10.1. A wire of length 12m is cut into two parts, one of which is bent into a square and the other into an equilateral triangle. If the sum of the area of the figures is maximum. Find the sum of maximum area of the two figures.

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

A: The total length of the wire is 40 cm and one piece is to be formed into a circle and another one is…

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A: We will create function and use derivative to maximize it

Q: 5. Find the dimensions of the rectangle in the figure shown below that will give the maximum…

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A: Given: Two poles are connected by a wire that is also connected to the ground.The first pole is 20…

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Q: 10. A wire of length 20m is cut into two parts, one of which is bent into a circle and the other…

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A: Given, Five identical pens are given below.

Q: Consider a wire 4 ft long cut into two pieces. One piece forms a circle with radius r and the other…

A: Given Length of the wire = 4 ft One piece forms a circle with radius r. The other piece forms a…

Q: 2. Helmut, an ostrich farmer, wants to build a rectangular fenced enclosure divided into five…

A: Given that, Total length= 120 m

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Q: 6. Find the maximum area of a rectangle in the first quadrant where one side of the rectangle lies…

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Q: A piece of wire 20 m long is cut into two pieces. One piece is bent into a square and the other is…

A: The area and circumference of the circle is πr2, 2πr respectively, where r is the radius of the…

Q: 8. A rectangular dog pen is being built against the side of a house using 96 ft of fencing for the…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Can you help with question 2?

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Q: 3. Two cities A and B are 8 km and 12 km, respectively, north of a river which runs due east. City B…

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Q: 19. A piece of wire of length 1 meter is cut into two parts, one of which is bent into the shape of…

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Q: A piece of wire 15 m long is cut into two pieces. One piece is bent into a square and the other is…

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Q: 5) The hypotenuse of a right triangle is 12 cm in length. Calculate the measures of the unknown…

A: To find the dimensions of given triangle such that it has maximum area.

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Q: 3. Prove that of all rectangles with a given area, the one with smallest perimeter is a square. (Let…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 10) A supplier of bolts wants to create open boxes for the bolts by cutting a square from each…

A: Given ,  A supplier of bolts wants to create open boxes for the bolts by cutting a square from each…

Q: A piece of wire 8 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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Q: 2. Suppose a wire three feet log is to be cut into two pieces, with each piece to be formed into a…

A: 2) as per our norms we have to write one question at a time kindly repost remaining questions.

Q: 4. A 12-meter string is cut into two pieces so that x meters will be used to form a circle and the…

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Q: 1. A supermarket employee wants to construct an open-top bax from a 14 by 30 in a piece four corners…

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Q: A piece of wire 13 m long is cut into two pieces. One piece is bent into a square and the other is…

A: We will use derivative test to solve this.

Q: 1. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

A: The solution is given in the next steps.

Q: 2. An open top rectangular tank with a square base is to have a volume of 10 cubic feet. The bottom…

A: To find out the sum of x and y for the most economical dimensions.

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Q: 1. Amazon wants to create an open-top box with a square bottom with only 149 in2 cardboard (the…

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Q: 6) A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

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Q: A piece of wire 21 m long is cut into two pieces. One piece is bent into a square and the other is…

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Q: 3. A divided field is to be constructed with 4000 feet of fence as shown. For what value of z will…

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Q: You and your friends are hosting a round pizza party, and you are tasked in determining what size…

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Q: Please

A: If we fold it we will get a cuboid with l=10-2x cm, b=8-2x cm and h=x cm Volume V for a cuboid = lbh

Q: 19. Suppose an airline policy states that all baggage must be box-shaped with a sum of length,…

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Q: Please help. Thank you!

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