suppose you have an outdoor pool measuring 25ft by 10ft. you want to add a cement walkway around the pool. if the walkway will be 1ft thick and you have 304ft of cement how wide should the walkway be?
write the quadratic equation to model the volume of the walkway
no
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To determine the width of the walkway, you can start by calculating the area of the entire pool, including the walkway.
The pool has dimensions of 25ft by 10ft, and you want to add a 1ft thick walkway around it. This means you need to increase the dimensions of the pool by 2ft in width and 2ft in length. Therefore, the dimensions of the entire area with the walkway will be 27ft by 12ft (25ft + 2ft and 10ft + 2ft).
Next, calculate the area of the pool (without the walkway) by multiplying the original length and width:
Area of the pool = 25ft * 10ft = 250ft²
Then, calculate the area of the entire area, including the walkway, by multiplying the new length and width:
Area of the entire area = 27ft * 12ft = 324ft²
The volume of the walkway is the difference between the two areas:
Volume of the walkway = Area of the entire area - Area of the pool
Volume = 324ft² - 250ft² = 74ft²
Now, to write the quadratic equation to model the volume of the walkway, we need to express the width of the walkway as a variable. Let's call the width of the walkway "w."
The length of the pool with the walkway is 27ft, and the original length of the pool is 25ft. Therefore, the width of the walkway on one side is (27ft - 25ft)/2 = 1ft.
Since the walkway is of uniform width, the width of the entire walkway, including both sides, will be 2w.
The length of the pool with the walkway is 12ft, and the original width of the pool is 10ft. Therefore, the width of the walkway at one end is (12ft - 10ft)/2 = 1ft.
Again, since the walkway is of uniform width, the width of the entire walkway, including both ends, will be 2w.
The total width of the walkway, including both sides and ends, will be: 2w + 2w = 4w.
So, the equation to model the volume of the walkway will be:
Volume = Width * Length * Height
Volume = (27ft * 12ft * w) - (25ft * 10ft)
Volume = 324w - 250
Therefore, the quadratic equation to model the volume of the walkway is:
V(w) = 324w - 250
yes
7.2 ft
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Let x=width of walkway.
Equate volume of cement (concrete) available to Area of walkway*1 ft deep
(25+x)(10+x)-25*10 = 304 ft³
x²+35x = 304
x(x+35) = 304
x²+35x-304=0
x=7.2 or x=-42.2
Can you take it from here?