## Search found 74 matches

- Thu Feb 21, 2008 7:28 pm
- Forum: Number
- Topic: Calculus with variating limits
- Replies:
**1** - Views:
**1446**

### Calculus with variating limits

The equation y = 3^x yielded 2a+3 for some x. What would it have yielded had we done y = 3^(x+2)? I'm curious as to how someone solves this normally... I have my own way revealed below. 54a+81 The answer comes from something I've been working which is related to calculus but instead of the limit of ...

- Fri Feb 08, 2008 5:55 pm
- Forum: Number
- Topic: Integration problem
- Replies:
**18** - Views:
**4642**

### Re: Integration problem

I agree with hk : the problem is not well defined... If the pipe is only one foot long does that mean we are looking at the work required to reduce the depth of the water from 2 feet to 1 foot? In which case, is the pipe fixed at an initial depth of one foot and suction maintained until the depth d...

- Wed Feb 06, 2008 9:06 pm
- Forum: Number
- Topic: Integration problem
- Replies:
**18** - Views:
**4642**

### Re: Integration problem

So far I have

W = F * D

Total Work = WorkByOutlet + WorkThroughTank

WorkByOutlet = ÃƒÂÃ¢â€šÂ¬r^2 / 2 * 8 * 62.5 * 1 ft = 16ÃƒÂÃ¢â€šÂ¬ * 62.5 = 1,000ÃƒÂÃ¢â€šÂ¬ ft lbs

Now I just need to set the work through the tank which is some integral...

W = F * D

Total Work = WorkByOutlet + WorkThroughTank

WorkByOutlet = ÃƒÂÃ¢â€šÂ¬r^2 / 2 * 8 * 62.5 * 1 ft = 16ÃƒÂÃ¢â€šÂ¬ * 62.5 = 1,000ÃƒÂÃ¢â€šÂ¬ ft lbs

Now I just need to set the work through the tank which is some integral...

- Wed Feb 06, 2008 8:53 pm
- Forum: Number
- Topic: Integration problem
- Replies:
**18** - Views:
**4642**

### Re: Integration problem

Yeah that's why I don't get it... It was "Find the work required to pump the water out of the 1 ft outlet at the top of the tank. Use the fact that water ways 62.5 pounds per cubic foot." Then it shows the semi-circle trough with diameter 4 ft, and length 8 ft.

- Wed Feb 06, 2008 8:43 pm
- Forum: Number
- Topic: Integration problem
- Replies:
**18** - Views:
**4642**

### Re: Integration problem

So I need to integrate with "slices" going up right? The top slice will essentially be 4 ft times 8 feet times some small change in x, then the bottom slice will be essentially nothing... But how do I multiply the work in there, can I do the one foot spout part all at once then add it to the work of...

- Wed Feb 06, 2008 8:34 pm
- Forum: Number
- Topic: Integration problem
- Replies:
**18** - Views:
**4642**

### Re: Integration problem

Oh thanks for some reason I kept trying to throw an extra t down there when I integrated.. ~~~~~ One other one I'm stuck on is how much work it takes to pump water out of this tank with a one foot pipe. The trough-like tank is a semicircle (diameter 4 ft) and length 8 ft. They tell me the weight of ...

- Wed Feb 06, 2008 8:28 pm
- Forum: Number
- Topic: Integration problem
- Replies:
**18** - Views:
**4642**

### Re: Integration problem

but I'm not sure how to integrate the pieces if I do it the other way... What's the integral of e^-2t? Is it -1/2 t e^-2t ???

- Wed Feb 06, 2008 8:23 pm
- Forum: Number
- Topic: Integration problem
- Replies:
**18** - Views:
**4642**

### Integration problem

I got stuck on integrating this problem and was wondering if someone could help me out... ÃƒÂ¢Ã‹â€ Ã‚Â«Ãƒâ€šÃ‚Â t^3 * e^ -2t dt I tried integration by parts u = 1/4 t^4 du = t^3 v = e^-2t dv = -2e^-2t Then using the rule ÃƒÂ¢Ã‹â€ Ã‚Â«du v = uv - ÃƒÂ¢Ã‹â€ Ã‚Â«dv u so... ÃƒÂ¢Ã‹â€ Ã‚Â« (t^3 * e^ -2t) d...

- Sat Jan 19, 2008 7:49 pm
- Forum: Recreational
- Topic: Math Jokes
- Replies:
**10** - Views:
**5908**

- Sat Jan 19, 2008 7:44 pm
- Forum: Geometry
- Topic: Integrating Absolute Values
- Replies:
**7** - Views:
**5740**

### Re: Integrating Absolute Values

Well all of the cases I'm doing this are actually definite integrals, so I was wondering if the other way would work. Integral from (-2 to 4) of |x^2 - x - 3| would that equal (x^2 - x - 3)(|x^2 - x - 3|)(2x - 1)/2 taken {-2, 4} based on: Integral of |x| is = to x|x|/2 so the integral of |f(x)| dx =...

