A farmer decides to build a fence to enclose a rectangular field in which he will plant a crop. He has 1400  feet of fence to use and his goal is to maximize the area of his field. A. What is the width of the field if the length of the field is 100  feet? B.  Define a function k that determines the length of the fence in feet in terms of the fence's width in feet, w , given the total amount of fence is 1400 feet.

Question

A farmer decides to build a fence to enclose a rectangular field in which he will plant a crop. He has 1400  feet of fence to use and his goal is to maximize the area of his field.

A. What is the width of the field if the length of the field is 100

 feet?

B.  Define a function k that determines the length of the fence in feet in terms of the fence's width in feet, w , given the total amount of fence is 1400 feet.

 

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Other

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: As viewed from above, a swimming pool has the shape of the ellipse x^2/4900+y^2/2500=1 where x and y...

A: To determine the volume of the three dimensional region R , defined by the pool

Q: Systems of Linear Equations and Matrices 292 CHAPTER 6 6.3 Exercises of Use systems of equations to ...

A: You have asked two questions in a single post. I will address the first one. Please post the other q...

Q: Consider the function f(x) = x3 + 4, and the point (1, 5). Write the equation of the line tangent to...

A: Compute the slope as follows.

Q: Explain how you would solve the following equation: ln ⁡ ( x ) + ln ⁡ ( x − 5 ) = ln ⁡ ( 21 − x ) De...

A: By using the property of logarithms, simplify the LHS

Q: Determine the equation of the tangent line to the given path at the specified value of t. (Enter you...

A: Given:Determine the equation of the tangent line to the given path at the specified value of t.

Q: Find the intervals on which is increasing or decreasing. Find the local maximum and minimum values...

A: Refer to the question , we have been provided with the function , f(x) = cos2x-2sinx, 0<=x<=2p...

Q: see attachment

A: Part(a):Given:

Q: answer these questions using the function, f(x) = 1 +(7/x) - (6/x^2)

A: We need to find second derivative of f(x) 

Q: Evaluate the integral. ∫1/x2+25 dx

A: Consider the given integral:

Q: Please answer question d, for h(x) = 5x^3 - 3x^5

A: Using Wolfram alpha the graph of the function is as shown below 

Q: This is a 2 part question, kind of.... Part 1: Find the derivative.f (t) = 3t sin2 t Part 2: Is ther...

A: Given function is:Applying the derivative with respect to t and using the chain rule i.e. (uv)' = u'...

Q: The base of the ladder in the figure is a = 5 ft from the building, and the angle formed by the ladd...

A: Given,

Q: Differentiate the function F(t) = (ln t)2 sin t

A: Given function is,       

Q: 17. Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1x 4, 0 y < 1

A: Click to see the answer

Q: Can you help me on #1

A: Distribute secx use 1/secx=cos xThen simplify.

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. 4. ...

A: We have to use area formula of polar coordinates with a= pi/2 and b=2pi

Q: Evaluate the integral 6 dx (x+1) (x2+4)

A: Given,

Q: Consider the sequence 4, 11, 18, 25, 32, .... a. Is 340 a member of the sequence? b. Is 738 a member...

A: It can be observed that the given sequence has a constant difference of 7 between the successive ter...

Q: Differentiate. f(x) = x2 sin(x)

A: To determine the derivative of the function.

Q: Evaluate the definite integral from 0 to 1 of dt/sqr(t^2-6t+13)

A: Given integral is

Q: Height At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate ...

A: Let the altitude be denoted by h, Diameter by d, Radius by rIt is known that d=2rAs per given criter...

Q: A tank contains 5000 L of pure water. Brine that contains 30 g of salt per liter of water is pumped ...

A: Obtain the limit of the concentration as t approaches infinity as follows.

Q: Find the derivative using the following information.

A: Given,

Q: Can you help with this problem step by step?

A: Given function is

Q: Use the properties of natural logarithms to simplify the function. f(x) = ln(e8x) − 5x − ln(1)

A: Properties of natural logarithm.

Q: f(x)-f(a) for the given function х -а Simplify the difference quotient 10 f(x)= 2 х

A: Write f(x) and f(a) and compute f(x)-f(a)

Q: A piece of wire of length 63 is cut, and the resulting tow pieces are formed to make a circle and a ...

A: The total length of the wire is 63.Let x be the length of the wire cut for the circle.Then, 63-x is ...

Q: see attachment

A: So the vector w is 

Q: To illustrate the Mean Value Theorem with a specific function, let's consider f(x) = x3 - x, a = 0, ...

A: Given,

Q: I need help with e. and d.   JUST THESE PARTS

A: (d)Consider the given function:

Q: If f(3) = 14 and f '(x) ≥ 2 for 3 ≤ x ≤ 5, how small can f(5) possibly be?

A: The given conditions are,

Q: Can you help with this problem step by step?

A: Given: -

Q: Problem 2 part A, B, and C

A: As per norms, three aspects of the question are answered. It is adivisable post multiplie parts sepa...

Q: The marketing division of a large firm has found that it can model the sales generated by an adverti...

A: Given,

Q: I need help with g. and h.   NOT THE REST OF THEM.

A: Given functions are

Q: The average length of the outer ear for men can be modeled as f(x)0.89 0.495 In x inches a s 70.T wh...

A: Find f (x(15)) as follows.

Q: Can you help with this problem step by step?

A: Given function is

Q: Evaluate the integral -2t sin(-3t) dt Note: Use an upper-case "C" for the constant of integration.

A: Given Integral;

Q: 2 Find the volume of the ellipsoid 2y 7z 16

A: Volume of the ellipsoid for the equation,

Q: 10 5 0 -1 -10 Identify the graphs A (blue), B( red) and C (green) as the graphs of a function and it...

A: A(blue) is the graph of the functionB(red) is the graph of the function's first derivativeC(green) i...

Q: Find equation of the tangent line to the curve at the following point.

A: To write an equation for tangent line to the curve at a given point, we calculate the slope at the g...