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	A bijection from (0,1)x(0,1) to (0,1)		2008-07-20
		From Adam: I'm trying to prove that the function that takes the open square (0,1)x(0,1) to (0,1) is a bijection (and hence a continuum). If we take an element (x,y) of (0,1)x(0,1) and represent (x,y) as (0.x1 x2 x3 x4..., 0.y1 y2 y3 y4...) aka x1 represents the tenths digit of x, x2 represents the hundredths, etc. Then we can define a function f((x,y)) = 0.x1 y1 x2 y2 x3 y3... However, this is not a bijection. I hypothesize this is because you'd be unable to create the number 0.1 as x=0.1 and would have to be y=0, which contradicts the open interval (0,1) defined for y. We have been told though, if we create the same function, except that we "group" 9's with their next digit into a "block" we can create a bijection. For example, if x=0.786923 and y=0.699213, then we define x1 to x3 as normal, but x4= 92, and x5=3. For y, we define y1 as normal, but y2=992, and y3 to y4 as normal. hence f((x,y)) = 0.7 6 8 992 6 1 92 3 3. My questions are a) is my hypothesis on why the original function is not a bijection correct? b) why does the special blocking in the new function make a bijection? Answered by Victoria West.
	A square is inscribed within a square		2008-07-19
		From Shirley: A square is inscribed within a square that has a side the measures 16 centimeters. The vertices of the smaller square are located at the midpoints of the sides of the larger square. What is the area of the larger square, area of a smaller square, the probability that a point chosen at random is in the shaded are? Express the answer as a simplified fraction. Answered by Penny Nom.
	Two numbers		2008-07-19
		From Jerry: while driving in my car early this morning, i 'discovered' something and want to ask if there is an equation that would fit it... Here it goes..... take any two numbers (with the exception of two of the same numbers), multiply the first number by 2, add the difference of the original two numbers, and the outcome will be the same as if you added the original two numbers together... example: 3+5=8... thus, 3+3+(5-3)=8... if you chose to reverse the numbers then..... 5+3=8... thus, 5+5-(5-3)=8 i know, simple stuff.. but i just want someone to tell me what exactly this is.. is there a 'law' that describes this? Answered by Victoria West.
	equation?		2008-07-19
		From Jerry: while driving in my car early this morning, i 'discovered' something and want to ask if there is an equation that would fit it... Here it goes..... take any two numbers (with the exception of two of the same numbers), multiply the first number by 2, add the difference of the original two numbers, and the outcome will be the same as if you added the original two numbers together... example: 3+5=8... thus, 3+3+(5-3)=8... if you chose to reverse the numbers then..... 5+3=8... thus, 5+5-(5-3)=8 i know, simple stuff.. but i just want someone to tell me what exactly this is.. is there a 'law' that describes this? Answered by Victoria West.
	solving four simultaneous equations		2008-07-18
		From Muhammad: -2B-2C+4E=1 A+B+C+D=0 -2B-2C-2D+E=0 B+C+4D-2E=0 Answered by Janice Cotcher.
	Choosing 5 numbers out of 39 numbers		2008-07-18
		From robert: Please list the way I can choose 5 numbers out of 39 numbers, without repeating them, starting at number 1. Please send me a list of all 120 combination. Answered by Harley Weston.
	The height of a triangle		2008-07-18
		From Becc: I have to find the height of a triangle. The base is 3.1cm say ab One of the top sides is 4cm say ca The other side is 2cmsay cb Answered by Penny Nom.
	The cube root of a really big number		2008-07-17
		From Pete: Is the only way to find a cube root of a really big number guess and check, as i read in other questions, or is there another way without a calculator? Answered by Harley Weston.
	Does the sequence 1 2 4 8 16 32 etc have a name?		2008-07-17
		From Richard: Just an idle thought really. Does the simple sequence 1 2 4 8 16 32 etc have a name? Answered by Victoria West.
	Graphing Using Double Angle Identities		2008-07-16
		From Hodan: the Question is: Describe how you could use your knowledge of Double angle formulas to sketch the graph of each function. Include a sketch with your description.A) F(x)=sin x cos x B)F(x)=2 cos(squared)x C) F(x)= tan(x) (divided) by 1-tan(squared) x Answered by Janice Cotcher.
	Rational numbers		2008-07-16
		From hinal: list 12 rational numbers which lie between a) -1 and 0 b) -3 and -3 Answered by Penny Nom.
	The units digit of (7*3)^21		2008-07-16
		From surender: what will be the unit digit of (7*3)^21?plz give me method 2 calculate such problems.thank you. Answered by Penny Nom.
	A cube inscribed in a right cone		2008-07-16
		From Steven: A cube is inscribe in a right cone of radius 2 and height 5. What is the volume of the cone? Answered by Victoria West and Harley Weston.
	1, 2, 4, 8, 16, 32 ...		2008-07-15
		From eve: I have to find out the fomula for: 1, 2, 4, 8, 16, 32 ... Answered by Penny Nom.
	An isosceles triangle inscribed in a circle		2008-07-15
		From Anne: Here is the math problem quoted from book: "An isosceles triangle is inscribed in a circle of radius R, where R is a constant. Express the area within the circle but outside the triangle as a function of h, where h denotes the height of the triangle." Answered by Penny Nom.

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