Mr. Phillips decides to have a completely fenced-in garden. It will be laid out so that one side is adjacent to his neighbor's property. The neighbor agrees to pay for half of that part of the fence which will border his property. The garden is to contain 432 square yards. What dimensions should Mr. Phillips select for his garden so that his own cost will be minimum?
im sorry, i just have so much other homework, im also failing calculus cause im not understanding but i have other stuff to worry bout, usually i would go to tutoring to get this done but he gave it to me last min cause i went to the hospital, im not looking for sempithy i know i should just man up and do it but i have no excuse for not doing it blah blah blah thank you so much for helping me so far
i promise you i didn't make that up, im not trying to scam ppl into giving me answers, i really wanna learn but i just don't wanna cost my grade in the process, if you understand what i mean
To find the dimensions of Mr. Phillips' garden that will minimize his cost, we need to set up an equation that represents the cost of the fence as a function of the dimensions. Let's assume that one side of the garden, adjacent to the neighbor's property, measures x yards.
The total cost of the fence will be divided into two parts: the portion of the fence that Mr. Phillips pays for, and the portion that the neighbor pays for.
The cost of the fence that Mr. Phillips pays for is equal to the perimeter of the garden minus the length of the side that the neighbor pays for. The neighbor's portion is equal to half of the length of the shared side.
So, the cost function is given by:
Cost = (Perimeter - x/2) * P
Here, P represents the cost per yard of fence. We want to minimize this cost function.
Now, let's find an equation that relates the dimensions of the garden to its area. The area of a rectangle is given by the product of its length and width. Since we are dealing with a square-shaped garden, the length and width are the same. Let's call this common dimension of the garden y yards.
The area of the garden is given by:
Area = x * y
According to the problem, the area of the garden is 432 square yards. Therefore, we have:
432 = x * y
Now, we can substitute the value of y from this equation into the cost function:
Cost = (Perimeter - x/2) * P
Cost = (2x + 2y - x/2) * P (substituting y = 432/x)
Simplifying, we get:
Cost = (3x + 864/x) * P
To find the minimum cost, we need to find the value of x that minimizes this cost function. We can use calculus to find the minimum. Taking the derivative and setting it equal to zero, we have:
dCost/dx = 3 - 864/x^2 = 0
Solving this equation, we find:
3 = 864/x^2
x^2 = 864/3
x^2 = 288
x = √288
Therefore, x ≈ 16.97 yards.
Substituting this value of x into the equation for the area, we get:
432 = 16.97 * y
Solving for y, we find:
y ≈ 25.47 yards.
Hence, the dimensions that Mr. Phillips should select for his garden to minimize his cost are approximately 16.97 yards by 25.47 yards.
I have now answered in detail several of your questions.
You have posted quite a few , but have shown no work of your own for any of them.
I will be glad to help with the others once you have shown me some effort on your part.