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yawa3891 [41]
3 years ago
6

Gina has 1200 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed ar

ea. What is the maximum​ area?
Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
8 0
We know the perimeter formula would be 1200=2x+2y. And the area will be A=x*y
We can to take the derivative of the area formula to find where it is a max but we must first substitute something in from the first formula so we only have one variable.

1200-2x=2y
600-x=y

A=(x)*(600-x)
A=600x-x^2

Now we take the derivative:
A'=600-2x (set equal to 0 and solve)
0=600-2x
2x=600
x=300 

Then when we plug this into the perimeter formula, we can solve for y
1200=2x+2y
1200=2(300)+2y
1200=600+2y
600=2y
y=300

So both the length and width are 300 yards, and the area would be 90,000 square yards

Hope this helps
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3 years ago
Rewrite the following equation in slope-intercept form. -3 = 13x – 11y Write your answer using integers, proper fractions, and i
n200080 [17]
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4 0
4 years ago
In 1990, the rate of change of the world population was approximately 0.09125 billion per year (or approximately 1 million peopl
babunello [35]

Answer: Option A

P = 5.3 + 0.09125t

Step-by-step explanation:

Note that for the initial year, 1990, the population was 5.3 billion.

The exchange rate is 0.09125 billion per year. In other words, each year there are 0.09125 billion more people.

In year 2 there will be 0.09125 * 2 billion people

In year 3 there will be 0.09125 * 3 billion people

In year 4 there will be 0.09125 * 4 billion people

In year t there will be 0.09125 * t billion of people

So the equation that models the number of people that there will be as a function of time is:

P = P_0 + rt

Where P_0 is the initial population

P_0 = 5.3 billion

r is the rate of increase

r = 0.09125 billion per year

finally the equation is:

P = 5.3 + 0.09125t

The correct answer is option A.

6 0
3 years ago
Read 2 more answers
How do I show my work, what do I say?
Juliette [100K]
Just write 3 to 4 sentences why you wrote that like why you agree or why not yk
3 0
3 years ago
Help me please I need help bad
Sergio039 [100]

Answer:

The number of photo albums can be solved using the equation: 1.375n + 5 =60 and n=40 photo albums.  

Step-by-step explanation:

In order to find the number of photo albums, we need to set up an equation to find out how many pounds the crate would weigh with just the albums and divide by the weight of just one album, or 1 3/8.  To make it easier to calculate, we can turn 1 3/8 into a decimal of 1.375.  Since we know that 1.375 is the weight of each album, we can multiply our variable 'n' by this number.  The question also says that the crate itself weighs 5 pounds, so we have to include this weight into our equation as well.  If we add 1.375 times 'n' plus the  weight of the crate (5 pounds), then we get a total of 60 pounds.  When we write it out, it becomes: 1.375n + 5 = 60.  To solve for 'n', we need to use inverse operations to subtract 5 from both sides and then divide by 1.375 to get 40 albums.  

3 0
3 years ago
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