A machinist is required to manufacture a circular metal disk with area 1000 cm
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Help with b and c
![### Problem 27
A machinist is required to manufacture a circular metal disk with an area of \(1000 \, \text{cm}^2\).
(a) **What radius produces such a disk?**
(b) **If the machinist is allowed an error tolerance of \( \pm 5 \, \text{cm}^2 \) in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius?**
(c) **In terms of the \( \varepsilon, \delta \) definition of \( \lim_{x \to a} f(x) = L \), what is \( x \)? What is \( f(x) \)? What is \( a \)? What is \( L \)? What value of \( \varepsilon \) is given? What is the corresponding value of \( \delta \)?**
### Problem Explanation:
In this problem, you are asked to solve a series of questions related to the machining of a circular metal disk of a given area. The problem explores geometric properties as well as the application of calculus concepts, specifically limits and error tolerance.
#### (a) Calculation of Radius:
You are required to find the radius of a disk given its area, utilizing the formula for the area of a circle:
\[ \text{Area} = \pi r^2 \]
#### (b) Error Tolerance in Radius:
You need to determine how small the variation in the radius must be to keep the area within a specified error tolerance. This involves understanding the relationship between the radius and the area.
#### (c) \( \varepsilon, \delta \) definition in Calculus:
You should interpret the given machining problem using the epsilon-delta definition of limits in calculus, identifying the variables, functions, and limits involved.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F157a1ece-fbf9-4e19-a1bf-2b46085fdcb1%2F06f48a06-f9c4-43b7-9047-ef23d5e5226d%2Fcd736wb.jpeg&w=3840&q=75)
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