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
-BARSIC- [3]
3 years ago
6

A farmer wants to put a fence around his vegetable garden. Only three sides must be fenced since a rock wall will form the fourt

h side. If he uses 40 m of fencing, what is the maximum area possible? What dimensions should the farmer use?
Mathematics
1 answer:
tankabanditka [31]3 years ago
8 0

Answer: Maximum area = 200m

Dimensions:

Length = 10m

Width = 20m

Such that there is only one side of 20m fenced because the other side of 20m is against the rock wall.

Step-by-step explanation:

We have the next problem.

Suppose that the vegetable area is a rectangle of length L and width W.

Such that the width side coincides with the rock wall, then we have that:

The perimeter is:

P = 2*L + 2*W

But because one of the width sides coincides with the wall, the amount of fence needed will be:

P = 2*L + W = 40m

And the area can be written as:

A = W*L

We want to find the maximum area that we can have.

First, write our two equations:

40m = 2*L + W

A = W*L

First we must isolate one of the variables in the first equation, and replace it into the second equation:

40m - 2*L = W.

then:

A = (40m - 2*L)*L = 40m*L - 2*L^2

We can write this as a quadratic equation:

A(L) = -2*L^2 + 40m*L

Now, notice that it has a leading coefficient negative, then the maximum of the area function will be at the vertex of the quadratic equation.

For a quadratic equation:

f(x) = a*x^2 + b*x + c

The vertex is at:

x = -b/2a

and the point is (-b/2a, f(-b/2a))

In this case we have:

b = 40m

a = -2

Then:

we must evaluate the area function in:

L = -40m/(-2*2) = 10m

A(L) = -2*L^2 + 40m*L

A(10m) = -2*100m^2 + 400m = 200m

Now we can find the width using one of the above equations:

W = 40m - 2*L = 40m - 2*10m = 20m

Then the dimensions that the farmer should use are:

Two sides of length 10m, and one side of length 20m

You might be interested in
Sally earns commission for selling cars at the Nissan dealership. She earns 5.5% on
cestrela7 [59]

Answer:

8800

Step-by-step explanation:

5 0
2 years ago
A park is 5 miles east of Roxana's home. A library is 4 miles north of the park. How far is Roxana's home from the library? ​
Ber [7]

Answer: 9 miles I think but I dont know where her house is exactly.

8 0
3 years ago
According to the Holy Bible, Jesus begins to perform healings. There were many healers during Jesus’ time. What made Jesus’ heal
Gekata [30.6K]

Healing was essential to the ministry of Jesus because He envisioned healing as a physical symbol of forgiveness. He guaranteed the ultimate glory of the human body through His personal resurrection, but forecast that restoration by healing twisted, shrunken, blinded limbs and organs. The paralytic's restoration is but one of many such examples (Mark 2:1-12).

Though there were many healers, Jesus was able to even raise up the dead, and also there was one instance where the Canaanite woman struggled through His disciples' desire to dismiss her, and His own initial, courteous refusal, to get what she knew she could trust Him to grant (Matthew 16:28). The crowds "begged him to let the sick just touch the edge of his cloak," (Matthew 14:36), for "all who touched him were healed."

Healers were not able to do that, and Jesus also claimed that he was God's son, so performing miracles like this was like proving the point. Also, healers were not always able to heal the person, but Jesus was able to do so all the time (for free even!) so many people traveled to meet him so he could heal them.

The woman with a hemorrhage crept silently through the crowd to merely touch His clothes (Mark 5:28). She also claimed that she went to many healers, but she didn't get healed, in fact, she got worse! So that's an instance that proves the point.

<em>Thank you :D</em>

3 0
3 years ago
Show work please I need help asap
rosijanka [135]

Answer:

12. -11

13. 2

Step-by-step explanation:

12. First recall the order of operations (BEDMAS): Brackets, Exponents, Division, Multiplication, Addition, Subtraction

For question 12 there is a division and its priority is before other operations in the equation so you must divide 16/-2 first which gives you -8.

From there because addition and subtraction is on the same level of order, you would do the question straight as it is shown (but replace 16/-2 with -8.

Your new equation is -10-8+7 = -11

13. follow the same as above using BEDMAS. It may help to look at it with additional brackets: ((-68)/(-4)) + ((5 x (-3))

  • keep in mind there’s an addition between the two

Division and multiplication is on the same level in BEDMAS so first divide -68/-4 = 17

Second multiply 5 x -3 = -15

Now you can combine the two answers using addition: 17 + (-15) = 2

5 0
2 years ago
5/8 - 3/4(8 - 1/3) + 1
Anon25 [30]
The answer is definitely -4 1/8
6 0
2 years ago
Read 2 more answers
Other questions:
  • Marina wants to purchase a rosebush ford dollars at a garden store. She has a coupon good for
    9·1 answer
  • Jane is making a suit which requires 2 5/8 yards for the jacket and 1 3/4 yards for the skirt. What’s the total amount of materi
    9·1 answer
  • Brent uses 3/4 cups of sugar for a batch of lemon bars. How much sugar will he need to make 6 batches of lemon bars?
    9·2 answers
  • Graph the inequality.<br> y&gt; -5x+1
    9·1 answer
  • DIG DEEPER At a restaurant, when a customer buys 4 pretzels, the fifth pretzel is free. Soft pretzels cost $3.90 each. You order
    14·1 answer
  • X+4=16 1&amp;2 step equation
    15·1 answer
  • Anyone wanna be freinds
    7·2 answers
  • Which of the following statements is true?
    7·1 answer
  • Pls help i put a picture with the question
    6·1 answer
  • A scientist drops a probe in the water. The depth of the probe changes −1 1/2 feet every second. How many seconds will it take f
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!