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Sagot :
A composite function to find the area of the region at time t is written as-
A(r(t)) = π(0.25 + 2t + 4t²)
What is composite function?
f(g(x)) or (f ∘ g)(x) represents the composition of functions f(x) & g(x), where g(x) acts first (x). It integrates a number of functions to produce another.
The output of one function inside the parenthesis is becoming the input of the other function in a function composition. i.e.,
- In f(g(x)), g(x) is f's input (x).
- In g(f(x)), f(x) is g's input (x).
Now, as per the given question;
To create a composite function, we pertain one function to another. In this scenario, we would like to find area in terms of time, so we apply the function A(r) to the function r. (t).
To accomplish this, we substitute r with r(t).
Since we know that r(t) = 0.5 + 2t, we can replace r to 0.5 + 2t:
A(r(t)) = π(0.5+2t)²
To make things easier, we'll simplify this same squared term:
A(r(t)) = π(0.5 + 2t)(0.5 + 2t)
A(r(t)) = π[(0.5×0.5) + (0.5×2t) + (2t×0.5) + (2t×2t)]
A(r(t)) = π(0.25 + t + t + 4t²)
A(r(t)) = π(0.25 + 2t + 4t²)
Therefore, the composite function to find the area of the region at time t is written as A(r(t)) = π(0.25 + 2t + 4t²).
To know more about the composite function, here
https://brainly.com/question/10687170
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The complete question is-
A circular oil spill continues to increase in size. The radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. The area of the circular region is given by the function A(r) = πr2, where r is the radius of the circle at time t. Explain how to write a composite function to find the area of the region at time t.
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