It is known that of all plane curves that enclose a given area, the circle has the

Question:

It is known that of all plane curves that enclose a given area, the circle has the least perimeter. Show that if a plane curve of perimeter L encloses an area A then 4πA ≤ L². Verify this inequality for a square and a semicircle.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Modern Engineering Mathematics

ISBN: 9781292253497

6th Edition

Authors: Glyn James

See More Books

Question Posted: Jan 03, 2024 05:00 AM

See More Questions

A certain light bulb manufacturer makes two types of bulbs, a low- cost short- life ( S-type) bulb and a more expensive long- life ( L- type) bulb. The two types of bulbs look identical and so the...
Olde World Windows and Doors is a manufacturer of steel windows and doors for both residential and commercial applications. The following problems are decisions that senior management faces in...
The article notes that the hospital did not fully understand how its electronic health record system would estimate expected revenue. This was obviously happening at the hospital for some time. How...
Explicitly justify relationships (11.5.3) between the compliances of the plane stress and plane strain theories. Equation 11.5.3 B11 B22 B66 = S11 S33-S2 $33 S22 S33-S23 S33 S66 S33 - S36 S33 B12 B16...
Determine the output of a linear time-invariant system if the impulse response h[n] and the input x[n] are as follows: (a) x[n] = u[n] and h[n] = a n u[n 1], with > 1. (b) x[n] = u[n 4] and h[n] =...
The GASB has identied four classes of nonexchange revenues: Derived tax Imposed Government mandated Voluntary For each of the following revenue transactions affecting a city, identify the class...
An option based on a variable that is not traded is called a real option or sometimes a soft option. Find the projection price of the soft option with the following parameters and compare with the...
Indicate whether each of the following describes an accounting treatment that is acceptable under IFRS, U.S. GAAP, both, or neither, by checking the appropriate box. Acceptable Under IFRS U.S. GAAP...
Vicky was an employee during 2 0 2 3 and she received the following income and benefits from her employer: Salaries paid and received in 2 0 2 3 - $ 4 2 , 0 0 0 Bonus declared by her employer on...
Regulations for taking a party of school children on a trip abroad requires that the ratio of accompanied teachers to children travelling must be 1:6. If 54 children sign up for the trip, how many...
Find the difference between 2 and the squares of (a) Verify that successive terms of the sequence stand in relation to each other as m does to (m + 2n)/(m + n). (b) Verify that if m is a good...
Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 0 In 2 0 (In 2)-y eVx + y dx dy
A pot of boiling water (212 F) is left to cool in a room that is 70 F. Newtons Law of Cooling states that the temperature of the water t minutes after it was left to cool will be T(t) = 70 Ae -kt...
A 5 kg weight is attached to a spring fixed to an inflexible beam. When the weight is at rest, the spring is 1 0 m long. The weight is pulled down from its equilibrium position by 2 m and released....
The Greenland ice sheet contains about 3 , 0 0 0 , 0 0 0 km ^ 3 of ice if completely melted the ice would release about 2 , 1 million kilometers of water which would spread out over earth...
Hau Lee Furniture, Inc., spends 60% of its sales dollars in the supply chain and finds its current profit of $10,000 inadequate. The bank is insisting on an improved profit picture prior to approval...
If Esther deposits $ 1 0 0 into a bank account which earns 1 0 % interest compounded quarterly for 3 years, how much money does she have at the end of 3 years?
At a temperature of 10C the percent relative humidity is R10, and at 40C it is R40. At each of these temperatures, the partial pressure of water vapor in the air is the same. Using the vapor pressure...
Carlton Stokes owns and operates a car-detailing business named SuperShine & Detailing. For $150, Carltons business will hand wash and wax customers cars, vacuum the interior, and thoroughly clean...
Using acetylene and methyl bromide as your only sources of carbon atoms, propose a synthesis for each of the following compounds: (a) (b) En Et Me En Et Me
Draw a mechanism and predict the major product for each reaction. a. b. c. d. e. f. ? 1) LAH H. 2) H20
Propose a molecular formula for a compound that exhibits the following peaks in its mass spectrum. a) (M) + at m/z = 72, relative height = 38.3% of base peak (M+1) + at m/z = 73, relative height =...
In the database you have built, you need to create a relationship between two fields in two tables. Field 1 in Table A has the Number Data Type and Field 1 in Table B has the Currency Data Type. Will...
The standard interface technology for wireless networks is _ _ _ _ _ _ _ _ _ _ . The hardware component necessary for computers to connect to these networks is a _ _ _ _ _ _ _ _ _ _ .
Write the SOP Boolean expressions for the 7 outputs. [ 3 . 5 marks ]

It is known that of all plane curves that enclose a given area, the circle has the

Question:

Step by Step Answer:

Lp where p is the perimeter of the circle of area A For the c...View the full answer

Modern Engineering Mathematics

Students also viewed these Sciences questions