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# Algebraic Geometry

### 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

### Sixth Term of Geometric Series

Determine the sixth term of geometric series a1 = -2, r = 2

### 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?

### Geometric Means Found

Insert 3 geometric means between 9 and 1/9.

### Hyperbola Equation Centers

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

### Parabola Equation Calculus

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

### Square area: What are the sides?

If the square area of an equal sided square is 144 ft sq. What are the sides?

### Enlargement

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?