From a 27-cm by 27-cm piece of cardboard, square cormers are cut out so that the sides can be folded up x to make a box. Complete parts a through c below. a) Express the volume of the box as a function of the side x, in centimeters, of a cut-out square. V

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A: Given:  208 ft of fencing is used to enclose a coral From given figure diameter of the semicircle is…

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A: Given: length l and the girth xie., length =l and sides of a square=x

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A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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A: This question can be solved using the concept of maxima and minima.

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Q: J (1,4) M(-1, 2) К(3,2) L (1, – 3)

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Q: Suppose that 202 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given that 202 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

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A: Given: Formula used: The area of a rectangle is length * width.

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A:

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A: After cutting side length x from each side length be l  , l=18-2x breadth be b , b=35-2x height be h…

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A: we have to find area.

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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A: Using area of trapezoid formula.

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A: We will create a rectangle inside the circle and find the length and breadth

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A: We are given that 465 ft of fencing is used to enclose a corral in the shape of a rectangle with a…

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Q: 1. find the dimenstors of a maximum Lwithout a top of capacity, 108 sq. cm. box who de Sunface area

A:

Q: Suppose that 477 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given that: Length of total fencing =477ft                             NOTE: As per our answering…

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A: So perimeter of the fence = x+w+60+x+w= 480 feet So,

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A: The length of the diagonal of a square is d. Now let a be the length of the side of a square. Now…

Q: Suppose that 404 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Area of the shape=Area of the semicircle+Area of rectangle .Area of semicircle=πx22x12…

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A: To find the maximum possible volume of the box in cubic inches

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A: given,             farmer adds fencing of 480feet.

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A:

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A: Area of rectangle= length×width For the maximum area will occur when the derivative of the area is…

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A: Please refer to the image below

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.