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
Amanda [17]
3 years ago
6

Apel Sinoman has 100 ft of fencing material to enclose a rectangular exercise run for her dog. One side of the run will border h

er​ house, so she will only need to fence three sides. What dimensions will give the enclosure the maximum​ area?

Mathematics
1 answer:
Olegator [25]3 years ago
5 0

Answer:

For maximum area of the rectangular exercise run dimensions will be 50ft by 25ft.

Step-by-step explanation:

Let the length of the rectangular exercise run = l ft

and width of the run = w ft

Sinoman has to cover a rectangular exercise run from three sides with the fencing material,

So length of the material = (l + 2w) ft

l + 2w = 100

l = 100 - 2w --------(1)

Area of the rectangular area covered = Length × width

A = lw

A = w(100 - 2w)    [(l = 100 - 2w)from equation (1)

For maximum area we find the derivative of area and equate it to zero.

\frac{dA}{dw}=\frac{d}{dw}[w(100-2w)]

A'=\frac{d}{dw}(100w-2w^{2} )

A' = 100 - 4w

For A' = 0

100 - 4w = 0

4w = 100

w = 25 ft

From equation (1)

l = 100 - 2w

l = 100 - 2×(25)

l = 50 ft

Therefore, for maximum area of the rectangular exercise run dimensions will be 50ft by 25ft.

You might be interested in
Hello I hope you have a wonderful day can you pls help me out it I will fail
ASHA 777 [7]
A. Independent goes on the x axis and dependent goes on the y axis
B. It shows his or hers miles per hour or mph or distance they run in a hour

Hope this helps have a great Monday ❤️
5 0
2 years ago
Can u help me do this
chubhunter [2.5K]
There will be 2 books left over if he fills each box.
7 · 4 = 28
30 - 28 = 2

Good Luck
5 0
3 years ago
Y = 3/2x + 3<br> The slope and y-intercept
ra1l [238]

Answer:

Slope=3/2

Y-intercept=3

Step-by-step explanation:

7 0
2 years ago
joe earns R25 per hour working at a pizza shop. How much will he earn over a weekend of two shifts, each six hours long​
NeX [460]

Answer:

R300

Step-by-step explanation:

<u>To solve:</u>

  • Multiply 25 by 6 to represent the earnings of a shift.
  • Multiply the shift earnings by 2 to represent how much he earned over the weekend.

<u>Multiply</u><u> </u><u>25 by 6:</u>

25 \times 6 = 150

<u>Multiply 150 by 2:</u>

<u>150 \times 2 = 300</u>

Joe will earn R300 over the weekend,

6 0
2 years ago
You are biking at a speed of 18 miles per hour. You are 3 miles behind your friend who is biking at a speed of
labwork [276]

Answer:

12t -3 = 18t

Step-by-step explanation:

Let

d = your friends distance in miles

t = time in hrs

Your equation:

d - 3 = 18t (1)

Because you are 3 miles behind your friend

Your Friend's equation:

d = 12t (2)

To find the amount of time t it takes for you to catch up with your friend,

Substitute (2) into (1)

d - 3 = 18t

12t - 3 = 18t

Equation to find the amount of time t it takes for you to catch up to your friend is 12t - 3 = 18t

Solving the equation

12t - 3 = 18t

Collect like terms

12t - 18t = 3

-6t = 3

t = 3/-6

= -0.5

t = 1/2 hour

Time can not be negative, therefore it will take 1/2 an hour to catch up with your friend

3 0
3 years ago
Other questions:
  • Plz help ASAP
    6·1 answer
  • What is the percent of change from 240 to 480?
    12·1 answer
  • What is the absolute value of [-2/3]
    7·1 answer
  • I need help with my homework please answer this correctly
    11·2 answers
  • Hi! If you have time, I am stuck on this problem. I don't get it. You need to find the net pay and I was wrong. Please help. No
    5·1 answer
  • Which statement best describes a ratio
    5·1 answer
  • The sum of integers p and q is modeled on a number
    10·1 answer
  • 100 POINTS
    7·1 answer
  • A manufacturer uses a mold to make a part in the shape of a triangular prism. The dimensions of this part are shown below.
    5·1 answer
  • Answer the following.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!