1. A square and a circle are placed so that the circle is outside the square and tangent to a side of the square. The sum of the length of one side of the square and the circle's diameter is 12 feet, as shown. Suppose the length of one side of the square is x feet. (a) Write a formula for f(x), the sum of the total area of the square and the circle. What is the domain of this function when used to describe this problem? (The domain should be related to the problem statement.) Sketch a graph of f (x) on its domain. (b) Suppose that the object (square or circle) with larger area is painted red, and the object (square or circle) with smaller area is painted green. The cost of red paint to cover 1 square foot is $4, and the cost of green paint to cover 1 square foot is $10. Let g(x) be the function which gives the cost of painting the square and circle. Describe the function g(x). Sketch a graph of g(x) on its domain. Hint Read the question carefully. The answer will be a piecewise-defined function. A complete answer should give all relevant information (c) Where is the function g(x) continuous? Where is it differentiable? Which value of x gives the least cost? 12
1. A square and a circle are placed so that the circle is outside the square and tangent to a side of the square. The sum of the length of one side of the square and the circle's diameter is 12 feet, as shown. Suppose the length of one side of the square is x feet. (a) Write a formula for f(x), the sum of the total area of the square and the circle. What is the domain of this function when used to describe this problem? (The domain should be related to the problem statement.) Sketch a graph of f (x) on its domain. (b) Suppose that the object (square or circle) with larger area is painted red, and the object (square or circle) with smaller area is painted green. The cost of red paint to cover 1 square foot is $4, and the cost of green paint to cover 1 square foot is $10. Let g(x) be the function which gives the cost of painting the square and circle. Describe the function g(x). Sketch a graph of g(x) on its domain. Hint Read the question carefully. The answer will be a piecewise-defined function. A complete answer should give all relevant information (c) Where is the function g(x) continuous? Where is it differentiable? Which value of x gives the least cost? 12
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:1. A square and a circle are placed so that the circle is outside the square and tangent to a side of
the square. The sum of the length of one side of the square and the circle's diameter is 12 feet,
as shown. Suppose the length of one side of the square is x feet.
(a) Write a formula for f(x), the sum of the total area of the square and the circle. What is
the domain of this function when used to describe this problem? (The domain should be
related to the problem statement.) Sketch a graph of f(x) on its domain.
(b) Suppose that the object (square or circle) with larger area is painted red, and the object
(square or circle) with smaller area is painted green. The cost of red paint to cover 1 square
foot is $4, and the cost of green paint to cover 1 square foot is $10. Let g(x) be the function
which gives the cost of painting the square and circle. Describe the function g(x). Sketch
a graph of g(x) on its domain.
Hint Read the question carefully. The answer will be a piecewise-defined function. A
complete answer should give all relevant information
(c) Where is the function g(x) continuous? Where is it differentiable? Which value of x gives
the least cost?
Ac Tly?
A s
12
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