- Sat Jan 19, 2008 3:15 am
- Forum: Geometry
- Topic: Integrating Absolute Values
- Replies:
**7** - Views:
**5740**

### Integrating Absolute Values

Integral of |x^2 - x - 3| dx. Is there any way to do these?

I know that Integral of |x| is = to x|x|/2 so would the integral of |f(x)| dx = f(x)|f(x)|* f'(x)/2 ???

This is related to area between to functions being that it's the integral of |f(x) - g(x)|.

I know that Integral of |x| is = to x|x|/2 so would the integral of |f(x)| dx = f(x)|f(x)|* f'(x)/2 ???

This is related to area between to functions being that it's the integral of |f(x) - g(x)|.

- Fri Jan 11, 2008 3:33 pm
- Forum: Applied Mathematics
- Topic: Ternary Operators
- Replies:
**2** - Views:
**2756**

### Re: Ternary Operators

I had nothing too specific in mind... at least not yet. just curiosity. Perhaps for the sport of it - we could work on some ternary group theory here! Now that I think about it, the identity could be local, binary, or global. Let's use addition as a ternary operator due to familiarity. +(1, 2, x) In...

- Thu Jan 10, 2008 10:41 pm
- Forum: Applied Mathematics
- Topic: Ternary Operators
- Replies:
**2** - Views:
**2756**

### Ternary Operators

I'm familiar with the rules of group theory for binary operators. Identities and inverses yadda yadda... But I'm curious as to the systematics of ternary group theory and was curious if anyone had info. Like how does an identity work in ternary... is there more than one type of identity? Like given ...

- Sun Jan 06, 2008 4:42 am
- Forum: Number
- Topic: The greater of two.
- Replies:
**23** - Views:
**7026**

### Re: The greater of two.

What I really need is a pure math function that does this. (absolute values are ok)

If a = 0 then c = anything but 0

Else if a = 'a number other than 0' then c = a

Once I can do that... the world will explode... or something...

If a = 0 then c = anything but 0

Else if a = 'a number other than 0' then c = a

Once I can do that... the world will explode... or something...

- Thu Jan 03, 2008 8:35 am
- Forum: Number
- Topic: The greater of two.
- Replies:
**23** - Views:
**7026**

### The greater of two.

( a + b + |a - b|) / 2 = c With any values for a and b, c will evaluate to be equal to the larger of the two. It's a nice trick when you have two variables and you need to use the bigger one but you're not sure which one it is. Also avoids the conditional statements for programming. Just thought it ...

- Sun Dec 02, 2007 10:47 pm
- Forum: Number
- Topic: Superincreasing Sequences
- Replies:
**6** - Views:
**2409**

### Re: Superincreasing Sequences

That's EXACTLY what I was looking for! Thanks rayfil and henk!

- Tue Nov 27, 2007 3:34 am
- Forum: Number
- Topic: Superincreasing Sequences
- Replies:
**6** - Views:
**2409**

### Superincreasing Sequences

So anyways the smallest super increasing sequence of the integers are spawned from 2^n, 1, 2, 4, 8, 16, 32... such that the sum of all previous terms is less than the next term My question is I have 3^n, what's the smallest n can increment such that it still creates a super increasing sequence. 3^k(...

- Sun Oct 28, 2007 7:26 am
- Forum: Number
- Topic: Tricky Census Problem
- Replies:
**3** - Views:
**1928**

### Tricky Census Problem

A Census-taker stopped at a lady's house and wanted to find out how many children she had. The lady, a math teacher, wanted to see if the Census-taker still knew his math. Census-taker to lady: How many children do you have? Lady: Three. Census-taker: How old are they? Lady: the product of their age...

- Fri Oct 12, 2007 10:12 pm
- Forum: Number
- Topic: Modular Arithmetic over R
- Replies:
**5** - Views:
**2740**

### Modular Arithmetic over R

Let Modular arithmetic be defined over R. And a (mod b) has an integer solution from [0,b). 42.3636363636...(mod 10) = 7 How is this justified? Let it be known a x (mod x-1) = digital root of a ; **Note this as "Definition of True Modulus" Ex: 124 (mod 9) = 7 because 1+2+4= 7 OR Ex: 124,000,000,000 ...

- Wed Oct 10, 2007 4:24 pm
- Forum: Applied Mathematics
- Topic: A little calculus help
- Replies:
**3** - Views:
**10076**

### A little calculus help

Okay so I have two problems in calc that I need a little help with. If you put solutions, please put in the hide tags, clues and tips can be left open. I prefer solutions for checking my work rather than using them to get answers, otherwise I would be screwed on the quiz haha ~Thanks 1. Differntiate...