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
padilas [110]
3 years ago
9

Jacob wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence

on that side. The other three sides will be enclosed with wire fencing. If Jacob has 400 feet of fencing, you can find the dimensions that maximize the area of the enclosure.
a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write an function for the area A of the enclosure in terms of w . (HINT first write two equations with w and l and A . Solve for l in one equation and substitute for l in the other).

A(w) =

b) What width
w would maximize the area?
w = _____ ft
c) What is the maximum area?
A = _______square feet
Mathematics
1 answer:
Citrus2011 [14]3 years ago
6 0

Jacob wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn,so he needs no fence on that side.

Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn).

one side of the length is not counted for perimeter because one side of length will be against the barn.

Perimeter = 400 ft

Perimeter of rectangle = L + W + W

400 = L + 2W

L = 400 - 2W

Area = L * W

Replace L by  400 - 2W

A(W) =  (400 - 2W) * W

A(W) = -2W^2 + 400W

Now we find out x coordinate of vertex to find the width that maximize the area

W = \frac{-b}{2a}

a= -2 and b = 400

W = \frac{-(400)}{2(-2)}=100

The width  w would maximize the area is w = 100ft

To find maximum area we plug in 100 for W in A(W)

A(W) = -2W^2 + 400W

A(W) = -2(100)^2 + 400(100)= 20000

the maximum area is 20,000 square feet

You might be interested in
Yen paid $10.50 for 2.5 pounds of pretzels. What price did she pay for each pound of pretzels?
Furkat [3]

Answer:

The first step is to multiply by a power of 10, so the divisor is a whole number.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Which shows the expression below simplified? 0.00028 ÷ (7 × 10-4)
Katyanochek1 [597]
0.\underbrace{00028}_{\rightarrow5places}=28\times10^{-5}\\\\0.00028:(7\times10^{-4})=\dfrac{28\times10^{-5}}{7\times10^{-4}}=\dfrac{28}{7}\times\dfrac{10^{-5}}{10^{-4}}\\\\=4\times10^{-5-(-4)}=4\times10^{-5+4}=\huge\boxed{4\times10^{-1}}\leftarrow\boxed{b.}\\\\used\ \dfrac{a^n}{a^m}=a^{n-m}
6 0
3 years ago
NEED HELP ASAP!!!!!!
melamori03 [73]
Okay so you can add up all the marbles to find a rate and divide.
Total: 20 marbles
Blue: 25% chance
Red: 40% chance
Green: 45% chance
8 0
3 years ago
Read 2 more answers
Someone please help me with this problem
Greeley [361]

Answer:

corresponding

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Which properties are present in a table that represents a logarithmic function in the form y=log8^(x) when b>1 I. The y-value
IRINA_888 [86]

Answer: its C:I, III, and IV just took the test.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the product of 4×7×25tell which strategy you used
    14·1 answer
  • Help Please
    12·2 answers
  • The units of the subway map below are in miles. Suppose the routes between stations are straight. Station​ G, not shown on the​
    9·1 answer
  • Solve the following proportion for v. v\13 = 7\17
    7·1 answer
  • Your summer job will pay you $75 for the first week. Your boss will give you a bonus of $25 per week.
    10·1 answer
  • Shobo's mother's present age is six times Shobo's present age. Shobo's age five
    10·1 answer
  • In the given figure poq is a line. if x=30 then find qor and ros​
    9·1 answer
  • Help meeeeeeeeeeessss​
    8·1 answer
  • Solve 4|x + 5| + 8 = 24.
    9·1 answer
  • I need help on way more then just thisT-T-math-
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!