Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

A plan for a park has a rectangular plot of wild flowers that needs to be enclosed by 54 feet of fencing. Only three sides need to be enclosed because one side is bordered by the parking lot. use Desmos to get your answers. 1. What is the largest area possible for the garden? DO NOT ROUND YOUR ANSWER. ____ squared feet2. What width will produce the maximum area? ____ feet3. What is the length of the garden that will produce the maximum area?

A Plan For A Park Has A Rectangular Plot Of Wild Flowers That Needs To Be Enclosed By 54 Feet Of Fencing Only Three Sides Need To Be Enclosed Because One Side I class=

Sagot :

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

a) What is the largest area possible for the garden?

Now, let the length of the rectangular plot be 54 -2x,

and the width of the rectangular plot be x,

so that:

[tex]\begin{gathered} \text{Area = (54 -2x) x = 54 x -2x}^2 \\ \frac{dA}{dx}=\text{ 54 - 4x = 0} \\ We\text{ have that:} \\ 54\text{ = 4x } \\ \text{Divide both sides by 4, we have that:} \\ \text{x = }\frac{54}{4} \\ \text{x = 13. 5} \end{gathered}[/tex]

Then, the largest area possible for the garden will be:

[tex]\text{Area = 54x -2x}^2=54(13.5)-2(13.5)^2=729-364.5=364.5ft^2[/tex]

b) What width will produce the maximum area?

[tex]Width,\text{ x = 13. 5 fe}et[/tex]

c) The length of the garden that will produce the maximum area:

[tex]\text{Length = 54 - 2x = 54 - 2( 13. 5) = 54 -27 = 27 fe}et[/tex]

View image KeiariB345550
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.