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Algebraic Geometry

Series problem

I got a answer but it didn't make sense here is my question again. A farmer is going to grant a sales man a reward for good work. So, the salesman said, "If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the th

Geometric Series and Sums : Checkerboard Story Problem - Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the ....

CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter's life. Mr. Brown

Geometric series: Good learning

Use the geometric series of numbers 1, 2, 4, 8,...to find the following: What is r, the ratio between 2 consecutive terms? Can you please show how you get the answers in detail to help me Thanks. Using the formula for the nth term of a geometric series, what is the 24th term? Using the formula for the sum of a geometr

Path components

(See attached file for full problem description with proper symbols and equations) --- Let X be a topological space. Mapping a point to the path component which contains x establishes a map . Show that for any continuous map between topological spaces, there exists a map such that the following holds: ? ? for two co

Dual Space and Isometrically Isomorphic Spaces

Let c be the set of all sequences *see attachment* , such that limit alpha_n exists. Let be the dual space of c , and c consist of all functions f -> F, F or such that for every e>0 {n E : |f(n)| >E} is finite. Show that c* is isometrically isomorphic to l'. Are c* and c isometrically isomorphic? Please see the att

Homomorphisms, Bijection Map and Continuous Map

1) Prove that the map GIVEN BY is a homomorphism between the real line and open interval (-1,1). 2) Let be the map given by a) show that f is a bijection map b) show that f is a continuous map c) If f a homomorphism? Justify your answer. Please see the attached file for the fully formatted problems.

Multipliers and Geometric Series: Application to U.S. Economy

Suppose that, throughout the U.S. economy, individuals spend 90% of every additional dollar that they earn. Economists would say that an individual's marginal propensity to consume is 0.90. For example, if Jane earns an additional dollar, she will spend 0.9(1)=$0.90 of it. The individual that earns $0.90(from Jane) will spend

Infinite Series: Geometric Progression

Summation of series from n=2 to infinity of (pi/4)^(n/2) I don't know if I should set the whole thing up as a power of e and then calculate it, or calculate it as geometric series.

Dimensions of the building

Three buildings abut as shown in the diagram below. What are the dimensions of the courtyard and what is the perimeter of the building? See attachment for diagram

Sum of infinite geometric series

A regular hexagon is inscribed in a circle of radius 100. The area of that hexagon outside the square is shaded. Another circle is inscribed in the hexagon, and hexagon is inscribed in the second circle. The area of the second circle which lies outside the hexagon is shaded. This process continues to infinity. What is the

Function Terminology of 'Onto' and 'One to One'

Assume f:A->B and g:B->C. a) Show that if f and g are both onto, then g o f is onto b) Show that if g o f is one-to-one, then f is one-to-one c) Show that if g o f is onto and g is one-to-one, then f is onto

Infinite Geometric Series: Square Inscribed in Circle Radius

A square is inscribed in a circle of radius 100. The area of that circle which lies outside of the square is shaded. Another circle is inscribed in the square, and then a second square is inscribed in that second circle. The area of the second circle which lies outside of the second square is shaded. This process is continued t

Volume and water displaced.

When a chunk of iron is completely submerged into a cylindrical tank of water, the water rises 6 inches. The diameter of the tank is 18 inches. What is the volume of the chunk of iron?

Find the location of a pole in a rectangle.

Johnny green has a rectangular piece of ground. He places a pole in the gound five feet from the upper right corner. The same pole is nine feet from the lower right corner. It is also thirteen feet from the lower left corner. How far is the pole from the upper left corner?

Annulus: X and Y cannot be Homomorphic

24. Let X,Y be the subspace of the plane shown as below. Under the assumption that any homomorphism from the annulus to itself must send the points of the two boundary circles among themselves, argue that X and Y cannot be homomorphic. (Question is also included in attachment).

Metric space

Let X be a metric space and x0 in X. Define a function f: X --> R (all real numbers) by f(x) = d(x,x0). Show that f is continuous. HINT: Prove the variant of the triangle inequality which says |d(x,z)-d(y,z)|< d(x,y) for any x,y,z in X


Note: C = containment int = interior ext = exterior cl = closure Could you please prove if S C T, then a)int(S) C int(T) b)ext(T) C ext(S) c)cl(S) C cl(T)

Geometric and arithmetic series, pulleys in parallell

Resistances in series can be reduced to a unique resistance R such that eq(1) R= r1 + r2 +...+ rn in Parallel , we have eq (2) 1/ (1/r1 +1/r2 +...+ 1/rn) For the pulleys , to reduce the effort to keep a block and tackle (which has a mass M at he end) in equilibrium , the necessary force F to

Urysohn's Lemma for Normal Spaces

A Hausdorff space is said to be completely regular if for each pt. x in X and closed set C with x not in C, there exists a continuous function f: X --> {0,1} s.t. f(x)=0 and f(C)={1}. Show that if a space is normal, it is completely regular. How do I use Urysohn's lemma along with Hausdorffiness to show this. Thank

Scale Model Mercury

I have a model of Mercury that is 5 inches in diameter the actual diameter is 4880 km. What is my scale?


Phil and Fran are photographers who develop their own pictures and also restore old photographs. They have an enlargement and reducing machine that can change the size of photographs. A customer asks Fran to enlarge a 3 inch by 5 inch photograph to 8 inch by 10 inch. Can this be done without cutting or distorting the picture?