A 21-foot ladder is used to make a service connection to a building. The bottom of the ladder cannot be more than five feet fro the buidling. What is the minimum height at which the ladder will be touching the building?

Q: A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is…

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Q: The volume of an open box with a square base is 4000 cm3. Find the dimensions of the box if the…

A: Given that volume =4000cm3 find the dimensions of the box that minimize the amount of material used…

Q: Find the minimum perimeter rectangle having area 64 square feet. Can you generalize this result?

A: Given that Area of the rectangle is 64 sq. ft We have to find the minimum perimeter. Let the length…

Q: A 10 meter long ladder is placed against a tall vertical wall to make a right-angled triangle. Find…

A: Maximum value of perimeter will be

Q: A gutter having a triangular cross section is to be made by bending in the middle of a strip of…

A: Here is the solution of the given problem.

Q: a 10 meter long ladder is placed against a tall vertical wall to make a right angle triangle , find…

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Q: A Norman Window has the shape of a rectangle surmounted by a semicircle. If a Norman window is to…

A: Given, The perimeter of the window = 28 ft  Height of rectangular part = y width of rectangular part…

Q: A piece of wire 10 m long is cut into two pieces. One piece is bent into a 30°-60°-90° triangle and…

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Q: How do you solve for the minimum surface area of a sphere that circumscribes a cone in which that…

A: Let R be radius of inner sphere and r be radius of cone. and let h be the height of cone.

Q: A box with no top and a square base has to be designed so that its volume must 108 cm³. Find the…

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

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Q: Two poles one 6cm tall and the other 15cm tall are 20m apart,the wire is attached to the top of each…

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Q: Fernando is a weightlifting athlete with a pulling strength of 140 lb. He practices. by carrying a…

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Q: What is the maximum size of the window frame you can create with 20 feet of materials? The window…

A: To Find: The maximum size of the window frame you can create with 20 feet of materials.

Q: A cow is tethered to one corner of a square barn, 20 feet by 20 feet, with a rope 100 feet long.…

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Q: Two vertical poles, one 8 ft high and the other 16 ft high, stand 18 feet apart on a flat field. A…

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Q: Two post, one 8 m and the other 12m high are 15 m apart. If the posts are supported by a cable…

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Q: Find the minimum cost of a rectangular box of volume 180 cm³ whose top and bottom cost 4 cents per…

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Q: A rectangular hole is to be cut in a wall for a vent. If the perimeter of the hole is 48 in. and the…

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Q: If a closed tin can of volume 16x cubic inches is to be in the form of a right circular eylinder,…

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Q: A farmer wants to fence in two rectangular corrals, equal in area, using an inner fence as shown in…

A: Given;

Q: what is the minimum perimeter that a rectangle with an area of 32 ft2 can have?

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Q: A wire of length Lis cut into pieces, one being bent to form a square and the other form an…

A: Let the length of the portion of the wire to form a square is x, then the length of wire to form a…

Q: Two poles, one 6 meters tall and one 15 meters tall, are 20 meters apart. A length of wire is…

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Q: A box with an open top and square base is to be created with a surface area of 300 square inches.…

A: The box is open  And base is square  Let square sides l = b = x in And height  =h in

Q: Find the minimum length l of a beam that can clear a fence of height h=3 ft and touch a wall located…

A: Consider the figure for the right triangles.Let angle B be theta.

Q: Paula plans to build a rectangular closure for her dogs using 140m of fencing. What is the maximum…

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Q: A tube of lip balm has a height of 2.75 inches and a diameter of 0.75inches.  a. if the cap on the…

A: Part (a):Diameter of the lip balm tube, d = 0.75 inches. Thus, the radius of the tube is r = d/2 =…

Q: A horizontal trough is 16m and its ends are isosceles trapezoids with an altitude of 4m, a lower…

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Q: A triangle is formed by the positive coordinate axes and a straight line through (6,3) . How large…

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Q: A box with no top has a square base. If 64 squared centimeter of material is used, what is the…

A: A box with no top has a square base and 65 cm^2 of material is used

Q: A 27-foot ladder is used to make a service connectio to a building. The bottom of the ladder cannot…

A: Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is…

Q: A piece of wire 10 m long is cut into two pieces. One pieceis bent into a square and the other is…

A: To find: The way to use the wire such that the area enclosed by the triangle and square would be…

Q: A gutter having a triangular cross-section is to be made by bending a strip of tin in the middle.…

A: In this we have to find the area formula with the angle thetha then the find the value of thetha for…

Q: Find the dimensions of the rectangular box, open at the top, which has a minimum surface area if the…

A: Let us consider the width, length and height of the rectangular box are x, y and z respectively.…

Q: Find the minimum cost of a rectangular box that is three times as long as it is wide and which holds…

A: Consider the dimension of rectangular box be x, 3x, and h. Then, volume is given by V=x×3x×h  =3x2h…

Q: A parcel delivery service will deliver a package only if the length plus the girth (distance around,…

A: Let the side of the rectangular box is l, b and h.  Maximum possible dimension is  2l + 2b + h = 108…

Q: A farmer wants to make a rectangluar enclosure using a wall of a barn as one side and 160 ft of…

A: Let x ,in feet, be the length of side of rectangular enclosure which is along the wall of barn and y…

Q: Find the dimensions of a rectangle with area 100 m? whose perimeter is as small as possible? Find…

A: to find:- dimensions of the rectangle. minimum perimeter.

Q: Find the minimum cost of a rectangular box of volume 100 cm³ whose top and bottom cost 6 cents per…

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Q: Find the rectangle of the maximum area that can be inscribed in a right triangle with legs of length…

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Q: A farmer would like to construct a cage to separate farm animals. He has 600 meters of materials to…

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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 rectangular building is to be built on a triangular corner lot with the perpendicular sides equal…

A: Given A rectangular building is to be built on a triangular corner lot with the perpendicular sides…

Q: A gutter having triangular cross-section is to be made by bending a strip of tin in the middle. Find…

A: Explained below

Q: A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals. What…

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Q: A rectangular tank that is 1372 ft° with a square base and open top is to be constructed of sheet…

A: The tank with minimum weight is the one with minimum surface area. Since the base is square, its…

Q: A cylindrical shampoo container is to have volume 750 cm³. Shampoo V%3DTT r?h 759cm3 ) Determine the…

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