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Geometry and Topology

Relations of Sets and Functions

Let U be the set {1,2}. There are four subsets. List them. If A and B are arbitrary subsets, there are 16 possible relations of the form "A is subset of B". How many true ones are there?

Sets and Functions : Sets and Set Inclusion

Let U be the single-element set { 1 }. There are two subsets, the empty set φ and { 1 } itself. If A and B are arbitrary subsets of U, there are four possible relations of the form "A is subset of B". Count the number of true relations among these.

Errors in Measuring Volume of Small Balls in Large Container

Consider an experimental procedure to measure the average volume of M&M Peanut candies. One hundred piece of the candy are poured into a graduated cylinder with a 30 diameter. The cylinder is then filled with 1 mm diameter beads and shaken so that the beads and candies pack as tightly as possible. Finally, the candies are remove

Plucker Coordinates

1. Let d = (1, 2, -2), m = (-8, 5, 1) (a) Check that d and m are orthogonal. I already check that it is orthogonal. DO NOT ANSWER THIS PART. (b) Find a vector v such that d x v = m. In other words, find an affine point on the line with Plucker coordinates (1, 2, -2, -8, 5, 1). 2. Describe a general way t

Weightage Method

Four cities plan to build a new airport to serve all four communities. City B (population 180,000) is 4 miles north and 3 miles west of city A (population 75,000). City C (population 240,000) is 6 miles east and 12 miles south of city A. City D (population 105,000) is 15 miles due south of city A. Find the best location for the

Euclidean Geometry Construction

Given a line l and a point P not on l, I contructed a line that contains P and meets l at a 45 degree angle using a compass. Now I need to construct a line that contains P and meets l at 30 angle and prove it. I attached what I have so far.

Tychonoff and Hausdorff Spaces

Let X and Y connected, locally path connected and Hausdorff. let X be compact. Let f: X ---> Y be a local homeomorphism. Prove that f is a surjective covering with finite fibers. Prove: a) Any subspace of a weak Hausdorff space is weak Hausdorff. b)Any open subset U of a compactly generated space X is compactly generated

Maximum Volume of an Open-Top Box

An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. 1. Find the function V that represents the volume of the box in terms of x. 2. Graph this function and sh

Geometry: Finding the angles of Polygons

Please help with the following problems on geometry and topology. Provide step by step calculations. See the attached files for diagrams to go along with the questions. Find the value of x and any unknown angles. Find the measure of one angle in the polygon. Round to nearest tenth if needed. 4. Regular 30-gon 5. Regular

Angles in Polygons

A- find the measure of one angle in the polygon. round to nearest tenth if needed. 1- regular 30- gon 2- regular 35- gon b- sum of angle and number of sides to polygon sum of angles number of sides to polygon 5040 1800 2160 4140 c- tell whether the stateme

Descriptions and Drawings of Regular and Non Regular Polygons

(a) Draw polygons with sides n = 4, 5, 6, 7, 8, 9, 10 for the following three cases. 1- non regular polygon 2- regular polygon 3- a shape that is not a polygon (b) Name the following polygons Number of sides name of polygon ------------------ -------------------- 4 5 6 7 8 9 10

Epsilon-Delta Definition of Continuity

Proof that f is continuous for each x in D in accordance with the epsilon-delta defitinition of continuity(can use the defintion involving f(x+h) (2 problems) f(x)=x/(x+1), D={x in R:x>-1} (can restrict |h|<(x+1)/2 f(x)=1/sqrt(x-4), D={x in R:x>4} (can restrict |h|<(x-4)/2

How do you calculate the volume of the cylinder?

The volume of a cylinder (think about the volume of a can) is given by V = pi*r2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters. Write h as a function of r. b) What is the measurement of the height if the radius of the cylinder is 3 centimete

Value of x, volume of a cylinder

1) Using the graph, what is the value of x that will produce the maximum volume? 2) The volume of a cylinder (think about the volume of a can) is given by V = &#960;r2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters. Write h as a function

Finding the cubic yard

An engineer's plan shows a canal with a trapezoidal cross section that is 8 ft deep and 14 ft across at the bottom with walls sloping outward at an angle of 45 degrees. The canal is 620 ft long. A contractor bidding for the job estimates the cost to excavate the canal at $1.75 per cu yd. If the contractor adds 10% profit, what s

Volume of a solid,.,

A solid whose base is the ellipse (x^2/16)+ (y^2/9)= 1 has cross sections perpendicular to the base and parallel to the minor axis are semi-ellipses of height 5. Find the volume.

Measurement of height of a cylinder

b. The volume of a cylinder(think about the volume of a can)is given by v=pir^2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters, what is the measurement of the height of the cylinder is 2 centimeters? show work c. Graph this function

Calculating the Measurement of Height of a Cylinder

What is the measurement of the height if the radius of the cylinder is 2 centimeters? Graph this function also The formula for calculating the amount of money returned for an initial deposit money into a bank or CD is given by A=P(1+r)^nt n A is the amt of

Maximizing the Volume of an Open-Top Box

An open top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and then folding up the flaps. Let x denote the length of each side of the square to be cut out. Find the function V that represents the volume of the box in terms of x. Show and explain the answer, and a

Maximizing the Area of a Rectangle Given Perimeter

John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 time width) He wants to maximize the area of his patio (area of a rectangle is length times width). What should the dimensions of the patio be?

Geometry and Construction : Finding the Hidden Vertex of an Angle

A farmer wishes to erect a striaght fence that will bisect the angle formed by two existing (straight) fences. Unfortunetly, the vertex of the angle is in the middle of a lake. How can we locate the fence line using straight edge and compass? Please see the attached file for the fully formatted problem.

Word Problem

John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). He wants to maximize the area of his patio (area of a rectangle is length times width). What should the dimensions of the patio be?

Vectors and analytic geometry

Please find the 1) length and 2) direction (when defined) of 1) A X B and 2) B X A Please show all work, including the grids for the determinants. Thank you. A = 2i - 2j - k B = i - k