The diagram shows a shape made from a rectangle and a semicircle. y + 1/4 x (

Question:

The diagram shows a shape made from a rectangle and a semicircle. y + 1/4 x (π + 2) = 25

a) Show that the area A square metres of the shape is given by A = 100x − 2x² − 1/2πx²

b) Find the maximum value of A and
explain why this value is a maximum.

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

Step by Step Answer:

Related Book For book-img-for-question

Complete Pure Mathematics 1 For Cambridge International AS & A Level

ISBN: 9780198427438

2nd Edition

Authors: Jean Linsky, Brian Western, James Nicholson

See More Books

Question Posted: Apr 14, 2023 11:19 AM

See More Questions

A large corporation with monopolistic control in the marketplace has its average daily costs, in dollars, given by The daily demand for x units of its product is given by p=60,000-50x dollars. Find...
The diagram shows a shape made from the arc of a circle with centre O and radius 30 cm and the straight line PQ. The size of angle POQ is 7/9 radians. P rad- 30cm Q
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 =...
Run experiments to determine the relative costs of Math.exp() and the methods from EXERCISE 1.3.38 for computing e x : the direct method with nested for loops, the improvement with a single for loop,...
Job order costing is frequently used by home builders. Required 1. You (or your team) are to prepare a job cost sheet for a single-family home under construction. List four items of both direct...
Mr. and Mrs. Tinker own a sizeable investment portfolio of stock in publicly held corporations. The couple has four children, ages 20, 22, 25, and 27, with whom they want to share their wealth....
Cloud Cover in San Francisco-Online The plots in Exercise 2.254 on cloud cover in San Francisco can be found online at weatherlines.zanarmstrong.com if you prefer Figure 2.99(a) or...
ParentCo owns all of the stock of DaughterCo, and the group files its Federal income tax returns on a consolidated basis. Both taxpayers are subject to the AMT this year due to active operations in...
Microchip began the year with $2,600 in its asset account, supplies. During the year, $7,100 in supplies were purchased and debited to supplies. At year-end, supplies costing $3,550 remain on hand....
In the Chapter 11 Data Analytics Case, you used Tableau to examine a data set and create calculations to compare the relative age of two companies assets. In this case you continue in your role as an...
The side of a cube is decreasing at a rate of 0.4 cm s . Find the rate of decrease of the surface area when the length of the side is 3 cm.
Find the coordinates of the stationary points of the curve y = (3x 2) 9x and determine their nature.
On January 1, 2015, the records of Smita Corporation showed the following: Truck (estimated residual value, $ 3,000) ............$ 18,000 Accumulated depreciation (straight line, two years) ..........
With a neat sketch, explain the following lathe operations. Facing, Cylindrical turning, Knurling, Thread cutting.
(LO3) If a business has an average of $\( \$ $ 29\) million or less of gross receipts over the last 3 years, may the business use the cash method of accounting?
(LO3) Describe the difference in the cash method of accounting and the accrual method of accounting.
(LO2) Is a state tax refund includible in income if the taxpayer did not itemize her deductions last year?
Draw the neat sketch of the horizontal milling machine and explain parts.
The stock price of XYZ is $100. One million shares of XYZ (a negligible fraction of the shares outstanding) are buried on a tiny, otherwise worthless plot of land in a vault that would cost $50...
A container holds 2.0 mol of gas. The total average kinetic energy of the gas molecules in the container is equal to the kinetic energy of an 8.0 10-3-kg bullet with a speed of 770 m/s. What is the...
Welfare payments for 1965 to 2015 were recorded. Draw the following line charts and briefly describe what the chart tells you about each variable. a. Original data b. Per capita data c. Per capita in...
Education spending from 1935 to 2015 was recorded. Draw the following line charts and briefly describe what the chart tells you about each variable. a. Original data b. Per capita data c. Per capita...
Interest on Federal Debt from 1935 to 2015 was recorded. Draw the following line charts and briefly describe what the chart tells you about each variable. a. Original data b. Per capita data c. Per...
Exercise 6-1 (Algo) Variable and Absorption Costing Unit Product Costs [LO6-1] Ida Company produces a handcrafted musical instrument called a gamelan that is similar to a xylophone. The gamelans are...
The finite automata FA1, and FA2 are shown below in Fig. 1 and Fig. 2 respectively. They accept the respective languages L1 and L2. a, b x2 FX1 b Figure 1: FA1: The FA accepting the language L.
Consider the following rendezvous code: while (1) { select { when a==TRUE : accept A() { f1%; b=FALSE } when b==TRUE : accept B() { f2; a=FALSE } else { a=TRUE; b=TRUE } Assume that there are no...

The diagram shows a shape made from a rectangle and a semicircle. y + 1/4 x (

Question:

2x metres 2y metres

Step by Step Answer:

a The shape consists of a rectangle ...View the full answer

Complete Pure Mathematics 1 For Cambridge International AS & A Level

Students also viewed these Mathematics questions