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
sesenic [268]
3 years ago
10

You have $6000 with which to build a rectangular enclosure with fencing. The fencing material costs $30 per meter. You also want

to have two partitions across the width of the enclosure, so that there will be three separated spaces in the enclosure. The material for the partitions costs $25 per meter. What is the maximum area you can achieve for the enclosure? (Round your answer to the nearest whole number.)

Mathematics
1 answer:
Roman55 [17]3 years ago
5 0
Refer to the figure shown below.
x =  the width of the rectangle (meters)
y = the height of the rectangle (meters(

The fencing for the perimeter of the rectangle costs  $30 per meter.
The two inner partitions cost $25 per meter.

The total cost of the fencing is
C = 2(x+y)*$30 + 2y*$25
   = 60(x+y) + 50y 
   = 60x + 110y

Because the amount available to spend is $600, therefore
60x + 110y = 6000
or
6x + 11y = 600
That is,
y = (600 - 6x)/11              (1)

The area is
A = x*y                           (2)

Substitute (1) into (2).
A = (x/11)*(600 - 6x) = (1/11)*(600x - 6x²)

To maximize A, the derivative of A with respect to x is zero.
That is,
600 - 12x = 0
x = 600/12 = 50
From (1), obtain
y = (1/11)*(600 - 6*50) = 300/11 = 27.273

Because the second derivative of A with respect to x is negative, x=50, y = 27.273 will yield the maximum area.

The maximum area is
50*27.273 = 1363.64 m² = 1364 m² (nearest integer)

Answer: 1364 m² (nearest integer)

You might be interested in
Factor x2 – 6x – 7.
SpyIntel [72]
You can make an cb chart. so to equal -6 you need the numbers -7, 1. so now the equation is ( x - 7 )( x + 1 ). if you want to solve it set it equal to 0 and solve. 
5 0
3 years ago
The average price of a barrel of crude oil in a recent year was 65.37. which estimated price is incorrect.
Nutka1998 [239]

Answer:

65.37 isn't an estimated price, it's an exact price....

5 0
3 years ago
Read 2 more answers
Corey drives 50 miles & the road is 200 miles, & he wastes 30 miles per gallon, how many more gallons to get 200 miles ?
Alenkinab [10]
I believe the answer is 5. Hope this was right for you.
6 0
3 years ago
A semicircle has a center at X and diameter WZ. The radius XY of the semicircle has a length of 2. The chord YZ has a length of
siniylev [52]
, it is important to recognize that the point (x,y) in the first quadrant represents any point on the semicircle. In Figure 2, the same semicircle is shown with the inscribed rectangle drawn for three different values of x.
4 0
3 years ago
An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Ro
krok68 [10]
Using the formula
L=rx  (x=angle)
x=L/r
x=8/3
x=2.6 radians
7 0
3 years ago
Other questions:
  • Please help me!! This is math 7th grade
    9·1 answer
  • Explain what you can tell just by comparing the symbols in a picture.
    6·2 answers
  • Lenore needs an apartment immediately. She
    6·1 answer
  • There are 36 forks on a table which represents 30% of the pieces of silverware. How many pieces of silverware are on the table?
    11·2 answers
  • True or false, an equation with an integer coefficient will always have an integer solution.
    14·2 answers
  • Is there a math Theorem for a right triangle
    14·1 answer
  • Geometry <br> Part of a quiz
    9·2 answers
  • Can someone please help for brainlest
    7·2 answers
  • Help and Plz make sure it’s right
    12·1 answer
  • A proportional relationship between the number of pounds of potatoes (x) and the price in dollars (y) is graphed, and the ordere
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!