ANSWER
The length of the rectangular field is 99 yards
EXPLANATION
Given information
The perimeter of a rectangle field is 372 yards
The width of the field is 87 yards
To find the length of the rectangular field, follow the steps below
Step 1: Write the formula for finding the perimeter of a rectangular field
![\begin{gathered} \text{ The perimeter of a rectangular field = 2\lparen l + w\rparen} \\ \text{ where l =length, and w = width} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7B%20The%20perimeter%20of%20a%20rectangular%20field%20%3D%202%5Clparen%20l%20%2B%20w%5Crparen%7D%20%5C%5C%20%5Ctext%7B%20where%20l%20%3Dlength%2C%20and%20w%20%3D%20width%7D%20%5Cend%7Bgathered%7D)
Step 2: Substitute the given data into the formula in step 1
![\begin{gathered} \text{ Perimeter = 2 \lparen l + w\rparen} \\ \text{ Perimeter = 372 yards} \\ \text{ width = 87 yards} \\ \text{ 372 = 2\lparen l + 87\rparen} \\ \text{ Divide both sides by 2} \\ \text{ }\frac{372}{2}\text{ = }\frac{2}{2}(l\text{ + 87\rparen} \\ 186\text{ = l + 87} \\ \text{ subtract 87 from each sides of the equation} \\ \text{ 186 - 87 = l + 87 - 87} \\ \text{ 99 = l} \\ l\text{ = 99 yards} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7B%20Perimeter%20%3D%202%20%5Clparen%20l%20%2B%20w%5Crparen%7D%20%5C%5C%20%5Ctext%7B%20Perimeter%20%3D%20372%20yards%7D%20%5C%5C%20%5Ctext%7B%20width%20%3D%2087%20yards%7D%20%5C%5C%20%5Ctext%7B%20%20372%20%3D%202%5Clparen%20l%20%2B%2087%5Crparen%7D%20%5C%5C%20%5Ctext%7B%20Divide%20both%20sides%20by%202%7D%20%5C%5C%20%5Ctext%7B%20%7D%5Cfrac%7B372%7D%7B2%7D%5Ctext%7B%20%3D%20%7D%5Cfrac%7B2%7D%7B2%7D%28l%5Ctext%7B%20%2B%2087%5Crparen%7D%20%5C%5C%20186%5Ctext%7B%20%3D%20l%20%2B%2087%7D%20%5C%5C%20%5Ctext%7B%20%20subtract%2087%20from%20each%20sides%20of%20the%20equation%7D%20%5C%5C%20%5Ctext%7B%20186%20-%2087%20%3D%20l%20%2B%2087%20-%2087%7D%20%5C%5C%20%5Ctext%7B%20%2099%20%3D%20l%7D%20%5C%5C%20l%5Ctext%7B%20%3D%2099%20yards%7D%20%5Cend%7Bgathered%7D)
Hence, the length of the rectangular field is 99 yards
Over 4 years, there will be a loss of 60,000 acres per year, so 60,000 times 4 is equal to 240,000 acres. 240,000 is positive because the problem asks for the change, not the increase.
This is the work you will show
c=-60,000(4)
c=-240,000
So -240,000 represents the change.
You could also just count by -60,000 four times.
-60,000-60,000-60,000-60,000=-240,000.
645/8= 80.625 lol why do u even need this
The length (L) of the rectangle can be written as a function of the width (W)
![L = 2W - 3](https://tex.z-dn.net/?f=L%20%3D%202W%20-%203)
:
Now since we know Area = Width*Length, we can write the area as a function of the width:
![A = L*W = (2W-3)*W](https://tex.z-dn.net/?f=A%20%3D%20L%2AW%20%3D%20%282W-3%29%2AW)
Distributing the W inside the parentheses we have:
![A = 2W^2 - 3W](https://tex.z-dn.net/?f=A%20%3D%202W%5E2%20-%203W)
We know the area is 54 ft^2, so we can rewrite it as:
![2W^2 - 3W - 54 = 0](https://tex.z-dn.net/?f=2W%5E2%20-%203W%20-%2054%20%3D%200)
Now solve for W by factoring (or by applying the quadratic formula):
![2W^2 - 12W + 9W - 54 = 0](https://tex.z-dn.net/?f=2W%5E2%20-%2012W%20%2B%209W%20-%2054%20%3D%200)
Factor out a common 2W from the first two terms and a 9 from the last two terms:
![2W(W-6) + 9(W-6) = 0](https://tex.z-dn.net/?f=2W%28W-6%29%20%2B%209%28W-6%29%20%3D%200)
Regroup the terms to get our fully factored equation:
![(2W + 9)(W-6) = 0](https://tex.z-dn.net/?f=%282W%20%2B%209%29%28W-6%29%20%3D%200)
This gives us the roots W = 6 and W = -9/2, but width can't be negative so we have width = 6 ft. Then remember that the length L = 2W - 3, so our length is:
![L = 2W - 3 = 2(6) - 3 = 12 - 3 = 9](https://tex.z-dn.net/?f=L%20%3D%202W%20-%203%20%3D%202%286%29%20-%203%20%3D%2012%20-%203%20%3D%209)
So now we know that our rectangle is 9 feet long and 6 feet wide.
9514 1404 393
Answer:
1414 cm³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h
For a radius of 5 cm and a height of 8 cm, the volume is ...
V = π(5 cm)²(18 cm) = 450π cm³ ≈ 1414 cm³
The volume of Nadia's sugar container is about 1414 cm³.
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<em>Additional comment</em>
The value will be 1413 cm³ if you use 3.14 for π.