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
irga5000 [103]
3 years ago
8

We are going to fence in a rectangular field. If we look at the field from above the cost of the vertical sides are $10/f t, the

cost of the bottom is $2/f t and the cost of the top is $7/f t. If we have 700 determine the dimensions of the field that will maximize the enclosed area.
Mathematics
1 answer:
Brut [27]3 years ago
7 0

Answer:

Dimensions are 350/9 ft and 17.5 ft

Step-by-step explanation:

We are given the cost per ft of all the 4 sides. Let the horizontal be x and the vertical be y.

Now, we will set up the constraint and equation that we are being asked to maximize.

Thus;

700 = 10y + 10y + 7x + 2x

700 = 20y + 9x

Maiking y the subject, we have;

y = (700 - 9x)/20

y = 35 - 9x/20

Now,area of a rectangle is: A = xy

Thus, A = x(35 - 9x/20))

A = 35x - 9x²/20

We can get the critical points by finding the derivatives and Equating to zero

Thus;

dA/dx = 35 - 0.9x

At dA/dx = 0,we have; x = 350/9

At d²A/dx², we have;

d²A/dx² = -0.9

This is negative, thus we will disregard and use the one gotten from the first derivative.

Thus, we will use x = 350/9 ft

Plugging this into the equation y = 35 - 9x/20, we have;

y = 35 - ((9 × 350/9)/20)

y = 17.5 ft

You might be interested in
the sum of two numbers is 45. the greater number is 9 more than the other number. Find each number. use a system of linear equat
SpyIntel [72]

Answer:

18 and 27

Step-by-step explanation:

Let x = first (smaller) number

Let y = second (larger) number

Sum of two numbers is 45:

⇒ x + y = 45

The greater number is 9 more than the other number:

⇒ y = x + 9

Substitute  y = x + 9  into  x + y = 45  and solve for x:

⇒ x + (x + 9) = 45

⇒ 2x + 9 = 45

⇒ 2x = 36

⇒ x = 18

Substitute found value for x into  y = x + 9  and solve for y:

⇒ y = 18 + 9

⇒ y = 27

Therefore, the two numbers are 18 and 27

5 0
2 years ago
Read 2 more answers
What is the value of n in the relationship 8n+9=-n+5
vitfil [10]
Subtract 5 from both sides.

8n + 4 = -n

Subtract 8n from both sides.

4 = -9n

Divide both sides by -9 to solve for n.

- \frac{4}{9} = n

The value of n is -4/9.
8 0
3 years ago
Two people independently each pick a number from 1 to 10. what is the probability that the two of them pick the same number?
Marysya12 [62]
1 in 10 is the probability of two people picking the same number.
7 0
3 years ago
What is the area of the triangle? ​
beks73 [17]
The area of a triangle is 180
4 0
2 years ago
Two cars leave the same place at the same time, but drive in opposite directions along a straight road. one car averages 35 mi/h
Goshia [24]

As we do not know the other cars avg speed we can not tell the answer. Please repeat the question.

6 0
3 years ago
Other questions:
  • Which graph represents the solution set for - 4(1-x)<-12+2x?
    8·2 answers
  • -3x(4+(-7)) in distributive property
    8·1 answer
  • Two angles are supplementary. The first angle has 20º more then the second angle. How many degrees are in each angle?
    10·1 answer
  • Can someone please help me with this
    9·1 answer
  • Given f(3) = 3x? + 8x2 - 10x – 12,
    8·1 answer
  • (-8)^2 pls help me... I need to answer the last question
    6·1 answer
  • The midpoint of AB is M(-2, 1) If the coordinates of AA are (-3, -5) what are the coordinates of BB?
    11·2 answers
  • The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is r
    9·1 answer
  • The ratio of bOYS to giris
    8·1 answer
  • Combine the like terms to create an equivalent expression. (6e−3f−4)⋅2
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!