A piece of wire of length 60 is cut, and the resulting two pieces are formed to
Question:
A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) Minimize. (b) Maximize the combined area of the circle and the square?
Step by Step Answer:
Let x be the length of the piece of wire used to make the circle then 60 x is the length f the p...View the full answer
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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 Mathematics questions
-
A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle, how should the wire be cut so that the total area enclosed is (a)...
-
A piece of wire is cut, and the length of the wire has a normal distribution with a mean 7.2 m and a standard deviation 0.11 m. If the piece of wire is then cut exactly in half, what are the mean and...
-
Answer Exercise 37 if one piece is bent into a square and the other into a circle. A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an...
-
Dominic and Jared were general partnership has equal partners Dominic contributes cash 25,000 securities values at 50,000 and they adjusted basis of 32,000 and equipment valued at 25,000 and an...
-
A stock with a current price of $78 has a call option available with a strike price of $80. The stock will move up by a factor of .95 or down by a factor of .80 each period for the next two periods...
-
If V1 = 456 mL, P1 = 308 torr, and P2 = 1.55 atm, what is V2?
-
Prepare an income statement from relevant financial information and interpret the information that it contains.
-
Continue with the facts of Problem 57. What are the Federal income tax withholding requirements with respect to Martinho's sale? Who pays the withheld amount to the U.S. Treasury?
-
Shine Limited (Shine), a Hong Kong-incorporated company, carrying on business in Hong Kong as a wholesaler of mobile phones in Hong Kong. For the year ended 31 March 2024, Shine's profit and loss...
-
While counseling an employee, a supervisor made the following statements. What is wrong with each statement? What would be a better alternative for each? a. Your laziness is becoming a real problem....
-
Find the function F that satisfies the following differential equations and initial conditions. F"'(x) = 4x, F"(0) = 0, F'(0) = 1, F(0) = 3
-
Make a complete graph of the following functions. If an interval is not specified, graph the function on its domain. Use a graphing utility to check your work. f(x) = 2 - x 2/3 + x 4/3
-
A harmonic wave with a frequency of 80 Hz and an amplitude of 0.025 m travels along a string to the right with a speed of 12 m/s. (a) Write a suitable wave function for this wave. (b) Find the...
-
The Doley Company has planned the following sales for the next three months: Budgeted sales Jan $40,000 Feb $50,000 Mar $70,000 Sales are made 20% for cash and 80% on account. From experience, the...
-
The traditional Banking and Financial Service Industry within the Caribbean should fully integrate with emerging blockchain technologies to improve security and transparency and reduce exposure to...
-
Now that the SEC has approved a Bitcoin ETF based on CME Bitcoin Futures symbol BTIO: Do you think it is more likely or less likely that they will approve an ETF in the near future based on the spot...
-
In addition to the Earth s magnetic field, list some other sources of the ambient magnetic field in the lab. Which source do you think provides the largest contribution to the overall magnetic field?
-
According to the paper, is city compactness a productive amenity or an unproductive amenity? Explain why. Recall that a productive amenity is one which lowers costs for the firm. An unproductive...
-
Taking each of the categories of the statement of cash flows in turn, in which direction would you normally expect the cash flow to be? Explain your answer. (a) Cash flows from operating activities...
-
Which of the following gives the range of y = 4 - 2 -x ? (A) (- , ) (B) (- , 4) (C) [- 4, ) (D) (- , 4] (E) All reals
-
Suppose 4 2 + 9y 2 = 25, where and y are functions of t. (a) If dy/dt = 1/3, find d/dt when = 2 and y = 1. (b) If d/dt = 3, find dy/dt when = 2 and y = 1.
-
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. d (tan?x) dx d (sec?x) dx
-
Differentiate. y = e
-
When teachers say they are color blind, they are usually saying that they do not discriminate and that they treat all their students equally. Of course, being fair and treating each student with...
-
The purpose of this activity is to identify and present how the brand uses different social media platforms to communicate its messages. ISocial Media Platforms (TikTok) Analysis (Value offered,...
-
Define a research question that can be answered (in full or in part) with qualitative data. Describe the sample of participants you might obtain to help you answer this research question. Draft an...
Study smarter with the SolutionInn App