A machinist is required to manufacture a circular metal disk with area 1000 cm2. (a) What radius
Question:
(a) What radius produces such a disk?
(b) If the machinist is allowed an error tolerance of ± 5 cm2 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 ε, δ definition of limx→a f(x) = L, what is x? What is f(x)? What is a? What is L? What value of ε is given? What is the corresponding value of δ?
Step by Step Answer:
a A 2 and A 1000 cm 2 2 1000 r 2 1000 r 1000 r 0 178412 cm b A 1000 5 55 r 2 1000 5 1000 ...View the full answer
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Calculus questions
-
A flat, circular metal disk of uniform thickness has a radius of 3.0 cm. A hole is drilled in the disk that is 1.5 cm in radius. The hole is tangent to one side of the disk. Where is the cm of the...
-
A circular ring with area 4.45 cm2 is carrying a current of 12.5 A the ring is free to rotate about a diameter. The ring, initially at rest, is immersed in a region of uniform magnetic field given by...
-
A 4-lb circular disk of radius r = 40 in. is suspended at its center C from wires AB and BC soldered together at B. The torsional spring constants of the wires are K1 =3 lb ?? ft/rad for AB and K2 =...
-
Ronnie owns 600 shares of a stock mutual fund. This year he received dividend distributions of 60 stock mutual fund shares ($ 40 per share) and long term capital gain distributions of 45 stock mutual...
-
Some have proposed the idea of an audit expectation gap which is the difference between what the auditor accomplishes using GAAS and what third-party users expect from audited financial statements....
-
Create an audit strategy for a business of your preference to assess the internal control system implemented by management in the Revenue and Expense Cycles. Emphasize the utilization of data...
-
An experiment was conducted to study the effects of temperature \(\left({ }^{\circ} \mathrm{C} ight)\) and quantity (g) on the solubility of a chemical in the laboratory. Analyze this experiment....
-
On June 30, the end of the first month of operations, Volker Energy Company prepared the following income statement, based on the absorption costing concept: If the fixed manufacturing costs were...
-
Sam Green was riding his bicycle along a road that was under construction; although he was riding against traffic instead of with traffic as required by law, he was off the pavement at the time...
-
The table below shows sales, cost of sales, and inventory data for Aladdin Products Supply Inc., a wholesale distributor of cleaning supplies. All amounts are in thousands. REQUIRED a. Calculate the...
-
Use the given graph of to find a number such that if |x - 1| 1.2 0.8 0 0.7 1 1.1
-
(a) Find a number such that if |x -2| < , then |4x - 8 < , where = 0.01. (b) Repeat part (a) with = 0.01.
-
In Problem each equation specifies a function. Determine whether the function is linear, quadratic, constant, or none of these. 1 + 5 y = 6
-
Does the Russian economy have a big percentage of small and medium enterprises in its economy? Why is that? How the size of companies affects the sustainability of the economy?
-
What would be the output of the following? [ ] x = 5 XNN X * 2 Y-3 A/
-
With a few strategies on how the health care facility's leadership team can determine if their changes were successful?
-
Many feel that the world's biggest retailer Walmart views Amazon as their biggest competitor/threat. In reading the Gartner Top 25 information on Amazon and doing some additional research on Amazon's...
-
A wheat disease has killed the majority of the U.S. wheat crop for the year, resulting in a very high wheat prices. The government decides to set prices lower than the equilibrium price. What name do...
-
Find an equation in rectangular coordinates for the equation given in spherical coordinates, and sketch its graph. ||
-
Express mass density in kg/m3 and weight density in lb/ft3. 1. Find the mass density of a chunk of rock of mass 215 g that displaces a volume of 75.0 cm3 of water. 2. A block of wood is 55.9 in. x...
-
Let P(x1, y1) be a point on the parabola y2 = 4px with focus F(p, 0). Let a be the angle between the parabola and the line segment FP, and let be the angle between the horizontal line and the...
-
For what value of does the equation e2x = k x have exactly one solution?
-
For which positive numbers is it true that ax > 1 + x for all?
-
What are the vulnerabilities of embedded operating systems, such as, but not limited to, IoT devices, programmable logic devices, and vehicle control systems.
-
Factor the polynomial completely. 7x-17x-12
-
What are some relevant recommendations about Coca-Cola's Planning, Design, and Implementation of an Enterprise Resource Planning System that other companies can apply to their own initiatives?
Study smarter with the SolutionInn App