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
Lemur [1.5K]
3 years ago
14

A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Seven h

undred and eighty feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum​ area?
Mathematics
1 answer:
Arisa [49]3 years ago
8 0

Answer:

Step-by-step explanation:

Suppose the dimensions of the playground are x and y.

The total amount of the fence used is given and it is 780 ft. In terms of x and y this would be 3x+2y=780 (we add 3x because we want it to be cut in the middle). Therefore,  y= 780/2-3/2x. Now, the total area (A )to be fenced is

A=x*y= x*(390-3/2x)=-3/2 x^2+390x

Calculating the derivative of A and setting it equals to 0 to find the maximum

A'= -3x+390=0

This yields x=130.

Therefore y=780/2-3/2*130=195

Thus, the maximum area is 130*195=25,350ft^2

You might be interested in
Todd plans to swim 18 laps in a pool. Each lap 50 yards.so far Todd has swam 738 yards what percentage of the total has Todd com
Paha777 [63]

Answer:

He is 82 percent done

Step-by-step explanation:

by multiplying 18 laps by 50 yards we have to total distance of 900 yards

so using the equation (738/900) * 100 we get 82

4 0
3 years ago
Show that ( 2xy4 + 1/ (x + y2) ) dx + ( 4x2 y3 + 2y/ (x + y2) ) dy = 0 is exact, and find the solution. Find c if y(1) = 2.
fredd [130]

\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}

\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}

so the ODE is indeed exact and there is a solution of the form F(x,y)=C. We have

\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)

\dfrac{\partial F}{\partial y}=4x^2y^3+\dfrac{2y}{x+y^2}=4x^2y^3+\dfrac{2y}{x+y^2}+f'(y)

f'(y)=0\implies f(y)=C

\implies F(x,y)=x^2y^3+\ln(x+y^2)=C

With y(1)=2, we have

8+\ln9=C

so

\boxed{x^2y^3+\ln(x+y^2)=8+\ln9}

8 0
2 years ago
Need asapppp !!!!!!!
alina1380 [7]
X=70, y=55

The triangle is an isosceles triangles. In an isosceles triangle, the base angles are congruent.

Then use the triangle angle sum theorem and set the equation to 180.

55+55+x=180
110+x=180
x=70

The angle with 55 degrees and the angle with the variable y are alternate angles. Meaning they are congruent.
5 0
3 years ago
Pleasee help ASAP!! No links pleaseee!!!
Ilya [14]

Given:

The vertices of the rectangle ABCD are A(0,1), B(2,4), C(6,0), D(4,-3).

To find:

The area of the rectangle.

Solution:

Distance formula:

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Using the distance formula, we get

AB=\sqrt{(2-0)^2+(4-1)^2}

AB=\sqrt{(2)^2+(3)^2}

AB=\sqrt{4+9}

AB=\sqrt{13}

Similarly,

BC=\sqrt{(6-2)^2+(0-4)^2}

BC=\sqrt{(4)^2+(-4)^2}

BC=\sqrt{16+16}

BC=\sqrt{32}

BC=4\sqrt{2}

Now, the length of the rectangle is AB=\sqrt{13} and the width of the rectangle is BC=4\sqrt{2}. So, the area of the rectangle is:

A=length \times width

A=\sqrt{13}\times 4\sqrt{2}

A=4\sqrt{26}

A\approx 20

Therefore, the area of the rectangle is 20 square units.

3 0
3 years ago
Alex has 48 stickers. This is 6 times the number of stickers Max has. How many stickers does Max have?
Fantom [35]
The opposite if multiplication is division. 48/6 = 8 Max has 8 stickers.
7 0
3 years ago
Read 2 more answers
Other questions:
  • After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1984​, the hay in that
    5·1 answer
  • Inequality help!<br><br>so I'm thinking it's choice one...would that be right?
    15·1 answer
  • Stephen, Gavin and Jim share some sweets in the ratio 4:1:2. Stephen gets 30 more sweets than Jim. How many sweets are there alt
    14·1 answer
  • Living with parents: The Pew Research Center reported that 36% of American Millennials (adults ages 18–31) still live at home wi
    5·1 answer
  • Find the missing angle.
    8·1 answer
  • Find the volume of the cylinder and cone, then add them together.
    11·1 answer
  • If sin Θ &lt; 0, cos Θ &gt; 0, and tan Θ &lt; 0, what quadrant are we in?
    5·1 answer
  • Juan wants to eat fewer than 800
    8·1 answer
  • Tom bought a banner for
    13·2 answers
  • Please answer. (No links please)
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!