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Topic: **How to write an equations for a step function****Question:**
Max has 15 yards of fencing to make a rectangular kennel for her dog. He will build the kennel next to his house h=so he only needs to enclose three sides. What dimensions maximize the area of the kennel? What is the maximum area?
How would I set this up in an equation?

June 21, 2019 / By Oran

SHORTCUT METHOD: I will show you how to set up the equation, but I will also show you a shortcut method to solving this: Step 1 : Divide your fencing material into two equal piles --> 7.5 yards each Step 2 : Use one half for vertical fencing, the other half for the horizontal fencing . _____ 7.5 yds _______ . | .................................. | . | .................................. | . | 3.75 yds ................... | 3.75 yds . | .................................. | . | .................................. | ==================== (house as the extra wall) The dimensions of this kennel are: 3.75 yds x 7.5 yds = 28.125 sq. yds LONGER METHOD: Let x be the length of each side fence perpendicular to the house (two of them) Let 15 - 2x be the length of the fence parallel to the house (one of them)* *If this isn't clear, you have 15 yds of fencing, but you've used up 2x for the two side fences. That leaves 15 - 2x for the last fence. . ____ 15 - 2x yds _____ . | .................................. | . | .................................. | . | x yds ......................... | x yds . | .................................. | . | .................................. | ==================== (house as the extra wall) Write a function for the area (length times width): f(x) = x(15 - 2x) or f(x) = -2x² + 15x To maximize that, take the first derivative and set it to zero: f'(x) = -4x + 15 = 0 4x = 15 x = 15/4 x = 3.75 yds Other dimension: 15 - 2x = 15 - 7.5 = 7.5 yds Area = 3.75 x 7.5 = 28.125 sq. yds.

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SHORTCUT METHOD: I will show you how to set up the equation, but I will also show you a shortcut method to solving this: Step 1 : Divide your fencing material into two equal piles --> 7.5 yards each Step 2 : Use one half for vertical fencing, the other half for the horizontal fencing . _____ 7.5 yds _______ . | .................................. | . | .................................. | . | 3.75 yds ................... | 3.75 yds . | .................................. | . | .................................. | ==================== (house as the extra wall) The dimensions of this kennel are: 3.75 yds x 7.5 yds = 28.125 sq. yds LONGER METHOD: Let x be the length of each side fence perpendicular to the house (two of them) Let 15 - 2x be the length of the fence parallel to the house (one of them)* *If this isn't clear, you have 15 yds of fencing, but you've used up 2x for the two side fences. That leaves 15 - 2x for the last fence. . ____ 15 - 2x yds _____ . | .................................. | . | .................................. | . | x yds ......................... | x yds . | .................................. | . | .................................. | ==================== (house as the extra wall) Write a function for the area (length times width): f(x) = x(15 - 2x) or f(x) = -2x² + 15x To maximize that, take the first derivative and set it to zero: f'(x) = -4x + 15 = 0 4x = 15 x = 15/4 x = 3.75 yds Other dimension: 15 - 2x = 15 - 7.5 = 7.5 yds Area = 3.75 x 7.5 = 28.125 sq. yds.

Perimeter = P, Area = A P= 2x+y 15= 2x+y A= xy Make a substitution and derive! I'm assuming you're using calculus!?

Perimeter = P, Area = A P= 2x+y 15= 2x+y A= xy Make a substitution and derive! I'm assuming you're using calculus!?

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There are 3 kinds of questions-open--in voting and resolved- Choosing a best answer will resove a question and it will be closed-When a majority vote chooses a best answer in voting then the question is resolved. :::::::::To choose a best answer to a question you have asked---Wait four hours after you post your question, click your avatar, this will bring you to your profile page. scroll down to your "my questions":::::click that and your questions come up, click the one you want::::There will be a blue bar under each answer you got that says choose as best answer::::Click on that blue button if you want to choose that answer as best answer, a new page comes up ::::Then you rate it 1-5 stars and write a comment in the space provided.. Click OK and it's Done::::::::::::::::::::::::::::::::::Yo... receive 3 points for choosing and the best answer gets 10 points and 1 extra for each thumbs up to a total of 50 ::::::::::::::::::::::::::::::::::::::::... A question goes to voting if you have not chosen a best answer after 4 days....Then you can vote for best answer and receive one point but there is no guarantee that the one you think is best will be chosen as the answer with the most votes will get best answer.... You can also vote no best answer (no points given) and if that is the question with the most votes it is removed and the posters 5 points are returned.....Any level can choose best answer for a question they have asked and any level can vote on any questions in voting.

Well...it's called "resolving a question" and yes, it's most definitely related to picking a best answer. That's how you resolve a question. You have to wait 4 hours minimum in order to resolve a question.

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