanation:

The area of the algae colony is a function of the radius r (meters), so A(r) = \pi r ^ 2.

The radius of the circle formed by the algae colony is a function of time t (in minutes), so M (t) = \frac{10t }{3}. So,

A(r) = \pi r ^ 2  [Substituting the expression for radius]

A(t) = pi (\frac{10t }{3})^{2} = pi \frac{100t^{2} }{9}

Then the expression provided by the area (square meters) is given by:  A(t) = pi \frac{100t^{2} }{9}.

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See the attached figure.

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