MATHEMATICS MIDDLE SCHOOL

Farmer Ed has 300meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?Width
Length
Largest area:

Answers

Answer 1

Answer:

The area of the farm is the amount of space on the farm.

The width of the farm is 150 meters
The length is 75 meters
The largest area is 11250 square meters

Given

$P = 300m$ --- the perimeter

$L \to Length$

$W \to Width$

Because one side of the farm is a river, the perimeter is calculated as:

$P = 2L + W$

So, we have:

$2L + W=300$

Make W the subject

$W = 300 - 2L$

The area of the farm is:

$A = L * W$

Substitute $W = 300 - 2L$

$A = L * (300 - 2L)$

$A = 300L - 2L^2$

Differentiate, and set the result of the differentiation to 0

$A' = 300 - 4L$

$300 - 4L = 0$

Solve for L

$4L = 300$

Divide by 4

$L =75$

Solve for W

$W = 300 - 2L$

$W = 300 - 2* 75$

$W =150$

Solve for A

$A = L * W$

$A = 75 * 150$

$A = 11250$

Hence,

The width of the farm is 150 meters
The length is 75 meters
The largest area is 11250 square meters

Read more about areas and perimeters t:

brainly.com/question/11957651

Answer 2

Answer:

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose the width is W.

Suppose the length is L.

Total fence is given as 300, so

$L+W+W=300$

$L+2W=300$ ......................(1)

$Area=Length*Width$

$Area=L*W$

Plugging the value of L from equation (1)

$Area=(300-2W)*W$

$Area=300W-2W^2$

For Area to be maximized, derivative of area should be equal to zero.

Means :

$(d)/(dW)Area= 300-4W = 0$

So, $So, W Width = (300)/(4)=75$

So, $L Length=300-2*75=150$

So, Largest area= $75*150=11250$ : Answer

Related Questions

X 9.2 13.8 can someone show me how to solve this
A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. The standard deviation of the amount in each can is 0.12 ounce. The machine is overhauled with new components, and ten cans are filled to determine whether the standard deviation has changed. Assume the fill amounts to be a random sample from a normal population.Perform a hypothesis test to determine whether the standard deviation differs from 0.12 ounce. Use the level of significance.
What are the steps of doing 309 times 29
For any two nonzero integers, the product and quotient have the same sign. True or False
What is the square root of 25/9?

The height of a tree sapling was 3.15 inches last year. This year, the height is 5.38 inches. How much did the height of the tree sapling increase?

Answers

well.... i would say to subract so it would be... 2.23

How could you describe this graph?

Answers

Skewed right, if its data is mostly on the left it’s skewed right, if it’s data is mostly on the right it’s skewed left

Answer: skewed right

Step-by-step explanation:

Write two irrational numbers between 1 and 2

Answers

$(\pi)/(2),√(\pi)$

$Answer : √(2)$ and $√(3)$

Danny charges $35 for three hours of swimming lessons mart charges $24 for two hours of swimming lessons who offers a better deal

Answers

Matt offers the better deal. He is exactly $1 dollar cheaper then Danny. In other to find this out i had to find what Matt charged per hour, so i took 24 divide 2 and got 12. So i learned that he charges 12 an hour. Then i added 12 to 24 to make 3 hours of lessons to match what Danny offers. It was $34 which makes it Matt's deal cheaper by $1.

Danny. Danny offers lessons for about $11/hr while mart charges $12

Zack divides 6 cups of fruits juice equally among 8 friends how much does each friend get?

Answers

number of cups you have / number of friends to share it between = 6/8

You can simplify 6/8 by dividing both the numerator and the denominator by 2.

6/8 = 3/4 or 0.75 of a cup

The average rate of the first part of Yi’s walk on a park loop was 4 miles per hour. She then met up with a friend and the two walked the rest of the way at an average rate of 5 miles per hour. The entire 3-mile walk took Yi 42 minutes (0.7 hour). Which equation can be used to solve for x, the time in hours that Yi spent walking before meeting her friend?

Answers

so she walked during this time with 4 miles per hour (x*4)

during the rest of the way (which is 0.7-x, as the whole way took her 42 minutes, so the rest is 0.7-x) she walked with 5 miles per hour - the distance was (0..7-x)*5 m/h

the total distance was 3 miles, so if we sum the two distances, we will get 3 miles:

x*4+ (0.7-x)*5=3

let's remove the bracket:

4x+0.7*5-5x=3

4x+3.5-5x=3

subtract 3.5 from both sides:
4x-5x=3-3.5
-x=-0.5

multiply both sides by (-1)
x=0.5:

so she walked for half an hour alone, that is for 30 minutes!

Answer:

D, 4x + 5(0.7 – x) = 3.

Step-by-step explanation:

yw egen2020

Other Questions

What's number is 35% of 20

Pls answer thi for me tyty

A teacher had 24 red pens. If the ratio of red pens to blue pens she owned was 8:7, how many pens did she have total

What is 80% of 400? show work