Wikipedia:Reference desk/Archives/Mathematics/2008 January 8

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[edit] January 8

[edit] Algebra Question

Hey,It`s Me The Physics Magazine guy only this time I`ve got an algebra question for you,from an algebra magazine.Well,several acutually.

The lateral area of a right prism,is the sum of the lateral area of two bases.

The lateral area of a right cylinder is the product of the circumference of the base and the height of the cylinder.The surface area is the sum of the lateral area and the areas of the two bases.

The lateral area of a regular pyramid is half the product of the perimeter of the base and the slant height.The surface area is the sum of the lateral area and the area of the base.

The lateral area of a right cone is half of the product of the circumference of the base and the slant height.The surface area is the sum of the lateral area and the area of the base.

Also,the problem from the magazine says you need a calculator to find the lateral aea and surface area of each figure,the figures are a cone,a pyramid an upside down cone,And another pyramid that is 10 meters to 16 meters long.

The next page says the volume of a space figure is the space that the figure occupies.Volume is measured in cubic units.

The volume of a prism is the product of the area of a base and the height of the prism. The volume of a cylinder is the product of the area of a base and the height of the cylinder.

Find the volume of each figure.You may leave answers in terms of pie.[I APOLGIZE,I DON`T HAVE MATHEMATICAL SYMBOLS ON MY COMPUTER.]

Number 14 is a box,number 15 is a cylinder,number 16 is a long box,number 17 is another cylinder lined across.

I have to compare the finding of the volume and the surface area of the prism.What are,the similarites and differences.

The volume of a pyramid is one third the product of the areaof the base and the height of the pyramid.

The volume of a cone is one third the product of the area of the base and the height of the cone.

I also,have to find the volume of a cone two pyramids 7ft to 8 ft wide,2m to 3m and one last one 8cm to 12 cm.

I also have to find the surface area and volume of a sphere with the given radius or diameter.Round answers to the nearest tenth.

A composite space figure combines two or more space figures.The volume of a composite figure is the sum of the volumes of the combined figures.

Find the volume of each figure.When an answer is not a whole number,round to the nearest tenth.

Also,in the magazine I have darts that are thrown at random at each of the boards shown.If a dart hits the board,find the probability that It will land in the shaded area.I have a pyramid,in which the left side is have shaded,a square in which two halves are shaded,and a circle in which there is a shaded triangle. —Preceding unsigned comment added by 68.161.74.60 (talk) 01:43, 8 January 2008 (UTC)

  1. Your question will be easier to read if you divide it to paragraphs (using an extra blank line).
  2. If you can edit Wikipedia with your computer, you can write mathematical symbols with it. Writing &pi; will give π; Writing <math>\pi</math> will give π; and below the edit box, there should be a collection of symbols, one of them is the greek letter π (and anyway, it's Pi, not pie).
  3. There is no such thing as the "lateral area of a base", hence the lateral area of a right prism is not "the sum of the lateral areas of the two bases". Rather, it is the product of the perimeter of a base and the height.
-- Meni Rosenfeld (talk) 08:40, 8 January 2008 (UTC)

Exciting algebra magazine PMajer (talk) 17:02, 8 January 2008 (UTC)

  • Tried to format the question with additional line breaks. --CiaPan (talk) 12:32, 10 January 2008 (UTC)

[edit] Numerals and numbers

what is the difference betweenthem?Invisiblebug590 (talk) 09:07, 8 January 2008 (UTC)

Both "numeral" and "number" can mean different things, so this is not easy to answer. Essentially, a "number" is an abstract entity used to describe some quantity, while "numeral" is a written symbol used to refer to numbers. Usually "numeral" just means "digit", such as "1", "3" or "7". More generally, the string of symbols "38" or words "thirty-eight" might also be called numerals. The number is the abstract concept referred to by those symbols. -- Meni Rosenfeld (talk) 09:21, 8 January 2008 (UTC)
To further sharpen this: "38", "thiry-eight", "XXXVIII" and "٣٨" are different numerals. But they all describe the same number. -- Meni Rosenfeld (talk) 13:59, 8 January 2008 (UTC)
See also numeral and number. PrimeHunter (talk) 15:29, 8 January 2008 (UTC)

[edit] A problem from Diophantus: Missing a step in understanding the solution

[This is part of Problem 1.2 in Invitation to the Mathematics of Fermat-Wiles] Find two (rational) numbers such that the square of each of them, augmented by the sum of these two numbers, forms a square.

Diophantus provided this solution:

We assume that the smallest number is x and the largest x+1, so that x2+(2x+1)=₳. But we also need (x+1)2+(2x+1)=₳. We set.
x2 + 4x + 2 = (x − 2)2
and find (1/4, 5/4).

Where I'm stumped is where does x2 + 4x + 2 = (x − 2)2 come from? The left hand side is the expansion of (x+1)2+(2x+1), but why is the right hand side (x − 2)2? 68.183.18.54 (talk) 17:53, 8 January 2008 (UTC)

I don't think it comes from anywhere. We just want x2 + 4x + 2 to be a square, so we arbitrarily choose it to be (x − 2)2. We could just as well take (x − 3)2 and get (0.7, 1.7). The choice of the numbers being x and x + 1 is likewise arbitrary. -- Meni Rosenfeld (talk) 19:01, 8 January 2008 (UTC)
I know it's not really relevant, but after digging into the Unicode charts (since my browser won't display it), I'd just like ask why you're using the symbol for a former currency of Argentina in your equation? —Ilmari Karonen (talk) 21:31, 8 January 2008 (UTC)
Because it looks like a square. 68.183.18.54 (talk) 21:57, 8 January 2008 (UTC)
Not quite, your browser just displays a square when it doesn't recognize the character. If you don't have the proper fonts installed this will happen with many characters.
You can display a square in LaTeX using \Box. -- Meni Rosenfeld (talk) 22:18, 8 January 2008 (UTC)
Or in Unicode text using □ (U+25A1, WHITE SQUARE). —Ilmari Karonen (talk) 22:46, 8 January 2008 (UTC)
Ah, I couldn't remember \Box, which is the bigger part of why I picked that character. I hadn't realized that I was grabbing an inappropriate symbol out of the symbols list... oops. 68.183.18.54 (talk) 00:15, 9 January 2008 (UTC)
Thanks for this comment -- I was thinking that my browser was messed up, because it was displaying currency symbols where I knew they shouldn't be... =) Tesseran (talk) 03:18, 10 January 2008 (UTC)