2. Michelle asks her husband to build a pen for her chickens. Three of the sides will be built with mesh fencing, while the fourth side will back up to the east side of her house. She wants the enclosed area to be 400 square feet. The cost of the fence meshing will be $4.18 per foot and the pen will also need 4 corner posts costing $9.50 each.

a. [6 pts] Let x be the length of the side of the chicken coop that backs up to the east side of the house. Write a function P(x), for the price of the materials for the pen in terms of x. Simplify your answer.

b. [3 pts] Use your calculator to find the dimensions of the pen that costs the least. Set your window with: 0≤x≤80 and 10≤ y ≤400, and round your answer to 2 decimal places. (Insert your graph here. You may hand draw the graph or insert an image of the graph from Desmos)

c. [1 pt] What is the total cost of the pen? Round to dollars and cents.

Question

20-07-2022
Mathematics

contestada

2. Michelle asks her husband to build a pen for her chickens. Three of the sides will be built with mesh fencing, while the fourth side will back up to the east side of her house. She wants the enclosed area to be 400 square feet. The cost of the fence meshing will be $4.18 per foot and the pen will also need 4 corner posts costing $9.50 each.

a. [6 pts] Let x be the length of the side of the chicken coop that backs up to the east side of the house. Write a function P(x), for the price of the materials for the pen in terms of x. Simplify your answer.

b. [3 pts] Use your calculator to find the dimensions of the pen that costs the least. Set your window with: 0≤x≤80 and 10≤ y ≤400, and round your answer to 2 decimal places. (Insert your graph here. You may hand draw the graph or insert an image of the graph from Desmos)

c. [1 pt] What is the total cost of the pen? Round to dollars and cents.

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topeadeniran2 topeadeniran2 · Answer 1 · 2022-07-21T01:21:19+02:00

The function P(x), for the price of the materials for the pen, is 4.18(800/x + x) + 38.

How to illustrate the function?

Based on the information, the function P(x), for the price of the materials for the pen will be:

P(x) = 4.18 (2 × 400/x + x) + 38

= 4.18(800/x + x) + 38.

The dimensions will be:

We'll differentiate the function which will give 20✓2. Therefore, the value for x will be 20✓2 which is 28.28 feet and that of y will be 10✓2 which is 14.14 feet.

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