A box with no top is to be built by taking a 12"-by-16" sheet of cardboard and cutting x-in. squares out of each corner and folding up the sides. Find the value of x that maximizes the volume of the box. a)

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Q: A closed, rectangular-faced box with a square base is to be constructed using only 16 m? of…

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Q: A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out…

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Q: The minimum surface area for a given volume of a square-based rectangular prism occurs when the…

A: Let us assume the length of a edge of the base=xAnd height =y And volume=VSo, V=x2yor, y=Vx2

Q: Find the volume of a square pyramid with base edges 9 and height 5.

A: Given Square pyramid with base edge 9 and height 5

Q: 3.) A fencing is limited to 50ft length. What is the maximum rectangular area that can be fenced in…

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Q: A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out…

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Q: On a sphere a sum of all angles of a triangle is larger than T. What is the largest possible sum of…

A: We know that  On a sphere sum of all angles of a triangles is larger than π. A spherical triangle is…

Q: A rectangular piece of metal is 5in. longer than it is wide. Squares with sides of 4in. long are cut…

A: Given: A rectangular piece of metal is 5in. longer than it is wide. Squares with sides of 4in. long…

Q: 7. If 300 cm³ of material is available to make a box with a square base and an open top, find the…

A: Assume side of the square box is x and height is y. Hence, volume of the box is given by…

Q: Prove that among all triangles with a fixed perimeter P, the equilateral triangle is the one that…

A: To Prove: Among all triangles with a fixed perimeter P, the equilateral triangle is the one that…

Q: . A box with an open top is to be constructed from a square piece of cardboard, 3 m wide, by cutting…

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Q: The sum ofthe measures of the intenor angles of a convex quadnlateral 18

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Q: Find the volume of a parallelepiped if four of its eight vertices are P(0,0, 0), Q(3, 4, 0), R(0,…

A: Let, P, Q, R, S be the four vertices of a parallelepiped. Then, we find the vectors, a=PQb=PRc=PS…

Q: A box with an open top is to be constructed from a square piece of cardboard, 3 feet wide, by…

A: Four square pieces at the corners of a square cardboard of size 3 × 3 feet.  And it was made into a…

Q: What are the dimensions of a rectangular wall that can be constructed with 100 feet of brick that…

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Q: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in.…

A: We have, a rectangular piece of poster board having dimension 20 inch wide and 30 inch long. Four…

Q: An open-topped box is constructed from a rectangula piece piece of cardboard that is twice as long…

A: An open-topped box is constructed from a rectangular piece of cardboard that is twice as long as it…

Q: Use calculus to find the volume of a tetrahedron​ (pyramid with four triangular​ faces), all of…

A: If a solid is from x =a to x= b and the area of its base is A then the volume of the solid is given…

Q: All nine edges of a right triangular prism are congruent. Find the length of these edges if the…

A: Solution: Consider the given right triangular prism. Also, it is given that the volume is 543 cm3 We…

Q: A box with an open top is to be constructed from a square piece of cardboard with dimensions…

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Q: A box with an open top is to be constructed from a square piece of cardboard 2m inches wide, by…

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Q: ind the volume of the tetrahedron having the given vertices. (-6, –6, –5), (5, 4, –4), (4, –6, –3),…

A: The given coordinates are -6,-6,-5,5,4,-4,4,-6,-3,0,0,10 We have to find the volume of the…

Q: A closed, rectangular-faced box with a square base is to be constructed using only 16 m² of…

A:

Q: A diagonal of a cube joins two vertices not in the same face. If the diagonals are 4V3 cm long, what…

A: Given: A diagonal of a cube joins two vertices not in the same face. Length of diagonals are 43  cm…

Q: The volume of the resulting open top box when identical squares with side x are cut off from the…

A: Given that, the dimensions of the aluminum sheet are three-meter by five-meter. To find: The volume…

Q: Suppose that each of the bases of the triangular prism in Exercise 2 has an area of 3.4 cm? and that…

A: Consider the given: Find the volume of Prism: The Volume of Prism = Base Area ×height It is given…

Q: 1. Find the total area and volume of frustum of regular square pyramid, whose base have sides 10 cm…

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Q: If we partion [1, 23 ] into 80 subintervals of equal length and [14, 40 ] into 45 subintervals of…

A: IDEA: Length of interval (a,b) is b-a. if we want n sub intervals of equal length divide b-a by n…

Q: A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out…

A: Suppose that the box height is h=4 in. and that it is constructed using 156 in.^2 of cardboard…

Q: Find the point that partitions segment AB in a 2 : 1 ratio.

A: Given that partition of segment AB in a  2:1 ratio . Where coordinates of point A  and B are 1,3 and…

Q: By cutting a wedge from paper disk of radius r, a cone shaped water cup can be made by joining the…

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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

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Q: A box is formed by cutting squares from the four corners of a 7"-wide by 9"-long sheet of paper and…

A: Volume= length*width*height

Q: A box with an open top is to be constructed from a square piece of cardboard, 24 inches wide, by…

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Q: A box with an open top is to be constructed from a square piece of cardboard with dimensions…

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Q: A box with an open top is to be constructed from a square piece of cardboard, 3 m wide, by cutting a…

A: 1) Given:

Q: if an open box has a square base and a volume of 256 in^3 and is constructed from a tin sheet.  Find…

A: Given

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Q: 2 Find the volume of the parallelepiped with sides u(1, -3, -1). v3(0. 4, -2). and न् 6. 3).

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Q: An open-topped box is constructed from a rectangula piece piece of cardboard that is twice as long…

A: Topic = Algebra

Q: ngr Thomas Pendot wants to construct a frustum from a right circular cone. At what distance from the…

A: Volume of cone with radius r and height h is given by…

Q: 2. Find the volume of tetraherdon with the vertices A(-1, 2,0), B(0,3,-1), C(3,3,0), and D(1,1,-1).…

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Q: The volume of an oblique prism is always greater than that of a right prism that contains a base…

A: We can answer the question as below.

Q: Given that a right circular cylinder is inscribed within a sphere, what is the least possible volume…

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Q: A box with an open top is to be constructed from a square piece of cardboard with dimensions 4 cm x…

A: The dimensions of the box is 4cm×4cm. Let each side of the square cut off from each corner be x cm.…

Q: 2. A rectangular sheet of cardboard 8 m by 4 m is used to make an open box by cutting squares of…

A: Volume of cube = a3Volume of cuboid =l×b×hWhere l is length , b is breadth and h is height .

Q: 1. Apply the slicing method to find the volume of a pyramid with height hand base an equilateral…

A: In this question, the volume using integration is applied. Integration Integration is a method of…

Q: A caterer wishes to serve a cocktail in a glass shaped like a cone of diameter 8 cm and height 4 cm…

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