Explore BrainMass
Share

Geometry and Topology

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

Unit square possible partition

Is it possible to partition a unit square [0, 1] X [0, 1] into two disjoint connected subsets A and B such that A and B contain opposing corners? I.e., such that A contains (0, 0) and (1, 1), and B contains (1, 0) and (0, 1)? *----0 | | | | 0----* Evidently, A and B couldn't be path-connected because a path running fr

Homology group

(See attached file for full problem description) --- Determine the structure of the homology group Hn(X), n &#61619; 0, if X is (a) the set of rational numbers with their usual topology; (b) a countable, discrete set.

Problem Set

1. Consider the graph of y = tan x. (a) How does it show that the tangent of 90 degrees is undefined? (b) What are other undefined x values? (c) What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)? (d) How does the graph show this? 2. A nautical mile depends on l

Fixed Point Theorem and Closed Unit Ball in Euclidean Space

The Brouwer Fixed-Point Theorem Let denote the closed unit ball in Euclidean space : . Any continuous map from onto itself has at least one fixed point, i.e. a point such that . Proof Suppose has no fixed points, i.e. for . Define a map , , by letting be the point of intersection of and the ra

Lebesque Number and Connectivity

Lemma. Let {Ui} be an open covering of the space X having the following properties: (a) There exists a point x0 such that x0Ui for all i. (b) Each Ui is simply connected. (c) If i≠j, then Ui Uj is arcwise connected. Then X is simply connected. Prove the lemma using the following approach: To prove that any loop f: I

Proofs : Collinear and Distinct; Boomerang Quadrilateral

1- Prove that if AF/FB = AF'/F'B where A, B, F, F' are collinear and distinct then F does not have to equal F' 2- Suppose that the sides AB, BC, CD and DA of a quadrilateral ABCD are cut by a line at the points A' B' C' D' respectively, show that AA'/A'B * BB'/B'C * CC'/C'D * DD'/D'A = +1