Write an expression where you multiply a decimal number by 100. Which direction and how many places does the decimal move?
2 answers:
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For this problem, we just have to use the values we're given to calculate the approximate value of pi.
The formula presented is
When you have a negative exponent, we can use the following property
Using this property, our problem turns out to be
Now, we just need to plug the given values on this equation
The approximated value for pi is 3.142.
Let us list out the given information:
Cost per foot = $5
Total fencing cost = $1200
Let L be the length of the barn that will maximize the area of the pasture and W be the width of the rectangular cow pasture.
From the given information, we need to do the fencing for three sides covering 1 L and 2 W's because other L will be the fourth side is part of the side of a barn. We need to write the equation based on the cost information.
If cost/foot is $5, then cost of length ' L ' will be 5L dollars and cost of '2W' width equals 10W dollars. Total cost is $1200. We can set up second equation as
5L + 10W = 1200. This can be simplified by dividing throughout the equation by 5 to get L+ 2W= 240. Solving for L we get L = 240 - 2W
Area of a rectangle is given by A = L ×W.
Substituting 240 - 2W for L we get the area function as..
A=(240 - 2W)×W= 240W-2W²
A = -2W²+240W.
When we have a function of the form f(x) = ax^2 + bx + c, then maximum value of the function can be obtained for x = -b/2a. Using that idea we can find the maximum area.
Here in the area function a = -2 and b = 240
For W = -b/2a = -240/2(-2) = -240/-4 = 60 feet, we get maximum area.
The question is asking us to find Length. We can substitute W = 60 in the equation L = 240 - 2W to find the Length.
L = 240 - 2(60) = 240 - 120 = 120 feet.
Conclusion: The length of the side parallel to the barn that will maximize the area of the pasture is 120 feet.
Note: Here the information 400 feet in the sentence "the fourth side is part of the side of a barn that is 400 feet long" given to distract us, we might not require that information to find the Length.
