School of Mathematics Help Desk

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Welcome to the School of Mathematics Help Desk!


This is the place to ask any questions you have about mathematics, mathematics homework, or anything else math related.

Note: You can use TeX mathematics markup to make formulae easier to read

Contents

[edit] Equal Temperament Question

(Moved to bottom of this page.) StuRat 16:07, 28 May 2007 (UTC)

[edit] Homework Questions

How can N dots be placed on the surface of a sphere, equally distanced or evenly spaced ? What kind of math is needed for this kind of problems ?

What does evenly spaced mean? The simplest example - put them all on the equator. Are you talking about the w:Platonic solids?
Find area of the sphere and divide it by N. If an area element can be devised that has this area with a dot in the middle then you can divide and place dots without pesky off by one errors. Square root of the area element might give an approximatation of the size of the area element. This type of approach is related to limits and calculus. Mirwin 06:23, 20 September 2007 (UTC)

What is a complex plane?

Expanding a bit. A complex number has two components which are different types of numbers. A common representation is a real number plus an imaginary number (a real number multiplied by the square root of minus one or i). The set of complex numbers x + y(i) represented as a plane can be plotted two dimensionally by treating the x as an x coordinate and the y(i) as a y-coordinate. Mirwin 11:41, 25 January 2007 (UTC)
"The" complex plane, rather than "a" complex plane, I'd say better. --Jorge 02:22, 6 February 2007 (UTC)

How do you find the capacity of a cylinder in litres?

The formula for the volume of a right cylinder is V =Ah. That is, the volume equals the area of one of the bases times the cylinder's height. In the case of a circular cylinder, the area of a base is A = πr2. So, the volume of a right circular cylinder is V = πr2h. Now, if you start with radius and height in centimeters, this will give you cubic centimeters. If you start with inches, this will give you cubic inches. The final step is to convert these volume units into liters. This site lists the conversion factors needed: [1]. StuRat 21:13, 17 April 2007 (UTC)

[edit] Petroleum Tank Measuring

How do you know how many gallons are in a petroleum tank that is horizontal ? What is the math equation. Note, I am not a math wizard so please use examples that a lay person can understand.

What shape is the tank? Also, do you have any more details about the tank (for example, do you know the height of the petroleum as measured from the bottom of the tank)? Deltinu 05:04, 19 January 2007 (UTC)

[edit] Interested in Brushing Up, Where Do I Start

I'm interested in brushing up on my math and have "Calculus by Discovery" on loan from a friend. I'm looking for something here that would complement that. I found the Intro to Calculus page very confusing. My question is where do I start, and is there someone to whom I can pose questions or talk to to make sure I'm understanding everything correctly.

Also, on an only tangentially related note, has there been any discussion of a mathematics-through-application course? One that would pose (word) problems and then explain the math in them. I ask because I'm 27 and it took until now for numbers to mean more to me than simply a grade on a report card.

Feel free to pose any question at my Talk Page or just right here. I'll try to answer them to my best. About the course you mention, I don't know if anything has been talked. --Jorge 07:36, 9 February 2007 (UTC)

A section on "Word problems" would be great! Feel to start it or continue asking word problems here. Eventually someone will probably edit the best of this archive into a page such as you suggest. Great idea! Thanks for contributing here. Mirwin 06:27, 20 September 2007 (UTC)

[edit] Equal Temperament Question

Hi, can you outline the steps to get the answer 261.626 by the below equation on a scientific calculator?

P_{40} = 440_{Hz} \times 2^\frac{40-49}{12} \approx 261.626_{Hz}

If possible, using this online calculator: http://www.calculator.com/calcs/calc_sci.html. Thank you.

You can do this, as is, using parens, but it's far easier if you do part of it in your head and/or use the calculator memory (or write down) parts of it. Here are some ways to do it:

Here's the long way:

440 × 2 yx ( ( 40 - 49 ) ÷ 12 ) =

Here's a slightly shorter way (doing the subtraction in your head):

440 × 2 yx ( 9 ± ÷ 12 ) =

Here's an even shorter way (doing the division in your head, too), which eliminates the need for parens:

440 × 2 yx .75 ± =

Note that the ± key is labeled +/- on the calculator at that site, and is located right under the + sign. It toggles the current displayed value between positive and negative. That calculator doesn't appear to do rounding, so you will need to round off to 3 decimal places yourself. StuRat 16:22, 28 May 2007 (UTC)

[edit] Different Fonts

Ergo, g = Ar = Rω2 = L(2π / T)2

  • and T = 2\pi\sqrt(L/g)

Why are the above equations in two different fonts? How can I change the top equation to the font size of the bottom eqation? Calgea 18:17, 28 May 2007 (UTC)

If the equation is simple enough, it will be rendered as HTML. There's an option in your preferences page to change this. You can also force PNG rendering by inserting and removing a space (\,\;) -- take a look: g = Ar = R\omega^2 = L(2\pi/T)^2 \,\;. See also m:Help:Displaying a formula. HTH. --HappyCamper 18:38, 28 May 2007 (UTC)
I agree with the above except you only need the "\;" part. So, this formula:

<math>g = Ar = R\omega^2 = L(2\pi/T)^2 \;</math>

gives you this:

g = Ar = R\omega^2 = L(2\pi/T)^2 \;

StuRat 02:16, 29 May 2007 (UTC)

[edit] Wikiversity Talk: Naming Conventions # Removing Course Numbering Scheme

At "Removing Course Numbering Scheme" Talk #1 & "Removing Course Numbering Scheme" Talk #2 are Discussions in which the Undersigned would wish to have the benefit of the thinking of our Mathematicians. Could some Mathematicians please weigh in on these Discussions. Thank you in advance for your assistance.

Best regards,

(s) Dionysios (talk), a Participant in the Wikiversity School of Advanced General Studies, Date: 2007-07-23 (July 23, 2007) Time: 1859 UTC

[edit] constant growth

how does this happen:

  • V_0=\frac{D_0(1+g)}{(1+k)}+\frac{D_0(1+g)^2}{(1+k)^2}+...+\frac{D_0(1+g)^n}{(1+k)^n}

simplifies into this:

  • V_0=\frac{D_0(1+g)}{k-g}

what's the rule or whatever? thanks.

-kv2 00:00, 27 August 2007 (UTC)

[edit] Power series

See w:Power series. Is this a homework problem?

\sum_{n=0}^{\infty} x^n = \cfrac{1}{1-x} \quad \text{for}~ |x| < 1

If you case, assuming that n \rightarrow \infty and g < k you get a series

\cfrac{D_0(1+g)}{1+k} \sum_{n=0}^{\infty} x^n

where

x := \cfrac{1+g}{1+k}

You result follows after a another step of algebra. -- Banerjee 02:13, 27 August 2007 (UTC)

[edit] These 2 phrases are equivalent?

Given that f(x) is a boolean function, if

g(x) \in \mathbb{R} \implies f(g(x))

Can we imply the following phrase?

x \in \mathbb{R} \implies f(x)

Are they equivalent? --Ans 11:19, 23 February 2009 (UTC)

Yes if g is sujective.

With, g(x) \in \mathbb{R} \implies f(g(x)) (1) and y \in \mathbb{R} \implies f(y) (2)

Indeed, to prove (2) from (1) : if g is surjective, for any y you can find an x such that y = g(x) then apply (1).

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