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
pashok25 [27]
3 years ago
15

A farmer has 520 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one s

ide of the pen. The length of the barn is 310 feet. Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions. (Hint: Be mindful of the domain of the function you are maximizing.)
Mathematics
1 answer:
Setler [38]3 years ago
5 0

Answer:

310\text{ feet and }210\text{ feet}

Step-by-step explanation:

GIVEN: A farmer has 520 \text{ feet} of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is 310 \text{ feet}.

TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.

SOLUTION:

Let the length of rectangle be x and y

perimeter of rectangular pen =2(x+y)=520\text{ feet}

                                                x+y=260

                                               y=260-x

area of rectangular pen =\text{length}\times\text{width}

                                       =xy

putting value of y

=x(260-x)

=260x-x^2

to maximize \frac{d \text{(area)}}{dx}=0

260-2x=0

x=130\text{ feet}

y=390\text{ feet}

but the dimensions must be lesser or equal to than that of barn.

therefore maximum length rectangular pen =310\text{ feet}

                              width of rectangular pen =210\text{ feet}

Maximum area of rectangular pen =310\times210=65100\text{ feet}^2

Hence maximum area of rectangular pen is 65100\text{ feet}^2 and dimensions are 310\text{ feet and }210\text{ feet}

You might be interested in
The length of the longer leg of a right triangle is 4 inches more than twice the length of the shorter leg. the length of the hy
Serjik [45]

The Pythagorean's Theorem for our situation would look like this:

shortleg^2+longleg^2=hypotenuse^2

So let's call the short leg s, the long leg l and the hypotenuse h. It appears that all our measurements are based on the measurement of the short leg. The long leg is 4 more than twice the short leg, so that expression is l=2s+4; the hypotenuse measure is 6 more than twice the short leg, so that expression is h=2s+6. And the short leg is just s. Now we can rewrite our formula accordingly:

s^2+(2s+4)^2=(2s+6)^2

And of course we have to expand. Doing that will leave us with

s^2+4s^2+8s+8s+16=4s^2+12s+12s+36

Combining like terms we have

5s^2+16s+16=4s^2+24s+36

Our job now is to get everything on one side of the equals sign and solve for s

s^2-8s-20=0

That is now a second degree polynomial, a quadratic to be exact, and it can be factored several different ways. The easiest is to figure what 2 numbers add to be -8 and multiply to be -20. Those numbers would be 10 and -2. Since we are figuring out the length of the sides, AND we know that the two things in math that will never EVER be negative are time and distance/length, -2 is not an option. That means that the short side, s, measures 10. The longer side, 2s+4, measures 2(10)+4 which is 24, and the hypotenuse, 2s+6, measures 2(10)+6 which is 26. So there you go!

6 0
3 years ago
Which is the simplified form of the expression 3(7/6x + 4) - 2(3/2-5/4x)<br><br><br>​
mars1129 [50]

Answer:

b

Step-by-step explanation:

8 0
2 years ago
Simplify (6x2 − 3 − 5x3) − (4x3 2x2 − 8). 9x3 − 4x2 − 5 −9x3 4x2 5 x3 − x2 − 13x3 −x3 x2 13x3.
Schach [20]

Like terms have the same variable and power. The simplification of the expression (6x²-3-5x³)-(4x³+2x²-8) is -9x³+4x²+5.

<h3>What are Like terms?</h3>

Like terms are those terms that are having the same variables, also the variables are of the same order as well.

for example, 25x and 5x are like terms; 30xy and 7xy are like terms, 9x³ and 4x² are not like terms, etc.

We know that to simplify an expression we need to add or subtract like terms, therefore,

(6x^2- 3 - 5x^3) -(4x^3+2x^2 - 8)\\\\= 6x^2- 3 - 5x^3 -4x^3-2x^2 + 8\\\\= - 5x^3 -4x^3+6x^2-2x^2+8-3\\\\ = -9x^3+4x^2+5

Hence, the simplification of the expression (6x²-3-5x³)-(4x³+2x²-8) is -9x³+4x²+5.

Learn more about Like Terms:

brainly.com/question/2513478

7 0
2 years ago
URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! DUE IN LESS THAN 12 MINS
Anettt [7]

Answer:

28.26m^2 (aka. 28.26 meters squared)

Step-by-step explanation:

The area of a circle is A=pi*r^2 where r is the radius of the circle.

Since r=3, then A=pi*3^2=9pi=28.26

Therefore, the area of the merry-go-round is 28.26 square meters

6 0
2 years ago
Order the numbers from least to greatest.<br> 54%, 2/5, -0.45<br><br> SHOW YOUR WORK!
Tom [10]

Answer:

-0.45, 2/5, 54%

Step-by-step explanation:

54%=54/100

=87/50

2/5=20/50

-0.45 must be the smallest as it is negative

7 0
2 years ago
Other questions:
  • Helppp pleaseee asap :((((((
    6·1 answer
  • How do I solve 74(10)^0.056x = 222 ?
    6·2 answers
  • NEED HELP IN MATH .THANKS
    10·1 answer
  • Which comparison is correct for the values of f(x) and g(x) when x=−1 ?
    10·1 answer
  • Jim earns a regular hourly rate of $5 and a premium hourly rate of $6. He worked 45 hours last week. What is his gross pay?
    14·1 answer
  • 2 Points
    8·1 answer
  • Which value of w will make the equation true? 6 + w = 37
    8·1 answer
  • Show all work <br><br> 14 +18 - 2 x 18 -7
    13·1 answer
  • CAN YOU PLEASE HELP ME!!....
    11·1 answer
  • Please help thank u!!!!!!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!