A farmer has 90 meters of fencing to use to enclose a rectangular garden that has one side against a barn. w Let I represent the length of the rectangular garden (in meters) and let A represent the area of the rectangular garde (in square meters). a. Write a formula that expresses A in terms of l. A = 451- ( I^2)/2 Preview b. What is the maximum area of the garden? (It may help to use a graphing calculator.) 2025/2 V square meters Preview c. What is the length and width of the garden that produces the maximum area? o Length: (45/2 * meters Preview o Width: 45/2 V meters Preview d. If the farmer instead had 300 meters of fencing to enclose the garden, what garden-length and garden-width will produce a garden with the maximum area?

Q: Find two positive numbers whose product is 179 and whose sum is a minimum.

A: Let one number is = x Another number is = y

Q: An open-top box is to be made from a 18-inch by 42-inch piece of plastic by removing a square from…

A: Diagram of the mentioned box will  be as following

Q: Find the dimensions of the rectangular corral split into 2 pens of the same size producing the…

A:

Q: Find two numbers whose sum is 40 and whose product is a maximum.

A:

Q: A page of 216 square inches is to have margins of 1 inch on either side and 1.5 inches at the top…

A: According to the question, Let x is the width of a the book page. Area given=216 square inches, Area…

Q: Find the maximum number of goldfish you can put in a cylindrical tank whose diameter is 8 meters and…

A: Fish would be put in the tank, that is, the volume of the tank. Hence the volume of the tank helps…

Q: The service elevator at AR Hector Financial Complex has a maximum capacity of 2870 lbs. If the…

A: Given:  The service elevator has a maximum capacity of 2870 lbs. The elevator operator weighs 205…

Q: Find the dimensions of the rectangular corral split into 2 pens of the same size producing the…

A:

Q: 5. Find two positive numbers whose sum is 110 and whose product is a maximum.

A: Let two positive numbers be x and y  x+y=110

Q: The path of a baseball after being hit is modeled by f(x) = −0.0032x2 + x + 3, where f(x) is the…

A: We have, the path of a baseball after being hit is modelled by the function given as…

Q: Find two non-negative numbers whose sum is 59  and whose product is a minimum.

A:

Q: Find a function that models the area of an equilateral triangle in terms of the length x of one of…

A: The function is equilateral triangle:   Concept used: The Area of equilateral triangle is defined…

Q: Find two positive numbers whose product is 324 and whose sum is a minimum. List them in non-…

A:

Q: Find two positive numbers whose product is 289 and whose sum is a minimum. List them in…

A: as per the guidelines we can provide solution to one question at a time , you can repost the other .

Q: ........ Find two positive numbers whose product is 49 and whose sum is a minimum. (Enter your…

A: Given,                  Two positive numbers whose product is 49  and whose sum is minimum

Q: Find two numbers whose difference is 170 and whose product is a minimum.

A:

Q: Find three positive numbers whose sum is 90 and whose product is a maximum.

A: Second derivative test: For critical points, fx=0 fy=0 A function f(x,y) has a local maximum value…

Q: The number 72 is to be represented as the sum of two positive parts, such that the product of one of…

A: Let the two numbers be: x and y Therefore we have to maximize:  f(x, y)=x y3 subjected to…

Q: Find two numbers whose difference is 118 and whose product is a minimum;

A:

Q: A carpenter has a 10 foot long board to mark off a triangular area on the floor in the corner of a…

A: The carpenter has a 10 foot longboard in the corner of a room. We have to find the maximum area of…

Q: A rectangular playground is to be fenced off and divided in two by another fence parallel to one…

A:

Q: A rope of 40cm long is bent into the shape of a rectangle. Find the maximum rectangle area that can…

A: Let the length and breath of rectangle be l and b respectively. If a rope of length 40cm is bent in…

Q: Find three positive numbers whose sum is 3 and whose product is a maximum.

A:

Q: Find the dimensions of the rectangle of maximum area that can be formed from a 50-m piece of wire.…

A: Given that: Length of wire=50m

Q: Find two numbers whose sum is 20 and whose product is a maximum

A:

Q: the dimesnions of the pasture that will

A: Given that: A rancher has 300 feet of fencing to enclose a rectangular pasture bordered on one side…

Q: A rectangular rice field is to be fenced along 4 sides and, in the middle, to divide it into two…

A:

Q: determine two numbers which have a difference of 7 and product which is a minimum

A: Let the two numbers be x and y. It is given that, the two numbers have a difference of 7. That is,…

Q: A gardener wants to enclose the area outside of his house for his plants and flowers. One side will…

A: Given that Area =150 m2Solution:Area =xy xy=150y=150xperimeter=2x+yp=2x+150xfor maximum perimeter…

Q: Find the dimensions of the rectangle that'll give the max rectangle area, of perimeter of entire…

A: The perimeter of the entire figure is 12 feet.

Q: A farmer plans to make 3 identical and adjacent rectangular pens, using an existing wall as one…

A:

Q: A farmer has 1800 m of fencing to make two equal rectangular pens that share a common side.…

A:

Q: Pedro wishes to use 100ft of fencing to enclose a rectangular garden. Determine the maximum possible…

A:

Q: A rectangular dog pen is constructed using a barn wall as one side 66 meters  of fencing for the…

A: NOTE: Refresh your page if you can't see any equations. . x=width of the rectangle y=length of the…

Q: Mr. Raymundo has enough materials to fence 90 meters. What are the dimensions of the rectangular lot…

A: Let the length and width of the rectangle be x and y. Then the perimeter of the rectangle is = 2x+y…

Q: Express the volume of a cube as a function of the length of an edge.

A: Cube:

Q: Find the length and width of a rectangle that has perimeter 80 meters and a maximum area.

A: Given: Perimeter of rectangle=80 meters

Q: An open-top box is to be made from a 12-inch by 18-inch piece of plastic by removing a square from…

A: We can find the value of x by using the second derivative test.

Q: Suppose that a ball is thrown straight up into the air and its height after t seconds is 5 + 24t-…

A: The function which gives the height is a quadratic function. To find the maximum height attained by…

Q: A farmer wants to build a rectangular fence around a plot of land. However, 1.5 sides of the plot of…

A: The farmer has total of 2000ft. fencing. 1.5 sides of the plot of land border a river. w is the side…

Q: Among all pairs of numbers whose sum is -18, find a pair whose product is as large as possible. What…

A: Find a pair whose product is as large as possible. What is the maximum product?

Q: What is the maximum area that can be completed with 240 feet of fencing? What are the dimensions?

A:

Q: Find two numbers whose sum is 11 and whose product is a maximum.

A: Let x and y be the two numbersx+y =11y =11-xProduct is maximumTherefore, xy is maximumx(11-x) is…

Q: WHAT IS THe MAXIMUM AREA ENCLOSED BY A RECTANGLE HAVING PERIMETER OF 52 INCHES?

A:

Q: A shipping company will ship a box only if the sum of its length and girth (distance around) does…

A:

Q: A rancher has 308 feet of fencing with which to build a rectangular corral along side an existing…

A: Maximization problem

Q: Divide 9 into two parts such that the product of one by the square of the other is a maximum. What…

A: 9 is divided in two parts such that the product of one and the square of the other is maximum.

Q: A grain silo has the shape of a right circular cylinder topped by a cone. The approximate area of…

A: Given- The approximate area of the circular base is 452.39 ft2, the total height of cylinder and…

Q: An open-top box is to be made from a 12-inch by 42-inch piece of plastic by removing a square from…

A:

Q: Find two numbers whose sum is 50 and whose product is a maximum.

A: To find two numbers whose sum is 50 and whose product is a maximum.