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
12345 [234]
3 years ago
11

A rectangular area is to be enclosed and divided into thirds. The family has $880 to spend for the fencing material. The outside

fence costs $10 per foot installed, and the dividers cost $20 per foot installed. What are the dimensions that will maximize the area enclosed
Mathematics
1 answer:
viva [34]3 years ago
5 0

Answer:

\W = Width

L = Length

Draw rectangle W x L

Divde rectangle into thirds with two lines parallel with width.

Outside fance perimeter = 2 W + 2 L

Inside fance length = 2 W

Total cost :

( 2 W + 2 L ) * 10 $ + 2 W * 20 $ = 400 $

( 2 W + 2 L ) * 10 + 2 W * 20 = 400

20 W + 20 L + 40 W = 400

60 W + 20 L = 400 Divide both sides by 20

60 W / 20 + 20 L / 20 = 400 / 20

3 W + L = 20 Subtract 3 W to both sides

3 W + L - 3 W = 20 - 3 W

L = 20 - 3W

Area :

A = W * L =

W * ( 20 - 3W ) =

20 W - 3 W ^ 2

First derivation :

dA / dW = 20 - 3 * 2 * W = 20 - 6 W

If first derivation = 0 a function has a local maximum or a local minimum.

dA / dW = 0

20 - 6 W = 0 Add 6 W to both sides

20 - 6 W + 6 W = 0 + 6 W

20 = 6 W Divide both sides by 6

20 / 6 = 6 W / 6

20 / 6 = W

2 * 10 / ( 2 * 3 ) = W

10 / 3 = W

W = 10 / 3 ft

If second derivative < 0 then function has a maximum.

If second derivative > 0 then function has a mimum.

In this case second derivative = - 6

Second derivative < 0 so function has a maximum.

For W = 10 / 3 ft

L = 20 - 3W = 20 - 3 * 10 / 3 = 20 - 10 = 10 ft

Amax = W * L = 10 / 3 * 10 = 100 / 3 ft ^2

You might be interested in
On July 31, Oscar checked out of the Sandy Beach hotel after spending four nights. The cost of the room was $76.90 per night. He
Radda [10]

Answer:

$307.60

Step-by-step explanation:

multiple $76.90 by the 4 nights he stayed. $76.90×4

5 0
4 years ago
Read 2 more answers
HELP ME ASAP PLSSSSSSSSSSS
adoni [48]

Answers:

  1. Plane EFGH
  2. Angle 2 and angle 3
  3. Alternate exterior angles
  4. See the explanation below

==================================================

Explanation:

Problem 1

The plane ABCD is the floor of the box or room.

The ceiling plane EFGH is parallel to the floor.

Parallel planes never intersect, must like how parallel lines in 2D never intersect. As such, parallel planes are the same distance apart.

In contrast, something like plane ABFE intersects with ABCD along the segment AB. This shows ABFE is not parallel to ABCD.

----------------------

Problem 2

Same side interior angles, aka consecutive interior angles, are inside the parallel (or nearly parallel) lines. One such example is angle 2 and angle 3. The other pair being angle 6 and angle 7. They must be on the same side of the transversal.

In contrast, alternate interior angles would be something like the pair angle 2 and angle 7. The other pair being angle 3 and angle 6. This time the angles are on alternating or opposite sides of the transversal.

----------------------

Problem 3

Angles 1 and 8 are exterior of the parallel (or nearly parallel) lines. They are on alternating sides of the transversal. Therefore, we consider them to be alternate exterior angles.

----------------------

Problem 4

The use of "alternate" refers to the idea the angles are on opposite or alternating sides of the transversal line. The transversal line is the line that crosses the two other lines that are almost parallel.

I like to think of the parallel (or nearly parallel) lines as train tracks. The transversal is the roadway that crosses both train tracks. Then we could have locations 1 and 8 on opposite sides of the roadways to represent the alternate exterior angles.

As you can probably guess or know by now, the "exterior" is from the angles being outside or exterior of the parallel (or nearly parallel) lines.

4 0
2 years ago
The Empire State Building, the Sears Tower, the
nadezda [96]

The Empire State Building, the Sears Tower, the Canadian National Tower - each of these structures was the tallest in the world at the time they were (Option D) built.

<h3>What is sentence correction?</h3>

Sentence correction or sentence improvement is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.

Now,

  • Here, we are talking about each of the mentioned structures.
  • By grammar, everything used for them must be singular.
  • But as mentioned in the sentence in part D, the plurals "they were" are used, which is the faulty part of the sentence.

Hence, Option D is the correct part that needs correction; the correction would be: "it was built."

To learn more about sentence correction, refer to the link: brainly.com/question/14632568

#SPJ4

4 0
2 years ago
Please help I only have 5 minutes left!
Zinaida [17]
Hi Briana.

All triangles have a total internal measurement of 180 degrees from their angles. Isosceles triangles have two similar side lengths, and one different side length also known as the base. Considering we have the base, we can determine the side lengths by using the following equation:
2x + 24 = 96
Let's get to solving!

2x + 24 = 96; subtract 24 from both sides.
2x = 72; divide both sides by 2 to solve for the measurement of each side length.
x = 36;

Your answer is B.) 36

I hope this helps!
3 0
3 years ago
Read 2 more answers
[Inequalities]<br> Please help and thanks.
sergeinik [125]

At least means it can be larger than or equal to.

X >= 15

No more than means less than or equal to:

X <= $7

3 0
3 years ago
Read 2 more answers
Other questions:
  • The equation is 4 1/5-7/10. How do u rename 4 1/5
    15·1 answer
  • Efgh is a parallelogram. find each measure
    9·1 answer
  • A school survey asked students which candidate they supported for class president. The survey data are shown in the relative fre
    12·2 answers
  • How do you simplify <img src="https://tex.z-dn.net/?f=7%5Csqrt%5B4%5D%7B80pq%5E%7B2%7Dr%5E%7B8%7D%20%20%7D" id="TexFormula1" tit
    5·1 answer
  • The quotient of two times a number and 19
    10·2 answers
  • If you wanted to measure how much your dog weighs, which unit of measure would you use?
    12·2 answers
  • There are 24 students in a class. 1/2 are boys. 1/3 of the boys are wearing hats. How many boys are wearing hats?
    10·1 answer
  • Question c please!!! done all the others. i have 2 minutes
    6·2 answers
  • (5x - 4) - (10x - 3)
    5·1 answer
  • 12:[-4(5-3)-2(-23+21)]
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!