A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure below. A Norman window with perimeter 30 ft is to be constructed.height(a) Find a function that models the area of the windowA(x) =(b) Find the dimensions of the window that admits the greatest amount of light. (Round your answers to one decimal place.)ftX=ftheight

Diameter of the semi circle = x ftSo, radius = (x/2) ftCircumference of the semi circle= pi*r =…

Answered: A Norman window has the shape of a…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.1: Quadratic Functions And Models

Problem 74E: Maximum Area A Norman window is constructed by adjoining a semicircle to the top of an ordinary...

See similar textbooks

Similar questions

Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.
Maximum Area A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). The perimeter of the window is 16 feet. (a) Write the area A of the window as a function of x. (b) What dimensions produce a window of maximum area?
In these problems you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use guidelines on page 273 to help you. Minimizing Costs A rancher wants to build a rectangular pen with an area of 100m2 . (a) Find a funtions that models the lenghth of fencing required. (b) Find the pen dimensions that require the minimum amount of fencing.
A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula r(t)=2t+1 , express the area burned as a function of time, t (minutes).
In these problems you are asked to find a function that model a real-life situation and then use the model to answer questions about the situation. Use the guidelines on page 273 to help you. Dividing a Pen A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel Lo one side of the rectangle (see the figure). (a) Find a function that models the total area of the tour pens. (b) Find the largest possible total area of the four pens.
Titanic At 2:00 p.m. on April 11, 1912, the Titanic left Cobh, Ireland, on her voyage to New York City. At 11:40 p.m. on April 14, the Titanic struck an iceberg and sank, having covered only about 2100 miles of the approximately 3400-mile trip. (a) What was the total duration of the voyage in hours? (b) What was the average speed in miles per hour? (c) Write a function relating the distance of the Titanic from New York City and the number of hours traveled. Find the domain and range of the function. (d) Graph the function in part (c).
Maximum Area A rancher has 200 feet of fencing to enclose two adjacent rectangular corrals (see figure). (a) Write the area A of the corrals as a function of x. (b) What dimensions produce a maximum enclosed area?
Field Trip A class of fourth graders walks to a park on a field trip. The function y=f(t) graphed below gives their distance from school in ft t minutes after they left school. What is the average speed going to the park? How long was the class at the park? How far away is the park? Graph the function y=0.5f(t). How is the graph of the new function related to the graph of the original function? What is the average speed going to the new park? How far is the new park? Graph the function y=f(t10). How is the graph of the new function related to the graph of the original function? How does the field trip described by this function differ from the original trip?

Recommended textbooks for you

College Algebra

Algebra

ISBN:

9781337282291

Author:

Ron Larson

Publisher:

Cengage Learning

Glencoe Algebra 1, Student Edition, 9780079039897…

Algebra

ISBN:

9780079039897

Author:

Carter

Publisher:

McGraw Hill

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781337282291

Author:

Ron Larson

Publisher:

Cengage Learning

Glencoe Algebra 1, Student Edition, 9780079039897…

Algebra

ISBN:

9780079039897

Author:

Carter

Publisher:

McGraw Hill

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

SEE MORE TEXTBOOKS