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    Geometry and Topology

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    Find the volume.

    Find the volume of the solid bounded by the surface z= xsquareroot(x^2 + y) and the planes x=0, x=1, y=0, y=1, z=0

    Functional Analysis: Topological Space Proof

    Just a note on notation: X*_w* is X* (set of all linear functionals) with a weak-* topology (the weakest topology in which all functionals are continuous) This posting is for #1 See attached. Let Y be a topological space...

    GCF and area

    How do you feel about mathematics now that you have completed MAT 115? Describe some coping mechanisms you developed in MAT 115 that you can use for your next math course. Example: Find the GCF of 24 and 18 Example: Calculate the area of a circle that has a radius of 8 cm (use 3.14 for pi). Example: Calculate the area o

    Solving Coordinate Geometry

    Please solve the following: Find an equation of the plane that passes through the line of intersection of the planes x + y - z = 2 and 2x - y + 3z = 1 and passes through the point (-1,2,1).

    Distance from Point to Plane

    See attached page for the rest of the question Let P be a point not on the plane that passes through the points Q, R, and S. Show that the distance d from P to the plane is....

    Geometry - Coordinate Planes

    Draw a rectangular box that has P and Q as opposite vertices and has its faces parallel to the coordinate planes. Then find the coordinates of the other six vertices of the box and the length of the diagonal of the box P(1,1,2) Q(3,4,5)

    Golden ratio

    The shape for a rectangle was one which the ratio of the length to the width was 8 to 5, the golden ratio. If the the length of a rectangular painting is 2ft longer than its width, then for what dimensions would the length and width have the golden ratio.

    Shell method

    Using the shell method to find the volume of a solid revolving about line x = 2 by the region bounded by y=x^3 +x +1, y=1 and x=1. Please show in detail thank you.

    Vertex Figures and Tessellations

    Another definition of a regular tessellation is one whose vertex figures are identical regular polygons. A vertex figure is made by connecting the midpoints of all the edges which touch a given vertex. (1) Sketch the vertex figures for the regular semiregular tessellation of the plane and verify the definition. (2) The

    Find the slope of the line containing the points

    1. Find the slope of the line containing the points (-3, 4) and (5, 4). State whether the line is vertical, horizontal, or neither. 2. Find the slope of the line containing the points (-2, -5) and (-2, 6). State whether the line is vertical, horizontal, or neither 3. Write an equation in slope-intercept form, , of the line

    Proofs - Give an indirect proof of the theorem

    Give an indirect proof of the theorem. 1. If two lines are parallel to a third line then they are parallel to each other 2. Solve the equation S=(n-2) 180 degrees for n when S is a given value. Find the number of sides of the polygon ( if possible) if the given value corresponds to the number of degrees in the sum of the in

    Constructing a polygon

    To construct a regular 5-gon , first draw a circle with the center O. Then proceed to find on the circle the vertices V1, V2, V3 and V5 of the Regular pentagon as follows: ___

    Word Problems - volume of solid

    Directions. 1.Find the volume of the solid generated by revolving the region about the y-axis. The region enclosed by the triangle with vertices (1,0), (1,2),(3,2) 2.Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. y=2/x (this is 2 over x, couldn

    Circle construction

    I am to draw any thee non collinear points. I am to construct a circle containing them on its circumference. Can you construct a different one? How many different circles are thee through the three points? Can you construct a circle through three collinear points.

    Geometrical Constructions - Angle Bisector

    Let R1 and R2 be two rays with a common vertex with an angle strictly less than pie(3.14). Construct the angle bisector ray B. In the setting of the previous problem, if you were given R1 and B, how would you construct R2?

    Basic Math Geometry: Circumference, Perimeter and Area

    Exercises 4, 10, 20. 4. Find the circumference of each figure. Use 3.14 for [ ] and round your answer to one decimal place. In a circle for 3.75 ft 10. Find the perimeter of the curves is semicircles. Round answer to one decimal place 10 inches. 20. Find the area figure of 5 inches and 7 inches.