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
mart [117]
3 years ago
14

A rancher wishes to build a fence to enclose a rectangular pen having area 24 square yards. Along one side the fence is to be ma

de of heavy duty material costing $6 per yard, while the remaining three sides are to be made of cheaper material costing $3 per yard. Determine the least cost of fencing for the pen.
Mathematics
1 answer:
Gnoma [55]3 years ago
8 0

Answer:

The  value  is  C \approx \$76

Step-by-step explanation:

From the question we are told that

   The  area of the rectangular pen is  A =  24 \ yard^2

     The  cost of material used to make one side is  z = \$ 6

    The  cost of material used to make the other sides is  r  =  \$ 3

Now  , the fence to be build around the rectangular pen  has four sides, the first opposite sides are equal, let assume each of the to be x yard   and the other opposite sides are also equal as well let assume of the to be y yard

So the cost is mathematically represented as

       C =  zx  +  r (x + 2y )

=>   C =  6x  +  3(x + 2y)

=>   C =   9x  +  6y

Now the area of the fence is mathematically represented as

      A =  x* y =  24

=>    y  =  \frac{24}{x}

=>  C =   9x  +  6[\frac{24}{x} ]

=>   C =   9x  +  [\frac{144}{x} ]

Now differentiating

     C'  =  9 + 144*  (-2) x^{-2}

     C'  =  9 - 288x^{-2}

At minimum C' =  0

So  

     9 - 288x^{-2} =  0

     x^{-2} =  0.03125

    x =  \sqrt{\frac{1}{0.03125} }

    x =  5.66

Now substituting for x in the equation above to obtain minimum cost

       C =   9(5.66)  +  [\frac{144}{5.66} ]

       C \approx \$76

   

 

You might be interested in
The question is in the photo​
nirvana33 [79]

Answer:

yes

Step-by-step explanation:

half of x which is 4 = y which is 2

you keep doing that with the rest of the xs and ys

6 0
3 years ago
Positive, negative, zero or undefined?
Liula [17]

Answer:

Negative.

Step-by-step explanation:

Hope this helps.

4 0
3 years ago
Read 2 more answers
What is the value of x then find the messures of Angles M and N​
AveGali [126]

Answer:

x=32

Step-by-step explanation:

sum of interior angles of a triangle = 180

add up all angles and equate to 180

(4x-13)+(x+18)+15=180

5x=160

x=160/5=32

x+18  =   32+18    = 50

4x-13  =  4x32-13 = 128-13 = 115

add up all to check whether ans = 180;  15+50+115=180

3 0
3 years ago
Read 2 more answers
Which square root is a whole number? A) 222 B) 223 C) 224 D) 225
zepelin [54]
225, the square root of 225 is 15
3 0
3 years ago
Read 2 more answers
Solve for x and y. Thank u so much!!​
Setler79 [48]
Y is 45 x is 30 I think
7 0
3 years ago
Other questions:
  • Use the information in the table to find the constant rate<br> of change in dollars per hour
    14·1 answer
  • Help pleasee!!!!!!!!!!
    7·1 answer
  • What is the exact volume of the cylinder (radius 13 in., height 30 in.)
    12·1 answer
  • (-1,-2) (2,7) in slope intercept form
    5·1 answer
  • Serena is making a model of the Egyptian pyramid. The square base has sides that are all 4.6 in. Each of the triangular faces ha
    6·1 answer
  • The John Deere company has found that revenue, in dollars, from sales of heavy-duty tractors is a function of the unit price p,
    14·1 answer
  • How is g(x) = (x - 1)^2 related to the graph of f(x) = x^2
    7·1 answer
  • Find the area of the composite figure
    9·2 answers
  • Find the volume of the composite solid.
    10·1 answer
  • What is the answer and how did you get it
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!