Consider the surface of a square. We divided each side of this square into three segments of equal size. Now, we build straight lines parallel to the sides of the square that pass through each endpoint of the segments, forming nine new squares. Delete the central square. With the remaining squares, we repeat the same process. These steps can be seen in the following figure, called Sierpinski carpet. Show that when the number of squares tends to infinity, the area of ​​the figure tends to be zero.

Q: A circle is having an area of 452 sq. m. is cut into two segments by a chord which is 6m from the…

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Q: IN a K MN is a quadrilateral with K = M and L e that: V\ %3D lelogram

A: Given:- Sumof angles of a quadrilateral is 360°.∠K = ∠M = x ∠L =  ∠N = y

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

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Q: What is the area of the triangle formed if it bounded by the x and y axes and the line,  2x - 3y =9?

A: Here we have to find the area of the traingle since Area of  Triangle = 1/2 *(hight)*base

Q: Use the Segment Addition Postulate and the diagram to find the value of x and the indicated length.…

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Q: The diagram below shows a right square pyramid with a base that is 6 centimeters (cm) on each side…

A: Volume of pyramid=13Area of basexheight 96=1362 x h h=96 x 36 x 6 h=8 cm

Q: For a paraboloid with two sheets, how do you find the shortest distance between the sheets in a…

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Q: The base of the rectangular pyramid shown above has one side that measures 5 inches, one side that…

A: To determine the area of the vertical cross-section of the pyramid that is parallel to longer side…

Q: 1. A Norman window is constructed by adjoining a semicircular window to the top of a rectangular…

A: According to bartleby guideliness we can answer only the first question.kindly repost the other…

Q: How far from its center should a grapefruit with a 5-inch diameter be sliced in order that both…

A: We have given

Q: 2 Find the volume of the parallelepiped whose edges are represented by A=i-13j+ 4k, B = 31+2j-7k and…

A: Given A→=i-13j+4k,  B→=3i+2j-7k and C→=i-2j+2k

Q: Without plotting the points or drawing the figure, find the coordinates of the new vertices of the…

A: given pentagon with vertices at V(3,2), W(5,10), X(6,12), Y(−0.5,1.25), Z(1,0)

Q: A Victorian building has one room in the shape of a rhombus with a ceiling height of 10.0 ft, shown…

A: The room is in the shape of a rhombus with Base=9 ft 7 inches=9×12+7 inches, since 1 ft=12…

Q: A 0.500m long hexagonal concrete shaft measuring 20.0cm across the corners has a triangular hole…

A: Given data :  Length of the shaft , h = 0.500 m                                      = 50 cm  side…

Q: 3. Find the dimension of the largest rectangle (in terms of area) that can be inscribed in a circle…

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Q: Generalize Exercise 42 to the case of an n-sided polygon inscribed in a circle of radius r. Express…

A: An n-sided polygon inscribed in a circle of radius r.

Q: A cuboidal box of dimension 1 m * 2m * 1.5 m is to painted except its bottom . Calculate how much…

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Q: Prove that if A is a point on the perpendicular bisector of line segment BC then A is the same…

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Q: Compute the areas of the polygons in Figure 28. Check your result for the area of the triangle in…

A: Consider the provided information, Find the area of the of the triangle.

Q: Find the radius of a circle whose area equals the sum of the areas of two circles with radii 3 in.…

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Q: Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r

A: Let the length of the rectangle be 2x and the width of the rectangle be y. From the figure, the…

Q: Consider a rectangular region of length 10 m and width 5 m. You would like to set up a tent over…

A: Let the length of OB=x, then the length of OC=(5-x) Applying Pythagoras theorem…

Q: 2 Find the volume of the parallelepiped whose edges are represented by A =î - 13ĵ+ 4k, B = 3î +2j-7k…

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Q: Find the area of an isosceles trapezoid with legs 5 and bases 4 and 12.

A: Given- An isosceles trapezoid with legs 5 and bases 4 and 12. To find- The area of the isosceles…

Q: Find the area of the parallelogram that has u = (1, 3, 0) and v = (−1, 0, 2) as adjacent sides.

A: Now cross product is,

Q: sides of length a and the smaller square has sides of length b. What is the area of the shaded…

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Q: = Boosi 28

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Q: Calculate the area of the given quadrilateral starting at A and going clockwise using the shoelace…

A: Topic = Area

Q: Find the area of the trapezoid in which the sum of its two bases is 0.14m and its altitude is 0.07m.

A: Using area of trapezoid formula.

Q: 2x, BD = 3x+ 4, and Point C is on line segment BD. Given CD BC = 2x - 1, determine the numerical…

A: The given information can be diagrammatically represented as shown below:

Q: Let AC and BD be two line segments that bisect each other at E, with AC & BD. Prove that ABCD......…

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Q: E. Prove that if semicircles are constructed on each of the sides of a right triangle, then the area…

A: In triangle ABC, using pythagorus theorem - c2 = a2+b2            .............(1)Semicircle on…

Q: Let AC and BD be two line segments that bisect each other at E, with AC & BD. Prove that ABCD......…

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Q: And the eguation of lines in which the blane 2x+47280 4u2-y2= 32²=0. ーザ cuts the cone Also find ind…

A: Hi! You have posted multiple sub-parts. As per norms, we will be solving only three sub-parts. We…

Q: Find the total surface area (cm2) of the square pyramid if its perpendicular height is 12 cm and its…

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Q: Solve the following problems completely. If there are seven distinct points on a plane with no…

A: Given: Total number of points is, n=7. No three points are collinear. The objective is to find the…

Q: 8. Find the exact perimeter and area of the segment shown, given that mz0 60° and OA %3D %3D 12 in.

A: Please see the below picture for detailed solution.

Q: Suppose that we are given a cube with edges 12 centimeters in length. Find the length of a diagonal…

A: The length of a cube l=12 cm. The breadth of a cube b=12 cm. The height of a cube h=12 cm. Consider…

Q: 1. Prove analytically that the lines joining the midpoints of the adjacent sides of the…

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Q: If x = 15.5 cm. and z = 23.8 cm., then the LATERAL AREA of the square based pyramid is _____cm2.…

A: The answer is found in step-2

Q: In a beehive, each cell is a regular hexagonal prism, open at one end with a trihedral angle at the…

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Q: Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of…

A: Area of semi circle having diameter of a is, Aa=πa222Aa=πa28         ...(1)  Area of semi circle…

Q: Two cubes whose edges measure 3 cm, 4 cm and 5 cm respectively to form a single cube.Find its…

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Q: A closed figure in a plane, determined by 3 or more line segments, is a(n)

A: Given , The closed figure contained in a plane with three or more sides.

Q: In the given figure, AD is a median, and the length of BC is 18 units. What is the distance from…

A: Consider the given triangle ∆ABC with AB=15, BC=18 and AD is the median from the vertex A to the…

Q: With α> 0, the circle of (x-2α) square + y square = 4α is rotated around the line x = -1. A torus is…

A: We find the volume of the solids using Washer method. Given equation of circle is…

Q: what is the surface area of the new box? What is the difference of the surface areas?

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Q: Find the length of segment LM for the given parallelogram below. x+13 2x +4

A: Given that       LMNK be a parallelogram. LM = 2x+4  and NK= x+13 Here we have to find the length of…

Q: Assuming that the (square) base of this building has a side length of 646 feet and that the pyramid…

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

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.