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KonstantinChe [14]
3 years ago
5

Jim wants to build a rectangular parking lot along a busy street but only has 2400 feet of fencing available. if no fencing is r

equired along the​ street, find the maximum area of the parking lot.
Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
7 0
<span>Length = 1200, width = 600
   First, let's create an equation for the area based upon the length. Since we have a total of 2400 feet of fence and only need to fence three sides of the region, we can define the width based upon the length as: W = (2400 - L)/2
   And area is: A = LW
    Substitute the equation for width, giving: A = LW A = L(2400 - L)/2
    And expand: A = (2400L - L^2)/2 A = 1200L - (1/2)L^2
    Now the easiest way of solving for the maximum area is to calculate the first derivative of the expression above, and solve for where it's value is 0. But since this is supposedly a high school problem, and the expression we have is a simple quadratic equation, we can solve it without using any calculus. Let's first use the quadratic formula with A=-1/2, B=1200, and C=0 and get the 2 roots which are 0 and 2400. Then we'll pick a point midway between those two which is (0 + 2400)/2 = 1200. And that should be your answer. But let's verify that by using the value (1200+e) and expand the equation to see what happens:
   A = 1200L - (1/2)L^2
 A = 1200(1200+e) - (1/2)(1200+e)^2
 A = 1440000+1200e - (1/2)(1440000 + 2400e + e^2)
 A = 1440000+1200e - (720000 + 1200e + (1/2)e^2)
 A = 1440000+1200e - 720000 - 1200e - (1/2)e^2
 A = 720000 - (1/2)e^2
   And notice that the only e terms is -(1/2)e^2. ANY non-zero value of e will cause this term to be non-zero and negative meaning that the total area will be reduced. Therefore the value of 1200 for the length is the best possible length that will get the maximum possible area.</span>
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the ratio of men and women in a certain factory is 3 to 4. there are 198 men. How many workers are there?
LUCKY_DIMON [66]

3 men

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using cross products

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If you mean 3 men and 1 women for a total of 4 workers when you state a  ratio of men and women in a certain factory is 3 to 4.

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Using cross products

3x = 4* 198

Divide each side by 3

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It all depends on how you define ratio of men and women in a certain factory is 3 to 4.   This is incorrect phrasing and I took it to be men to women.   You cannot have a ratio of men and women.




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Complete Question

The complete question is shown on the first uploaded image

Answer:

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Step-by-step explanation:

From the question we are told that

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Step-by-step explanation:

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