Explore BrainMass

# Geometry and Topology

### Maximizing the Volume of an Open Top Box

The total surface area of a square based open-top rectangular box is 12 cm^2. Find the dimensions of the box of maximum volume.

### 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

### Determining the Dimensions of a Rectangle

The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?

### Explain how to compute the volume of a regular Octahedron of edge length alpha.

Euclidean Geometry (III) Computing the Volume of a regular Octahedron of edge length alpha Explain how to compute the volume of a regular Octahedron of edge length alpha. Or, To fin

### 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&#61616;) exactly. A). 1 + B). 1 - C). -1 + D). -1 - [show the steps in completing this problem]

### Mensuration - This sum will be useful for high school student

A rectangular tank 5m X 4.5 m X 2.1m is dug in the center of a rectangular field 13.5m X 2.5m. The earth dug out is spread out evenly over the remaining portion of the field. How much is the level of field raised?

### Equation of a straight line using coordinate geometry

Write an equation of the line below. ----------- Graph ----------

### 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

### Connected Set Topology on R^2 Q^2

Let S = R^2 Q^2. Points (x,y) in S have at least one irrational coordinate. Is S connected? Can we disprove with a counterexample?

### Length of the inside diagonal of a cube.

Each edge of a cube is 100cm long. What is the length of the inside diagonal of the cube to the nearest centimeter?

### 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.

### Finding the volume of the solid formed by revolving a bounded region.

Please see the attached file for the fully formatted problems.

### 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.

### To show that the function f is an equivalence relation

Topology Sets and Functions (XLV) Functions Let f : X --> Y be an arbitrary mapping. Define a relation in X as follows: x_1 ~ x_2 means that f(x_1) = f(x_2).

### 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 (A_1×B_1)U(A_2×B_2) = (A_1UA_2)×(B_1UB_2).

Topology Sets and Functions (XLIV) Functions Let X and Y be non-empty sets. If A_1 and A_2 are subsets of X and B_1and B_2 subsets of Y, show that (A_1

### 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

### 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 (A_1×B_1) intersection (A_2×B_2) = (A_1 intersection A_2)×(B_1 intersection B_2).

Topology Sets and Functions (XLI) 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.

### Let X be a non-empty set and f a mapping of X into itself. Show that f is one-to-one onto iff there exists a mapping g of X into itself such that fg = gf = iX. If there exists a mapping g with this property, then there is only one such mapping. Why?

Topology Sets and Functions (XXXIX) Functions Let X be a non-empty set and f a mapping of X into itself. Show that f is one-to-one onto iff there exists a mapp

### Let X and Y be non-empty sets and f a mapping of X into Y. Show that f is onto iff there exists a mapping h of Y into X such that fh = iX.

Topology Sets and Functions (XXXVIII) Functions Let X and Y be non-empty sets and f a mapping of X into Y. Show that f is onto iff there exist