Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
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
#SPJ4
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.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
