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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.

Tangent Plane Parametric Surfaces

Find an equation of the tangent plane to the given parametric surface at the specified point. 1.) r(u,v)= (u+v)i + ucos(v)j + vsin(u)k; (1,0,0)

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

Tangent plane

Please see the attached file - solution has to be in terms of z. Find an equation of the tangent plane to the given surface at the specified point.

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....

Equation to tangent

Find an equation of the tangent plane to the given surface at the specified point. Please see the attached file.

Find the projection of the given vector

The material attached is from Inconsistent Systems and Projection. Please show each step of your solution. If you have any question or suggestion on my posting, please let me know.

Decide if each of the following is a subspace

The material is from ABSTRACT VECTOR SPACE. Please kindly show each step of your solution. (The material is from ABSTRACT VECTOR SPACE. Please solve for parts (b) & (d). means the space of the collection of continuous functions on R which is differentiable 0 time. Please explain each step of your solution sufficiently.

Volume of a solid

Find the volume of a solid generated by revolving the region enclosed by y=x^2, y=4x-x^2 about the line x=2

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

Connected Convex Subsets

Please see the attached file for the fully formatted problems. Let A and B be separated subsets of some Rk, suppose and , and define for . Put , . [Thus if and only if .] (a) Prove that Ao and Bo are separated subsets of R1 . (b) Prove that there exists such that . (c) Prove that

Subspaces, Basis, Dimension and Rank

Please solve no. 12 and no. 30 in file scan005.jpg. For problem 30; when claiming that a vector is in a space, demonstrate correctness by giving the coefficients.

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 Profit and Minimizing Surface Area of a Cylinder

9) A shop can sell 30 radios at $20 each, per week. For every $1 increase in the price there will be a loss of one sale per week. How much should the shop charge in order to make the maximum profit If the cost to make each radio is $10 10). A closed can (top and bottom), in the shape of a cylinder, is to hold 2000pi cm^3 of