Chapter 4.7, Problem 14E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Minimum Perimeter In Exercises 13 and 14, find the length and width of a rectangle that has the given area and a minimum perimeter.Area: A square centimeters

To determine

To calculate: The dimensions of the rectangle that provide the minimum perimeter under the specified conditions where area of the rectangle is A square feet.

Explanation

Given:

The area of the rectangle is A square feet.

Formula Used:

For a function f that is twice differentiable on an open interval I, if f'(c)=0 for some c, then,

If f''(c)>0 the function f has relative minima at c if f''(c)<0 the function f has relative maxima at c. If f''(c)=0, the test fails.

Calculation:

Consider the length and the breadth of the rectangle to be x and y.

Then the quantity to be minimized or the primary equation is:

P=2(x+y)

The perimeter of the rectangle is A square units. This gives:

xy=Ay=Ax

Substitute this back in the primary equation to obtain:

P=2(x+Ax)

Here as both the length and breadth are positive and the area is 49, the feasible domain is:

0xx

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Symmetry Test the equation for symmetry. 105. y = x4 + x2

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 6372, evaluate the expression. 68. 1+22

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In problem 18 and 19, determine whether each graph represents as a function of . 19.

Mathematical Applications for the Management, Life, and Social Sciences

Prove the identity. 46. (sin x + cos x)2 = 1 + sin 2x

Single Variable Calculus: Early Transcendentals
{"ft_lang_label":"__label__en","ft_lang_prob":0.73628974,"math_prob":0.9912405,"size":2062,"snap":"2019-43-2019-47","text_gpt3_token_len":430,"char_repetition_ratio":0.1511176,"word_repetition_ratio":0.07457627,"special_character_ratio":0.17216295,"punctuation_ratio":0.09422492,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99944955,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-16T11:57:27Z\",\"WARC-Record-ID\":\"<urn:uuid:d791f077-1ef5-4225-a8bf-539926ecdd26>\",\"Content-Length\":\"942008\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:899ee41b-307b-4ae2-b6df-d42d29dcd7e1>\",\"WARC-Concurrent-To\":\"<urn:uuid:1daa63c6-02cb-4b05-9afe-d2c140c90e0e>\",\"WARC-IP-Address\":\"99.84.181.97\",\"WARC-Target-URI\":\"https://www.bartleby.com/solution-answer/chapter-47-problem-14e-calculus-early-transcendental-functions-7th-edition/9781337552516/minimum-perimeter-in-exercises-13-and-14-find-the-length-and-width-of-a-rectangle-that-has-the/5be06912-99cd-11e8-ada4-0ee91056875a\",\"WARC-Payload-Digest\":\"sha1:543LIMOFNNZ5E4FXPL72F5PJ3IFVGCWO\",\"WARC-Block-Digest\":\"sha1:M4ZY5KPTSSH3NG2MPTYA4T34ABMAUXQ7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986668569.22_warc_CC-MAIN-20191016113040-20191016140540-00291.warc.gz\"}"}