The diagram shows a window made from a rectangle with base 2r m and height h m

Question:

The diagram shows a window made from a rectangle with base 2r m and height h m and a semicircle of radius r m. The perimeter of the window is 6 m and the surface area is A m².

a. Express h in terms of r.

b. Show that A = 6r – 2r² – ½ πr².

c. Find dA/dr and d²A/dr².

d. Find the value for r for which there is a stationary value of A.

e. Determine the magnitude and nature of this stationary value.

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

Step by Step Answer:

Related Book For book-img-for-question

Cambridge IGCSE And O Level Additional Mathematics Coursebook

ISBN: 9781108411660

2nd Edition

Authors: Sue Pemberton

See More Books

Question Posted: Sep 01, 2021 01:03 AM

See More Questions

The diagram shows a simplified household circuit. Resistor R1 = 240.0 Î© represents a light bulb; resistor R2 = 12.0Î© represents a hair dryer. The resistors r =...
The diagram shows a solid cylinder of radius r cm and height 2h cm cut from a solid sphere of radius 5 cm. The volume of the cylinder is V cm 3 . a. Express r in terms of h. b. Show that V = 2h(25 h...
A thin glass rod is a semicircle of radius R , see the figure(Figure 1) . A charge is nonuniformly distributed along the rod with a linear charge density given by ? = ? 0sin ? , where ? 0 is a...
What are the advantages and disadvantages of the net realizable method of allocating joint costs?
Order the following elements by increasing atomic radius according to what you expect from periodic trends: Se, S, As.
Under the provisions of IAS 16, what is the credit entry when noncurrent operating assets are written up to reflect an increase in market value?
Discuss the specific advantages and disadvantages to Angela Larson if she initiates an EEOC sexual harassment charge (or lawsuit) in this case.
In February 2015, Arctic Cat, Inc., acquired the assets and liabilities of MotorFist, LLC, a privately owned company based in Idaho Falls, Idaho, in exchange for $9.118 million in cash and contingent...
what is Segregation of Duties in accounting and how it can prevent fraud
Denise is divorced and files a single tax return claiming her two children, ages 7 and 9, as dependents. Her AGI for 2018 is $81,500. Denise's child tax credit for 2018 is: Oa. $0 Ob. $2,000 Oc....
Find the gradient of the curve y = x + 4/x 5 at the points where the curve crosses the x-axis.
The curve y = x 2 + a/x + b has a stationary point at (1, - 1). a. Find the value of a and the value of b. b. Determine the nature of the stationary point (1, - 1).
The first 25 years of the twentieth century were momentous for the rapid pace of change in scientists' understanding of the nature of matter. (a) How did Rutherford's experiments on the scattering of...
3 Below is financial information for December Inc., which manufactures a single product: 4 5 5 7 3 #units produced October Low activity November High activity 7,000 11,000 Cost of goods manufactured...
(b) The satellite's booster rockets fire and lift the satellite to a higher circular orbit of radius 2R1. The satellite follows the path shown in the diagram below, moving a total distance S during...
D. An airplane flies at a speed of 250 kilometers per hour (kph) at an altitude of 3000 m. Assume the transition from laminar to turbulent boundary layers occurs at critical Reynolds Number, RE cr, =...
1. (35 points) by Qet = QoQ = Q0Q2 N!37 N/A (1-B, (r), where A- B(T) V * 4R (e-(R)/KT - 1) R dR is the second virial coefficient. The classical partition function for an imperfect gas comprising N...
es Farm has 28 employees who are paid biweekly. The payroll register showed the following payroll deductions for the pay period ending March 23, 2021. Gross Pay 85,950.00 EI Premium Income Taxes...
Maria Alvarez is investing $300,000 in a fund that earns 4% interest compounded annually. What equal amounts can Maria withdraw at the end of each of the next 20 years?
Should U.S. antidumping laws be stated in terms of average total costs or average variable costs?
Burns Company incurred costs for the following items. 1. Salary of chief financial officer 2. Factory insurance 3. Salary for salespeople 4. Raw materials used in production easily traced to the...
Leighton, Inc., incurred costs for the following items. 1. Janitorial services in the production facility 2. Personnel department supplies 3. Shipping costs for raw materials purchased from a...
The income statement from Fords annual report appears as follows in summary form. (This information was obtained from the companys Web site,www.ford.com.) Required: a. The financial information in...
This is a partial adjusted trial batance of Cullumber Compary manualys
Which of the following journal entries will record the payment of a $1,500 salaries payable originally incurred for Salaries Expense? Select one: A. Debit Salaries Expense; credit Salaries Payable B....
What is the definition of substantially appreciated inventory? A. Inventory with a FMV greater than its basis B. Inventory and unrealized receivables with a FMV greater than their basis C. Inventory...

The diagram shows a window made from a rectangle with base 2r m and height h m

Question:

rm hm 2rm

Step by Step Answer:

a h 2 r b A 6 r 2 r 2 r 2 c d A dr 6 4 r r d 2 A dr 2 4 d The value for r for which there is a stati...View the full answer

Cambridge IGCSE And O Level Additional Mathematics Coursebook

Students also viewed these Business questions