A piece of wire 40 cm long is to be cut into two pieces. One piece will be bent to form a circle, the other will be bent to form a square. Find the lengths of the two pieces that cause the sum of the area of the circle and the are of the square be a minimum. Circumference of the Circle= 17.596 cm, Perimeter of the Square 22.404 cm

Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

A: topic - application of derivatives

Q: The sum of two numbers is 5. Find the minimum value of the sum of their cubes.

A: Let the first number be x. Let the other number be y.   Thus, x+y=5y=5-x   The sum of the cubes of…

Q: *. .. The sum of the perimeters of an equilateral triangle and a square is 21. Find the dimensions…

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Q: truck travelling west at 100km/h is 250km due east of a sports car going north at 120km/h.…

A: At t = 1.04 hour, they are closests to each other. Minimum distance between them is 192.07 km.

Q: Find two positive numbers whose product is 36 and whose sum is a minimum. (If both values are the…

A: let the two numbers be x and y so  x×y=36sum=x+y since         xy=36⇒y=36x Substitute y value in sum…

Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 81…

A: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 81…

Q: Can you please answer this question and show the steps

A: Given: The two numbers whose difference is 236 and whose product is minimum.

Q: A closed rectangular box to contain 16 ft³ is to be made of three kinds of materials. The cost of…

A: Let's find dimension for minimum cost of given rectangular box.

Q: To get into the 250 Club, a bowler must score an average of 250 for a three-game series. If a bowler…

A: Average score is 250 for a three game series.

Q: Hagrid now wants to make a contraption that will be used to feed his animals. He needs touseawire…

A: Let x m was used for the circle and (10-x) m was used for the square. Let the radius of the circle =…

Q: The sum of two numbers is 6. Find the minimum value of the sum of their squares.

A: The sum of two numbers is 6. Find the minimum value of the sum of their squares.

Q: 5. Find the length and width of a rectangle that has an area of 32 square feet and a minimum…

A: Given, area A=32 sq.ft Let, x be the length and y be the width. The formula for the area of a…

Q: The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions f the…

A: Given that: Sum of perimeter of an equilateral triangle and a square is 10

Q: A tile setter plans to use 5 1/2 inch square tiles along the base of a room that is 7 feet long.…

A:

Q: A rectangular hole is to be cut in a wall for a vent. If the perimeter of the hole is 104 in. and…

A: Let, Length = L inches. Width = W inches. Given that the perimeter = 104 inches. That means:…

Q: Find two positive numbers whose product is 25 and whose sum is a minimum. (If both values are the…

A: Given: Two number whose product is 25.

Q: Find two positive numbers whose product is 49 and whose sum is a minimum. (If both values are the…

A:

Q: he sum of the perimeters of an equilateral triangle and a square is 23. Find the dimensions of the…

A:

Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 49…

A:

Q: The perimeter of a rectangle is to be no greater than 80 centimeters and the width must be 10…

A: let length be x and width is given to be 10. Perimeter of a rectangle is defined as 2(length +…

Q: A 12-meter string is cut into two pieces so that x meters will be used to form a circle and the…

A: Here we can note the following  (a) Area of an equilateral triangle with side a = 34a2 Area of a…

Q: Find two numbers whose difference is 166 and whose product is a minimum.

A: Topic = Algebra

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: A rectangular poster is to contain 722 square inches of print. The margins at the top and bottom of…

A: Follow the procedure given below.

Q: manufacturer estimates that the cost (C) of production of (x) units of a certain item is ? = 40? −…

A: Given query is to find the production level for minimum cost.

Q: The sum of two numbers is k. Find the minimum value of the sum of their cubes.

A: Answer and explanation is given below...

Q: The perimeter of a rectangle is to be no less than 72 centimeters and the width must be 17…

A: In the question we have to find minimum length of the rectangle.

Q: A 12-meter string is cut into two pieces so that x meters will be used to form a circle and the…

A:

Q: The Perimeter of a rectangle is 20 feet. Of all possible dimensions, the maximum area is 25 square…

A: Let the length = x Width= y So, perimeter= 2(x+y)=20  x+y=10 y=10-x

Q: The sum of two positive integers is 25. What is the minimum sum of their squares ?​

A: Given that, the sum of two positive integers is 25. Let x and y be the two positive numbers whose…

Q: The sum of the perimeters of an equilateral triangle and a square is 18. Find the dimensions of the…

A: Given that the sum of perimeter of equalatral triangle and square=18To find :dimention of…

Q: Among all pairs of numbers (x,y) such that 3x+y=8 , find the pair for which the sum of squares,…

A: Given condition,           3x + y = 8                     y  = 8 -3x             —1Function to be…

Q: The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than…

A: Let the shortest side= x cm  so the longest side= 3x cm  third side= 3x-2 cm

Q: A pience of cardboard is 14 inches by 10 inches and the corners were to be cut out and fold up the…

A:

Q: Find two positive numbers whose product is 64 and whose sum is a minimum. (If both values are the…

A: first we find factors of 64 2   64 2   32 2   16 2    8 2    4  2    2  1 therefore  64= 2 x32 and…

Q: A rectangular poster is to contain 648 square inches of paint. The margins at the top and bottom of…

A:

Q: A piece of wire 40 cm long is to be cut into two pieces. One piece will be bent to form a circle,…

A:

Q: Find two numbers whose difference is 154 and whose product is a minimum.

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Q: Solve the given item on a separate sheet of paper. A rectangular box with open top and has a square…

A: It is given that the rectangular box is open at top. The rectangular box is having a square base.…

Q: Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter.…

A:

Q: . The sum of two numbers is b, what is the minimum value for the sum of their cubes?

A:

Q: The perimeter of a rectangle is to be no greater than 100 centimeters and the width must be 15…

A: Perimeter of rectangle = 2 ( length + width)  Given width = 15 cm  and  perimeter of a rectangle…

Q: Solve the given item on a separate sheet of paper. A rectangular box with open top and has a square…

A:

Q: A length of wire that is 160 cm long is cut into two pieces: one to form an equilateral triangle and…

A: We will use Second derivative test to find the maximum and minimum area And first derivative to find…

Q: A piece of wire 40 cm long is to be cut into two pieces. One piece will be bent to form a circle,…

A:

Q: Find two numbers whose difference is 166 and whose product is a minimum. Step 1 If two numbers have…

A:

Q: A 4-pen kennel of 1,960 square feet is to be constructed as shown. The cost is $20 per foot for the…

A: The area of the rectangular land is 1800 sq feet. let the side parallel to divider be y and the side…

Q: You are given a rectangular piece of paper that has length x=35.4 cm and height y=28 cm. The lower…

A: Since, we have been given a rectangular piece of paper that has lengthx=35.4 cm and height y=28 cm.…

Q: The difference of two numbers is 18. What are numbers so that their product is a minimum?

A: The difference of two numbers is 18. Find the numbers such that their product is a minimum.   x-y =…

Q: The sum of the perimeters of an equilateral triangle and a square is 23. Find the dimensions of the…

A: Let x be the side of equilateral triangle and y be side of square . Then respective perimeters are…