1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mrs_skeptik [129]
3 years ago
5

A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If 18 meters of fencing are use

d, what is the maximum area that can be enclosed?

Mathematics
1 answer:
Rashid [163]3 years ago
8 0

Answer:

A = L W= 9*\frac{9}{2}=\frac{81}{2} m^2

Step-by-step explanation:

For this case we assume that the total perimeter is 18 ft, we have a wall and the two sides perpendicular to the wall measure x units each one so then the side above measure P-2x= 18-2x.

And we are interested about the maximum area.

For this case since we have a recatangular area we know that the area is given by:

A= LW

Where L is the length and W the width, if we replace from the values on the figure we got:

A(x)= x *(18-2x) = 18x -2x^2

And as we can see we have a quadratic function for the area, in order to maximize this function we can use derivates.

If we find the first derivate respect to x we got:

\frac{dA}{dx} = 18-4x=0

We set this equal to 0 in order to find the critical points and for this case we got:

18-4x=0

And if we solve for x we got:

x=\frac{18}{4}=\frac{9}{2} m

We can calculate the second derivate for A(x) and we got:

\frac{d^2 A}{dx^2}= -4

And since the second derivate is negative then the value for x would represent a maximum.

Then since we have the value for x we can solve for the other side like this:

L= 18-2x = 18-2 \frac{9}{2}= 18-9 =9m

And then since we have the two values we can find the maximum area like this:

A = L W= 9*\frac{9}{2}=\frac{81}{2} m^2

You might be interested in
The volume of the rectangular prism is 240 cubic centimeters. A rectangular pyramid has the same length, width,and height as a p
LuckyWell [14K]
The volume of the pyramid would be 80 cubic centimeters. The reason for this is because the formula for volume of a pyramid is 1/3bh, so if all the dimensions are the same for both figures, just divide the volume of the prism by three to find the volume of the pyramid. If you do this 240÷3=80 or the volume of the pyramid.
4 0
3 years ago
Read 2 more answers
The sum of one and the product of a number and two is thirteen
Zigmanuir [339]

Answer:

2x + 1=13

Step-by-step explanation:

the product of a number and 2 (2x)

sum of 1 (+1)

is 13 (=13)

6 0
3 years ago
Find the area of the blue triangle <br><br><br> Omg pls help muehhh
Alik [6]

Answer:

B) 42 units squared

Step-by-step explanation:

12 * 7 = 84

84 / 2 = 42

<em><u>Hope this helped! Have a nice day! Plz mark as brainliest!!!</u></em>

<em><u>-XxDeathshotxX</u></em>

4 0
2 years ago
Read 2 more answers
How can I get the anserw of 6.3 divided 0.7
gayaneshka [121]
You can use your calculator if you have one or do long division. just make sure to move the decimal so it looks like this: 63 divided by 7. you answer should be 9
6 0
3 years ago
Read 2 more answers
2. Find the mean, median, mode and range of the following numbers.
vekshin1

Answer:

mean-175.5

median-18

mode-18

range-11

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • Carolyn is making a quilt using blocks like the one shown below. All the shaded squares are the same size and all the shaded tri
    7·2 answers
  • The letters c, a, t are placed in a bag. Each letter is randomly drawn from the bag and not replaced. Complete the table to show
    6·1 answer
  • If two angles are supplementary, then they form a linear pair. IS THIS STATEMENT TRUE OR FALSE? WHY?
    7·1 answer
  • What is the value of r? Enter your answer in the box. Round your final answer to the nearest whole number. r = units A right tri
    14·2 answers
  • Solve the system by the method of elimination.
    12·2 answers
  • A computer is priced at $400 this year, and will be sold at 90% of its original value next year. What is next year's price for t
    14·1 answer
  • A gas station sells 1400 gallons of gasoline per hour if it charges $2.50 per gallon but only 1000 gallons per hour it charges $
    9·1 answer
  • Can y’all help me on question five?!
    5·2 answers
  • Does the graph represent an linear or nonlinear function
    10·2 answers
  • What is (5.03x -8.03) - (3.5x +6.2)?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!