A 60 m long pipe of metal is cut into two pieces. One piece is used to form a square and the other an equilateral triangle. Show that whether the total area covered by pipe is maximum or minimum. Also calculate the total area.

Q: A big cube is made of 216 smaller cubes of length 1 cm. If the centre cube on each face and all…

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Q: A 216 m2 rectangular pea patch is to be enclosed by a fence and divided into two equal parts by…

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Q: Determine the Maximum area of a rectangle lot that can be created with a 1000m length of fencing…

A: Given: Length of fencing is 1000m We know that fencing means boundary Let x, y be the length and…

Q: What is the total surface and lateral area of these 3 cylinders?

A: 4) given that, r(radius)=2m and h(height)=10m  we have to find the lateral surface area and total…

Q: the base of the prism is a rectangle whose length is 3 cm more than the width. of the altitude of…

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Q: The Great Pyramid of Giza has a square base with one side measuring 750 ft and height of 484 ft.…

A: Given : Side of a square base of a pyramid is 750 ft and height is 484 ft

Q: A pool in the shape of a right rectangular prism is 15 m long, 9m wide, and 2 high. What is the…

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Q: A home owner wishes to use 600 feet of fence to enclose two identical adjacent pens, as in the…

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Q: A rancher wants to enclose two rectangular areas near a river. There are 240 yd of fencing…

A: Perimeter of rectangle = 2(l + b)

Q: A landscape architect wishes to enclose a rectangular garden of area 1000 m2 on one side by a brick…

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Q: Find the minimum amount of tin sheet in square inches that can be made into a closed cylinder having…

A: Find the minimum amount of tin sheet in square inches that can be made into a closed cylinder having…

Q: Find the area of the largest rectangular field that can be enclosed with 600 m of fencing. Assume…

A: Perimeter without one side length =600m

Q: Find the area of the largest rectangle that can be inscribed in an equilateral triangle of side…

A: Given: A rectangle inscribed in an equilateral triangle of side L assuming one side of the rectangle…

Q: A farmer with 800 ft of fencing wants to enclose a rectangular area and then divide it into four…

A: NOTE: Refresh your page if you can't see any equations. . as we can see from the figure, the…

Q: Find the area of the largest rectangle that can be inscribed ina right triangle with legs of lengths…

A: Let x and y be the length and width of the rectangle that is inscribed in a right triangle. The…

Q: A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges 90°.…

A: Given:    Wide = 12 in     Edges = 90°  At least 16 square

Q: A farmer with 780 ft of fencing wants to enclose a rectangular area and then divide it into four…

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Q: Find the dimensions of a rectangle with a perimeter of 160 ft that has the largest possible area.…

A: Perimeter of a rectangle=2l+bArea of a rectangle=length×breadthGiven: Perimeter = 160

Q: Find the length and width of a rectangle with area 64 m that give minimun perimeter.

A: Let length of rectangle be x and breadth be y . Area of rectangle is 64 m2 xy = 64  y = 64x Let P be…

Q: A chemical power plant is rectangular and has a length of 100 m and a width of 60,000mm. A safety…

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Q: A rectangular lot has an area of 1600 sq.m. Find the least amount of fence that could be used to…

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Q: One side of an open field is bounded by a straight river. Determine how to put a fence around the…

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Q: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four…

A: Solution: Let x be the width of the rectangle and y the height. we can form the equation  5x +…

Q: the length of a side of a cube is equal to the radius of a sphere. which solid has the greater…

A: The length of a side of a cube is equal to the radius of a sphere. Let x be the side of a cube, then…

Q: A wire 20 inches long will be cut into two parts, one to be bent to form a square and the other to…

A: We have to find side of Square and diameter of the circle

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: Find the dimensions of the right circular cylinder of greatest volum that can be inscribed in a…

A: Given query is to find the dimensions of a right circular cylinder that can be fit inside a sphere…

Q: If I have a cube that is 1 meter on each side, what is the surface area of one side in square…

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Q: A rectangular water-tank has length of 50 m, width of 34 m and height of 24 m. Calculate the total…

A: A rectangular water tank has a length of 50 m, a width of 34 m, and a height of 24 m. Then we have…

Q: The perimeters of the ends of a frustum are 48 cm and 36 cm. If the height of the frustum be 11 xm,…

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Q: A box is to be constructed from a piece of zinc 20 inches square by cutting equal squares from each…

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Q: Find the height of a storage tank in the shape of a right circular cylinder that has a circumference…

A: The storage tank is cylindrical in shape. Let r be the radius of circular base and h be the height…

Q: A farmer has 400 ft of fencing with which to enclose a rectangular field adjacent to anexisting…

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Q: A rectangular pool is to be built on a lot that measures 20 m by 12 m. A lawn uniform width, equal…

A: formula used are  * quadratic formula = for equation ,ax^2 + bx + c =0 =  [- b +…

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: A closed cylindrical tank is made of a metal sheet having an area of 43.82 square meter. If the…

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Q: The post office will not ship a cylindrical container if the sum of circumference of the base plus…

A: If we have a function f(x), the points at which the function takes a maximum or a minimum is given…

Q: Find the dimension of the rectangular corral producing the greatest enclosed area given 200 meters…

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Q: A rectangular lot which has an area 120sq.m will be divided into two portions such that the product…

A: Consider the rectangular is divided into two portions with areas x and y. So, x +y = 120…

Q: he face of the right triangular

A: Given,

Q: Find the dimentions of a cylinder. See images

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Q: A farmer with 750 ft of fencing wants to enclose a rectangular region and then divide it into four…

A: Solve for the lager rectangle dimension and area of large rectangle

Q: Find the minimum amount of thin sheet that can be made into a closed cylinder having a volume of 108…

A: Topic: calculus

Q: Find the minimum amount of tin sheet that can be made into a closed cylinder having a volume of 108…

A: For the solution follow the next steps.

Q: The standard running track size for track and field events is 400 m. The track consists of two…

A: Given that: Size of the track = 400 m Area enclosed = 9430 m2

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

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Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: This question involves the concept of find the local extrema using calculus.

Q: if the lateral area of right circular cylinder is 88 and its volume is 220, find its radius

A: A= 88 V = 220 A= 2πrh V = πr²h Now we take ration of volume by area  V/A = πr²h/2πrh r = 2V/A  r =…

Q: A piece of wire is shaped to enclose a square whose area is 169 sq. cm. It is then reshaped to…

A: area and perimeter

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.