Folks on Reddit had been amused by the primary sentence of this math drawback.
The primary sentence displays what number of math issues are introduced to be “actual world” functions however they appear a bit contrived.
Some dude needs two rectangular enclosures towards his home for some motive. He has 300 ft of fencing. Discover the next:
a) Space when it comes to x
b) Most space
c) Dimensions for max space. Embrace items in your reply.
As standard, watch the video for an answer.
Or maintain studying.
.
.
“All will probably be nicely in case you use your thoughts to your choices, and thoughts solely your choices.” Since 2007, I’ve devoted my life to sharing the enjoyment of sport idea and arithmetic. MindYourDecisions now has over 1,000 free articles with no advertisements because of group help! Assist out and get early entry to posts with a pledge on Patreon.
.
.
.
.
.
.
M
I
N
D
.
Y
O
U
R
.
D
E
C
I
S
I
O
N
S
.
P
U
Z
Z
L
E
.
.
.
.
Reply To Humorous Math Downside
(Just about all posts are transcribed rapidly after I make the movies for them–please let me know if there are any typos/errors and I’ll appropriate them, thanks).
If one facet of the rectangle is x, then the 2 sides parallel to it additionally equal x. The fencing enclosure makes use of the home for one facet, and the remaining fence can be utilized for the fence. The three vertical fences whole 3x, so the remaining fencing size is 300 – 3x.
Thus the realm of the fence is its top occasions its width which is:
A(x) = x(300 – 3x) = 300x – 3x2
How can we maximize the realm?
Parabola symmetry
Discover the realm operate will be represented by a parabola with minimal values at x = 0 and 300 – 3x = 0, or x = 100. The world could have constructive values in between. By symmetry of a parabola, this parabola has its most precisely midway between the 2 x intercepts, so its most is at x = 50. So the scale are x = 50 ft and 300 – 3x = 150 ft, giving a most space of fifty(150) = 7500 ft2.
Finishing the sq.
A(x)
= 300x – 3x2
= -3(x2 – 100x)
= -3(x2 – 100x + 502 – 502)
= -3((x – 50)2 – 502)
= 3(502) – 3(x – 50)2
= 7500 – 3(x – 50)2
The squared time period is non-negative, so the second time period solely subtracts from the constructive 7500 potential. We maximize the realm by subtracting as little as doable, which occurs when x = 50. Thus we once more discover the rectangle has a most space of 7500 sq. ft and dimensions of fifty ft by 150 ft.
Calculus
It is a simple calculation.
A‘(x) = 300 – 6x
A”(x) = -6
A‘(x) = 300 – 6x = 0
x = 300/6 = 50
The rectangle has dimensions of x = 50 ft and 300 – 3x = 150 ft with a most space of fifty(150) = 7500 ft squared.
Reference
Reddit
https://www.reddit.com/r/humorous/feedback/74c34o/hands_down_best_first_sentence_of_a_math_problem/
MY BOOKS
If you are going to buy via these hyperlinks, I could also be compensated for purchases made on Amazon. As an Amazon Affiliate I earn from qualifying purchases. This doesn’t have an effect on the value you pay.
Ebook scores are from January 2025.
(US and worldwide hyperlinks)
https://mindyourdecisions.com/weblog/my-books
Thoughts Your Selections is a compilation of 5 books:
(1) The Pleasure of Sport Principle: An Introduction to Strategic Considering
(2) 40 Paradoxes in Logic, Likelihood, and Sport Principle
(3) The Irrationality Phantasm: How To Make Sensible Selections And Overcome Bias
(4) The Greatest Psychological Math Methods
(5) Multiply Numbers By Drawing Strains
The Pleasure of Sport Principle exhibits how you should utilize math to out-think your competitors. (rated 4.2/5 stars on 564 critiques)
40 Paradoxes in Logic, Likelihood, and Sport Principle comprises thought-provoking and counter-intuitive outcomes. (rated 4.2/5 stars on 81 critiques)
The Irrationality Phantasm: How To Make Sensible Selections And Overcome Bias is a handbook that explains the numerous methods we’re biased about decision-making and presents methods to make good choices. (rated 4.2/5 stars on 55 critiques)
The Greatest Psychological Math Methods teaches how one can appear like a math genius by fixing issues in your head (rated 4.3/5 stars on 148 critiques)
Multiply Numbers By Drawing Strains This guide is a reference information for my video that has over 1 million views on a geometrical methodology to multiply numbers. (rated 4.5/5 stars on 57 critiques)
Thoughts Your Puzzles is a group of the three “Math Puzzles” books, volumes 1, 2, and three. The puzzles matters embrace the mathematical topics together with geometry, likelihood, logic, and sport idea.
Math Puzzles Quantity 1 options basic mind teasers and riddles with full options for issues in counting, geometry, likelihood, and sport idea. Quantity 1 is rated 4.4/5 stars on 138 critiques.
Math Puzzles Quantity 2 is a sequel guide with extra nice issues. (rated 4.2/5 stars on 45 critiques)
Math Puzzles Quantity 3 is the third within the collection. (rated 4.3/5 stars on 38 critiques)
KINDLE UNLIMITED
Lecturers and college students around the globe usually e-mail me in regards to the books. Since schooling can have such a huge effect, I attempt to make the ebooks obtainable as broadly as doable at as low a value as doable.
At the moment you possibly can learn most of my ebooks via Amazon’s “Kindle Limitless” program. Included within the subscription you’ll get entry to tens of millions of ebooks. You do not want a Kindle gadget: you possibly can set up the Kindle app on any smartphone/pill/laptop/and so forth. I’ve compiled hyperlinks to applications in some international locations under. Please verify your native Amazon web site for availability and program phrases.
US, listing of my books (US)
UK, listing of my books (UK)
Canada, guide outcomes (CA)
Germany, listing of my books (DE)
France, listing of my books (FR)
India, listing of my books (IN)
Australia, guide outcomes (AU)
Italy, listing of my books (IT)
Spain, listing of my books (ES)
Japan, listing of my books (JP)
Brazil, guide outcomes (BR)
Mexico, guide outcomes (MX)
MERCHANDISE
Seize a mug, tshirt, and extra on the official website for merchandise: Thoughts Your Selections at Teespring.
