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Geometry and Topology

Rectangle length and perimeter

Please look at the attached file. Only solve problem No. 3 3. A rectangle is a parallelogram with four right angles. A rectangle has a width of 15 feet and a diagonal of a length 22 feet; how long is the rectangle? What is the perimeter of the rectangle? Round to the nearest foot. Show all work to receive full credit.

Understanding the geometric principles

How would you incorporate the use of standard units, the use of tools to measure, the importance of precision and accuracy, estimation and the use of manipulatives and other visual aides to a group of third graders to make them understand the common concept behind measurements regardless of what is being measured? Why is it impo

Topological Spaces and Continuity

Please see the attached file for the fully formatted problems. Let be a real valued function on a topological space . Show that is continuous if and only if for each real number the set and are open. Show that is continuous if and only if for each real number the set is open and is closed

Half-Angle Identities

Please show the steps in completing this problem. Please see attached file for full problem description. 10). Use the half-angle identities to evaluate tan(67.5) exactly. A). 1 + B). 1 - C). -1 + D). -1 - [show the steps in completing this problem]

Volume of a Regular Tetrahedron and Octahedron

Please show how to compute the volume of a regular tetrahedron of edge length 1. this is an Euclidean geometry class. and how to compute the volume of a regular octahedron of edge length 1.It does not have to be a written proof, just a step by step approach on how you got the answer, that is it. I probably would use the formula

Simple equations in one variable.

1.) t+4=-9 2.)98=7z 3.)37=y/5+14 4.)2/7x-4/3=-3/2 5.)8(x-8)-5x= -37 6.)u+3>19 7.)-4x-17 is less than or equal to 19 8.)word problem a local hamburger shop sold 577 hamburgers and cheeseburgers on Tuesday. they sold 73 fewer cheeseburgers than hamburgers.how many hamburgers did they sell? 9.)a=1/2h

Geometry : Area and Distance

Area For locations between 20degrees and 60degrees north latitude a solar collector panel should be mounted so its angle with the horizontal is 20 greater than the local latitude. Consequently, the solar panel mounted on the roof of Solar Energy, Inc., in Atlanta (latitude 34degrees) forms a 54degree angle with the horizontal.

Importance of geometry in the math curriculum

The importance of geometry's role in the math curriculum is debated in many high schools and colleges. Some schools offer the course while others have done away with it. Based on what you have learned within this unit, do you think geometry is a valuable tool for students to learn? Choose one side of this debate, state your vi

Point and Segment, Volume and Dimensions

Please see attachment for full problem description. 1. (4 pts) Use the figure below to find the following: Hint: Your answers will be points or segments from this figure. See attachment 2. Lines A and B are parallel and are cut by the transversal shown. Determine the measures of angles 1 throu

Writing Equations from Word Problems

The length of a rectangle is 3 cm more than 5 times its width. If the area of the rectangle is 76 cm2, find the dimensions of the rectangle to the nearest thousandth.

Reflexivity, symmetry, and transitivity

Topology Sets and Functions (XLVIII) Functions Decide which ones of the three properties of reflexivity, symmetry, and transitivity are true for each of the following relations in

Equivalence Relation and Equivalence Sets

Topology Sets and Functions (XLVI) Functions In the set R of all real numbers, let x ~ y means that x - y is an integer. Show that this is an equivalence relation and describe the equivalence sets. See the attached file.

Minimizing Volume using Lagrange Multipliers

An aquarium has a slate bottom that costs 8 cents/sq inch and glass sides which cost 1 cent/sq inch. The aquarium is to have a volume of 1024 cubic inches. Find the dimensions of the least expensive aquarium. Use the Lagrange multipliers.

Circumference of Center Rectangle

Please see attached file for full problem description. In the circumference of center O, ABCD is a rectangle, arc (AB) = 60º, the radious measeaure is 4 cm, ¿ what measure have the grey area?

18 basic math problems

10. In the number 456,719 A) What digit tells the number of thousands? B) What digit tells the number of tens? 12. In the number 324,678,903 A) What digit tells the number of millions? B) What digit tells the number of thousands? 32. Business and finance. Inci had to write a check for $2,565. There is a space on

Area of Rectangle

The width of a rectangle is 1 foot less than the length. The area is 20 feet squared. Find the length and width.

Difference of the product of sets

Topology Sets and Functions (XLII) Functions Let X and Y be non-empty sets. If A_1 and A_2 are subsets of X, and B_1 and B_2 subsets of Y. Show that