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Geometry and Topology

Al metal reacts with HCl produces AlCl3 and hydrogen gas.

Let C_0 be the space of functions f:R --> R such that lim f(x) = 0 as x goes to infinity and negative infinity C_0 becomes a metric space with sup-norm ||f|| = sup { |f(x)| : x in R } Prove that if A is a family of functions in C_0 such that A is uniformly bounded and equicontinuous, then every sequence of functions

Break Even Point and Capital Budgeting

2. (Payback period, net present value, profitability index, and internal rate of return calculations) You are considering a project with an initial cash outlay of $160,000 and expected free cash flows of $40,000 at the end of each year for 6 years. The required rate of return for this project is 10 percent. a.) What is the pr

Compact Set, Convergent Sequences and Subsequences and Accumulation Points

Prove that a set A, a subset of the real numbers, is compact if and only if every sequence {an} where an is in A for all n, has a convergent subsequence converging to a point in A. For the forward direction, I know that a compact set is closed and bounded, thus every sequence in A is bounded, and so has a convergent subsequen

Geometry

Exactly how many minutes is it before eight o'clock, if 40 minutes ago, it was three times as many minutes past four o'clock?

Use double inegrals to find the volume of a region.

Find the volume of the following region in space: The first octant region bounded by the coordinate planes and the surfaces y=1-x^2, z=1-x^2. This question is #12 (section 9.3) in Advanced engineering mathmatics (8th ed.) by Kreyszig. This section deals with the evaluation of double integrals.

Continuity proofs

Show that if {Aa} is a finite collection of sets... --- (See attached file for full problem description)

Clock problem involving angles

I am studying for a geometry test and am having trouble with a review problem at the end of the chapter. This is not homework. One problem asks the following: At 3:00, the hands of a clock form an angle of 90 degrees. To the nearest second, at what time will the hands of the clock next form a 90 degree angle? I figure t

Length of an Arc and Volume of Dirt

See the attached file. A. The diagram over shows an area of a railway cutting that has failed in the form of a shallow rotational slip. Using radians as a measure of angular displacement determine the length of the failure surface AB. b. A partially completed site survey of a quadrilateral site is given below. You are

Geometry

If you answers are different from minds, please show steps? 1. Find the perimeter of a rectangle that is 12 ft. by 4 1/2 ft. ____a. 16 1/2 ft. _x__b. 33 ft. ____c. 48 1/2 ft. ____d. 54 ft. 2. Find the area of a rectangle that is 2.5 ft. by 4.6 ft. ____a. 38.28 ft ^2 ____b. 14. 2 ft ^ 2 __x_c. 11.5 ft ^2

5 Topology Questions (Including: de Morgan's Laws)

1. Prove the following de Morgan's laws: (a) ... (b) ... 2. Let A be a set. For each p E A, let Gp be a subset of A such that p C Gp C A. Then show that A = Up E A Gp. 3. Let f : X ---> Y be a function and A, B C Y. Then show that (a)... 4. Let f : X ?> Y be a function and A C X, B C V. Then show that (a) A C f-1 o f(A).

Find the Variables and Internal Dimensions For a Studio and Patio

I am building a rectangular studio on south side of house, so that the north side of the studio will be a portion of the currrent south side of the house. The studio walls are 2 feet thick, and the studio's inside south wall is twice as long as its inside west wall. Also, I am building a semicircular patio around the st

Area of circle

An Indian sand painter begins his picture with a circle of dark sand. He then inscribes a square with a side length of 1 foot inside the circle. What is the area of the circle?

Functional Analysis

1) Let E be an infinite dimensional normed space, and let S =... Find the weak closure of S. Please see attached for full question.

Parametric Equations; Orthogonal Vector; Point of Intersection

Please assist me with the attached problems, including: 1. Find the parametric equations for each of the given curvbes 2. Show that the given vector is orthogonal to the line plassing through the given points. ----- 1. Find the point of intersection of each line with each of the coordinate planes 2. Tell whether t

Cycloid Geometry

The circle has a radius of 8. As the circle rolls along the line, the point P (a pencil point) draws a curve. a) Draw the curve for three complete revolutions of the circle. b) Find the area between the curve (one loop) and the line. c) Find the length of the curve - all three loops.

Volume of Cone from Circle with Missing Sector

A circle has a radius of 5. A sector of that circle has a central angle of 120 degrees. This sector is cut out and the two radii folded together thus forming a cone. Find the volume of that cone.

Volume of Box Containing Spheres

240 spheres, each of radius 2, are placed in a box in 5 layers. There are 6 rows with 8 spheres in each row at each layer. The outside spheres are each tangent to the box and the spheres are tangent to those spheres next to them. Find the volume of the box which is between the spheres.