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# Geometry and Topology

### Constructing a polygon

To construct a regular 5-gon , first draw a circle with the center O. Then proceed to find on the circle the vertices V1, V2, V3 and V5 of the Regular pentagon as follows: ___

### Word Problems - volume of solid

Directions. 1.Find the volume of the solid generated by revolving the region about the y-axis. The region enclosed by the triangle with vertices (1,0), (1,2),(3,2) 2.Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. y=2/x (this is 2 over x, couldn

### Circle construction

I am to draw any thee non collinear points. I am to construct a circle containing them on its circumference. Can you construct a different one? How many different circles are thee through the three points? Can you construct a circle through three collinear points.

### Basic Math Geometry: Circumference, Perimeter and Area

Exercises 4, 10, 20. 4. Find the circumference of each figure. Use 3.14 for [ ] and round your answer to one decimal place. In a circle for 3.75 ft 10. Find the perimeter of the curves is semicircles. Round answer to one decimal place 10 inches. 20. Find the area figure of 5 inches and 7 inches.

### A rectangular storage container with an open top is to have a volume of 10m3. The length of its base its twice the width. Material for the base costs of \$10 per square meter. Material for the sides costs \$6 per square meter. Find the cost of materials for the cheapest such container.

A rectangular storage container with an open top is to have a volume of 10m3. The length of its base its twice the width. Material for the base costs of \$10 per square meter. Material for the sides costs \$6 per square meter. Find the cost of materials for the cheapest such container.

### Golden ratio

The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than its width, then for what dimensions would the length and width have the golden ratio?

### Poincare's model of Lobachevskian geometry

Poincare's model of Lobachevskian geometry was to say that points of the plane are represented by points in the interior of a circle and lines by both the diameters of the circle and the arcs of circles orthogonal to it. Draw a diagram(s) to illustrate his model and explain his theory.

### Need to know the differences between regular Tic Tac Toe and cylindrical

A careful player can always guarantee at least a draw at regular tic tac toe. (a) Is this also true with cylindrical tic-tac-toe? Explain. (b) In cylindrical tic-tac-toe, can two players co-operate to play a draw? Explain. I know this must be simple but I can find nothing on it anywhere.

### Functions and Coordinate Geometry

Functions and Coordinate Geometry - (1) Find an equation of the line having the given slope and containing the given point m= , (6,-8) (2) Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b (7,8); x+7y=5 ... ... (6) The table lists data regard

### A=(LP)/2-L^2, gives the area of a rectangle of perimeter P and length L.

A=(LP)/2-L^2, gives the area of a rectangle of perimeter P and length L. Suppose that you have 600 feet of fencing which you plan to use to fence in a rectangular area of land. Choose any two lengths for a rectangle and find the corresponding area for each using the given equation. Include units and show all calculations. Which

### Relationship between volume and cone angle

Please help with the attached problem. Shown at the right is a cone with a slant height of 10 cm. Let's explore the relationship between the volume and the angle at the top of the cone....

### Solve equilibrium of price, estimate population, and dimension of rectangular

Need assistance in solving the attached problems. My answers are falling short of the choices given in the problem. Please explain the steps to get answers. Thank you. 1. Find the equilibrium price. Suppose the price p of bolts is related to the quantity q that is demanded by: P=520-5q^2 where q is measured in hundred

### Minimizing cost of materials to build an aquarium

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.

### Maximizing the Volume of a Box

A box is made from a sheet of metal that is 8 meters by 10 meters, by removing a square from each corner of the sheet and folding up the sides. Find the width of the square to removed in order to have a box of maximum volume.

### 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.

### 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

### 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

### Equation of a straight line using coordinate geometry

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

### 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.

### 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

### 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

### 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.