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
(See attached file for full problem description) --- Determine the structure of the homology group Hn(X), n  0, if X is (a) the set of rational numbers with their usual topology; (b) a countable, discrete set.
Assume X and Y are arcwise connected and locally arcwise connected, X is compact Hausdorff, and Y is Hausdorff. Let f: X-->Y be a local homeomorphism. Prove that (X,f) is a covering space.
Prove that a non-simple quadrilateral can be inscribed in a circle <=> opposite angles are equal (both directions).
A circular table measures about 0.9 m around its edge. What is the approximate length of its diameter.
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
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
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
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
(See attached file for full problem description)
A Car leaves Oak Corner at 11:33 a.m traveling south at 70km/h. at the same time, another car is 65 km west of Oak Corner traveling east at 90km/h. a. Express the distance d between the cars as a function of the time t after the first car left Oak Corner. b. show that the cars are closest to each other at noon.
A balloon is inflated in such a way that is volume increases at a rate of 20cm^3/s. a. If the volume of the balloon was 100cm^3 when the process of inflation began what will the volume be after t seconds of inflation b. Assuming that the balloon is spherical while it is being inflated, express the radius r of the balloon a
A stone is thrown into a lake, and t seconds after the splash the diameter of the circle of ripples is t meters A. Express the circumference C of this circle as a function of t. B. express the area A of this circle as a function of t.
Problem 1 Prepare financial analysis of Panorama. The analysis should include a summarization of the ratio analysis, explanations of what those ratios tell about the financial condition of Panorama, and a summarization of the financial strength and weaknesses of Panorama. What information do I need to use for the Financia
The wheels of a car have a 24-in. diameter. When the car is being driven so that the wheels make 10 revolutions per second, how far will the car travel in one minute?
Let V be an inner product space and W ⊂ V be a finite dimensional space with ONB {u1...u2}. For every x Є V define P(x) =Σ i=1-->n <x,ui>ui i) Prove that x-P(x)ЄW ii) Prove that P is the orthogonal projection of W. iii)... Please see the attached file for the fully formatted problems.
The region in the first quadrant that is bounded above by the curve y=1/√x, on the left by the line x=1/4, and below by the line y=1, is revolved about the y-axis to generate a solid. Find the volume of the solid by (a) the washer method, and (b) the shell method. Please be detailed in your response.
Revolving the solid about the y-axis, use the shell method to find the volume of the solid bounded by: the line x=√2/2 on the right y=1/√(1-x²) above. The shaded area in the drawing is bounded by the y-axis to the left, and the x-axis on the bottom.
Use the shell method formula to find the volume of the solid generated by revolving the shaded region bounded by the curves and lines below about the x-axis: V=∫2π(shell radius)(shell height)dy = ∫2πx f(y)dy a≤y≤b Shaded region:: x=y² x= -y y=2
Use the shell method formula to find the volume of the solid generated by revolving the shaded region bounded by the curves and lines below about the y-axis: V=∫2π(shell radius)(shell height)dx = ∫2πx f(x)dx a≤x≤b Shaded region:: y=2x y=x/2 x=1
Use the shell method formula to find the volume of the solid generated by revolving the shaded region about the x axis: V=∫2π(shell radius)(shell height)dy = ∫2πx f(y)dy a≤y≤b Shaded region:: Lower boundary x=3-y² intersecting the y axis at (0, √3) and the x axis at (3,0)
Use the shell method to find the volume of the solid generated by revolving the region described about the y-axis: Shell formula: V=∫2π(shell radius)(shell height)dx = ∫2πx f(x)dx a≤x≤b The shaded region is bounded by the y axis from the point (0,2) to (0.0) and the x axis from (0.0 )
Determine the limits of integration and then Find the volume of the solid generated by revolving the region about the line x= -2 The region in the second quadrant bounded above by the curve y = -x³, below by the x-axis, and on the left by the line x = -1. Rotate about the line x = -2. Using the formula V=∫π[R
First, find the limits of integration. Then calculation the volume of the solid created by rotating the region between the line and curve around the Y-axis: Above by the curve y=√x Below by the line y=x Using the formula V=∫π[R(y)]²dy Please show all the steps to make understanding easy.
Find the volume of the solid generated by revolving the region described about the Y axis: Between (0,0) and (0,2), the triangular region between those points on the y-axis and the straight line x=3y/2 using the formula V=∫π[R(y)]²dy
The surface area A of a steel cylinder is given by the formula A= 2.pi.r²+2.pi. r h Where r is the radius and h the height a) find the required radius if A = 12500mm² , and h = 150mm b) Determine the number of 2.5 liter tins of paint that are needed to coat 500 cylinders with a thickness of
Can you tell me what the answer would be if I traveled north for 35 kilometers then traveled east 65 kilometers. How far am I from my starting point? using: 35^2+65^2?
You are part of a panel of parents, teachers, and administrators working to revise the geometry curriculum for the local high school. On tonight's agenda, you will be brainstorming creative ways to teach surface area and volume. The teachers are especially interested in methods which will help the students connect geometry to li
Suppose the volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Now suppose the volume of the can is 100 cubic centimeters. How do would you write h as a function of r? What is the measurement of the height if the radius o
Find sin2x, cos2x, and tan 2x under the given conditions. 23. sinx=5/13 (0<x<pie/2) ans. sin 2x = 120/169, cos 2x = 119/169, tan 2x = 120/119 Please explain in detail step by step how to come up with this ans. 25. cos x=-3/5 (pie<x< 3pie/2) ans. sine 2x=24/25, cos2x=-7/25, tan2x=-24/7