How many half miles are in 12 miles?

Vlada [557]

Well a chicken has 2 legs so do 2 times however many chickens there are to get the total of chicken legs. a pig has 4 legs so do 4 times however many pigs there are to get the total of pig legs. once u have those answers, do the total of pig legs plus the total of chicken legs to get your total of legs. for the number of heads, do the number of chickens plus the number of pigs.

4 0

3 years ago

A rectangular cow pasture is enclosed on three sides by a fence and the fourth side is part of the side of a barn that is $400$

Degger [83]

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.