### Transformation of Half Plane to Interior of a Circle

2. Show that when c1<0 the image of the half plane x<c1 under the transformation w = 1/z is the interior of a circle. What is the image when c1=0?

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2. Show that when c1<0 the image of the half plane x<c1 under the transformation w = 1/z is the interior of a circle. What is the image when c1=0?

4. Let C denote the circle |z|=1, taken counterclockwise, and following the steps below to show that: {see attachment for steps and equation} Please specify the terms that you use if necessary and clearly explain each step of your solution.

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19. Let X be a topological space and let Y be a subset of X. Check that the so-called subspace topology is indeed a topology of Y. (question is also included in attachment)

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Please see the attached file for the fully formatted problems. B6. (a) Define what it means for a topological space to be connected. (b) Suppose that A and B are subspaces of a topological space X, and that U C A fl B is open in both A and B in the relative topologies. Show that U is open in A U B in the relative topology.

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The metal used to make the top and bottom of a cylindrical can costs 4 cents/in^2, while the metal used for the sides costs 2 cents/in^2. The volume of the can is to be exactly 100 in^3. What should the dimensions of the can be to minimize the cost of making it? Could you please show all work so I can better grasp the conce

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For any quadrilateral one can define the so-called maltitudes. A maltitude on a side of a quadrilateral is defined as the line through the midpoint of the side and perpendicular to the opposite side. Generally the four maltitudes of a quadrilateral are not concurrent, but if the quadrilateral is cyclic they are. Prove that i

(Extreme Value Theorem) prove if f:K->R is continuous on a compact set K subset or equal to R, then f attains a maximum and minimum value.In other words there exists Xo,X1 belong to K such that f(Xo)<=f(X)<=f(X1) for all X belong to K.

If P is a perfect set and K is compact is the intersection P intersection K always compact?always perfect?.

Let A be an mxn matrix. show that 1) If x Є N(A^TA), then Ax is in both R(A) and N(A^T). 2) N(A^TA) = N(A.) 3) A and A^TA have the same rank. 4) If A has linearly independent columns, then A^TA is nonsingular. Let A be an mxn matrix, B an nxr matrix, and C=AB. Show that: 1) N(B) is a subspace of N(

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I need to know how to find all possible lengths, widths & heights of a given volume of a rectangular prism. I'm writing a program in Java that takes the user inputted volume of a rectangular prism and then tells the user all of the possible lengths, widths & heights are for that given volume. I just don't know the calculations t

If 2400 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume = cubic centimeters.

James wanted a photo frame 3 in. longer than it was wide. The frame he chose extended 1.5 in. beyond the picture on each side. Find the outside dimensions of the frame if the area of the unframed picture is 70 in.^2 (square inch.)

A rectangular building whose depth is twice its frontage is divided into two parts, a front portion and a rear portion, by a partition that is 30 feet from and parallel to the front wall. Identify the front (width) by the letter "x" and write the following: Depth (length) of the building Length of the rear portion Writ

Construction- To construct two angles the same measurement Please construct the following. Please make it large enough. not very small thank you Step1. Draw an acute angle. Label the vertex P. Step 2. Use a straightedge to draw a ray on your paper. Label the endpoint T. Step 3. With P as the center , draw a large arc

A) Reals with the "usual topology." Is there a way to prove this space is normal other than just saying it is normal because every metric space is normal? b) Reals with the "K-topology:" basis consists of open intervals (a,b)and sets of form (a,b) - K where K = {1, 1/2, 1/3, ... } Why connected? Why 2nd countable?

Which of the following topological spaces is normal? a) Reals with the "usual topology." b) Reals with the "finite complement topology:" U open in X if U - X is finite or is all of X. c) Reals with the "countable complement topology:" U open in X if X - U is countable or is all of X. d) Reals with the "lower limit topolog

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#26 Please see the attached file for full problem description. (a) A cylindrical drill with radius r1 is used to bore a hole through the center of a sphere of radius r2. Find the volume of the ring-shaped solid that remains. (b) Express the volume in terms of height (h).

In the taxi-cab plane show that ifA=(-5/2,2),B=(1/2,2), C=(2,2), P=(0,0), Q=(2,1) and R=(3,3/2)then A-B-C and P-Q-R. Show that line segment AB~to line segment PQ,line segment BC~line segmentQR, line segment AC~line segment PR. Sketch an appropriate picture.