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Algebraic Geometry

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?


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

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

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


Find equation for hyperbola with center at (4,9); a=5; c=13; traverse axis parallel to the x axis


Find equation for parabola: focus at (11,7) and vertex at (6,7)


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?