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Geometry and Topology

Use the cylindrical shell method to find volume of solid of revolution.

Show step by step work using cylindrical shell method to find the volume of the solid formed by revolving the given region about the y-axis. 22) the region bounded by the curve y=SQRT(x), the y-axis, and the line y=1. 24) the region bounded by the parabolas y=x^2, y=1-x^2, and y axis for x≥0. 26) the region ins

Volumes of Solids of Revolution and Sketches of Bounded Regions

Sketch the given region and then find the volume of the solid whose base is the given region and which has the property that each cross section perpendicular to the x-axis is a square. 2) the region bounded by the x-axis and the semi circle y = SQRT (16-x^2). Sketch the given region and then find the volume of the solid

Volume of a Tetrahedron

Find the volume of a tetrahedron with height h and base area B. Hint: B=(ab/2)sin(theta) Also, please see the attached document for the provided diagram of the tetrahedron. I already know that the answer is V=(Bh/3). I am simply looking for how my teacher came to this answer. Please show as many steps as possible so that

Topologies

Determine, for each of these topologies, which of the others in contains. --- (See attached file for full problem description)

Continuity proofs

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

Topology proofs

Let A be a set. Let {Xa} be a family of spaces.... --- (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

General and Differential Topology

Find conditions under which the box topology is strictly finer than the product topology. See attached file for full problem description.

Open maps

Show that .... are open maps (see attachment)

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

Derive an mathematical equation for a beehive puzzle

In Fig.1 a beehive is enclosed in a bee cage. The bees can fly with a speed C. Each bee is flying non-stop from the hive to the wall of the cage and then back. Each time one returns to the hive, it is counted as one hit. There are hundreds and hundreds of bees in the cage and they fly out from the beehive in all directions. In s

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).

Circles and Coordinates : Distance from the Center

I have solved this question and I would like to know if I am correct. " A pizza shop delivers to all customers within a circle determined by the equation X squared + Y squared = 400, If the pizza shop is at coordinates (0,0), would they delvier to someone who lives at coordinates (16,-11) x + y = 20 Therefore the radius of t

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?

Circles

Secants QM and RM intersect the circle at S and T as shown, a) IF RV=12,VS=4,and TV=8 find VQ. OK so i figured it follows this theorem : If 2 secant segments are drawn to a circle from the same external point, then the products of the length of each secant and the length of its external segment are equal.... So i mapped

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.