Consider the following sequence of problems related to grazing goats tied to a rope. A circular corral
Question:
Consider the following sequence of problems related to grazing goats tied to a rope.
A circular corral of unit radius is enclosed by a fence. A goat is outside the corral and tied to the fence with a rope of length 0 ≤ a ≤ π (see figure). What is the area of the region (outside the corral) that the goat can reach?
Rope stretches along fence
Step by Step Answer:
Again suppose that the goat is tethered at the origin and that the center of the corral is 1 Th...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
-
Consider the following sequence of reactions: a) Explain how you could use IR spectroscopy to differentiate between compounds F and G. b) Explain how you could use IR spectroscopy to differentiate...
-
Consider the following sequence of steps to describe the high-temperature kinetics of NO reduction by CH4 on La2O3 and Sr = La2O3 in the absence of O2: (a) Provide any necessary stoichiometric...
-
Consider the following sequence of page references (each element in the sequence represents a page number): Define the mean working set size after the kth reference as And define the missing page...
-
What aspects of control must exist before a subsidiary is consolidated?
-
What is the equation for the present value of a growing perpetuity with a payment of C one period from today if the payments grow by C each period?
-
An international mining company has two mines in Voiseys Bay and Hawk Ridge. The composition of the ore from each field is given in the table. How many tons of ore from each mine should be used to...
-
Determine the minimum number of workers needed, and a schedule for the following staffing requirements, giving workers two consecutive days off per cycle (not including Sunday). Day Mon Tue Wed Thu...
-
Operating cash flows, rather than accounting profits, are listed in Table 11-4.What is the basis for this emphasis on cash flows as opposed to net income?
-
Telreja Corporation uses a predatermined overhead rato based on labor hours to apply manufacturing overhead to jobs. The Corporation has provided the following estimated costs for next year: Direct...
-
A firm needs to fully satisfy the demand, which is fixed to 900 units and generates unit revenue of $10. However, its production is subject to the random yield. That is, only a random percentage of...
-
Consider the following sequence of problems related to grazing goats tied to a rope. A circular concrete slab of unit radius is surrounded by grass. A goat is tied to the edge of the slab with a rope...
-
Let a polar curve be described by r = f() and let be the line tangent to the curve at the point P(x, y) = P(r, ) (see figure). a. Explain why tan = dy/dx. b. Explain why tan = y/x. c. Let be the...
-
What three aspects can be used to describe the relationship between variables?
-
Use your own academic report, issued by your institute, as an example. Ask a database administrator how they use normalization steps to transform the details of the report into a set of relations in...
-
Francis Corp. has two divisions, Eastern and Western. The following information for the past year is for each division: Francis has established a hurdle rate of 9 percent. Required: 1. Compute each...
-
The enzyme lipase catalyzes the hydrolysis of esters of fatty acids. The hydrolysis of p-nitrophenyloctanoate was followed by measuring the appearance of p-nitrophenol in the reaction mixture: The...
-
Use values of r cov (Table 17.1) to estimate the XY bond lengths of ClF, BrF, BrCl, ICl and IBr. Compare the answers with values in Fig. 17.8 and Table 17.3, and comment on the validity of the method...
-
From a square whose side has length \(x\), measured in meters, create a new square whose side is \(10 \mathrm{~m}\) longer. Find an expression for the sum of the areas of the two squares as a...
-
Determine the effects of the following on a cash basis taxpayers gross income for 2021 and 2022: a. On the morning of December 31, 2021, the taxpayer received a $1,500 check from a customer. The...
-
In Exercises 1558, find each product. (9 - 5x) 2
-
Which polar coordinate pairs label the same point? a. (-2, /3) b. (2, -/3) c. (r, ) d. (r, + ) e. (-r, ) f. (2, -2/3) g. (-r, + ) h. (-2, 2/3)
-
Give parametric equations and parameter intervals for the motion of a particle in the xy-plane. Identify the particles path by finding a Cartesian equation for it. Graph the Cartesian equation....
-
Find the eccentricity of the ellipse. Then find and graph the ellipses foci and directrices. 7x 2 + 16y 2 = 112
-
The Regal Cycle Company manufactures three types of bicyclesa dirt bike, a mountain bike, and a racing bike. Data on sales and expenses for the past quarter follow: Total Dirt Bikes Mountain Bikes...
-
?? A local college is deciding whether to conduct a campus beautification initiative that would imvolve various projects, such as planting trees and remodeling bulidings, to make the campus more...
-
A company has net income of $196,000, a profit margin of 9.7 percent, and an accounts receivable balance of $135,370. Assuming 70 percent of sales are on credit, what is the companys days sales in...
Study smarter with the SolutionInn App