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# Geometry and Topology

### 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

### Find the dimensions that minimize a amount.

A cardboard box with a lid is to have a volume of 32,000 cm^3. Find the dimensions that minimize the amount of cardboard used.

### The Dimensions of a Rectangle

If the length is 5 inches longer than the width.. the area is 84 in^2, what are the dimensions of the object?

### 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...

### Finding the volume of unbounded solids of revolution

(a) Find the volume of the unbounded solid generated by rotating the unbounded region of y=e^(-x) with x>=1 around the x axis (see the attached figure) (b) What happens if y=1/sqrt(x) instead?

### 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).

### Grasping Concepts of Angles

Will you give insight as to how I can grasp the concepts of angles?

### Coterminal angle

Find an angle between 0 and 2pi that is coterminal with 51pi/2

### 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.

### Regular Polygons - 1. The area of a regular hexagon is 900ft². Find the length of its side and the radius of the circumscribing circle. 2. Find the perimeter and area of a decagon inscribed in a circle of radius 10 inches.

1. The area of a regular hexagon is 900ft². Find the length of its side and the radius of the circumscribing circle. 2. Find the perimeter and area of a decagon inscribed in a circle of radius 10 inches.

### Regular Polygons - 1. A regular hexagon is inscribed in a circle of radius 8 inches. Find the length s of its side. 2. Find the area of a regular octagon that can be inscribed in a circle of radius 18 inches.

1. A regular hexagon is inscribed in a circle of radius 8 inches. Find the length s of its side. 2. Find the area of a regular octagon that can be inscribed in a circle of radius 18 inches.

### 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

### supplementary and complementary angles

Please explain thoroughly the solution for the problems. 1 .What is the complement of the supplement of an angle measuring 130 degrees?

### Supplementary Angles

How to find the supplementary angles of this. 1. 71.57° 2. 2π / 3.

### 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: ___

### Calculating the area under curve

Calculate area using polar equations. See attachment.

### 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.

### Rectangular Equation Center and Radius

5)convert 5 =5cos(theta) to a rectangular equation. Use the rectangular equation to find the center and radius. Please explain the steps in this.

### 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?

### Geometrical Constructions - Parallelogram

Suppose L is a given line and A a given point. Construct the reflection of A about the line L.

### Geometrical Constructions - Construct the Fourth Vertex

Suppose the three vertices A, B and C of a parallelogram ABCD are given. Construct the fourth vertex D.

### Geometrical Constructions - Midpoint of a Line Segment

Given two distinct points A and B in the plane, construct the midpoint of the line segment AB.

### 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.