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Geometry and Topology

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

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.

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.