Need help with math problem

[midhvac]

In this formula b = 6

a = (2 x 20^4) / b^6
So the answer is 6.8587

If I already knew that a = 6.8587, and b was the unknown, how would I solve that problem so that the answer to b didn't come out in exponential form. I mean, so that the answer would come out as "6" instead of something to the something power?

If it did come out as something to the something power, how would I convert that to a regular number?

[coolwhip]

Holy cow...your asking me to remember my pre calculus days. When your trying to solve to that power things get tuff. Well, I will tell you right now Im not going to do it!





































Im glad thats over.

[condenseddave]

Mid-

You are going to sprain your brain if you keep this up.

[westcoast refer man]

midhvac,

Do the basic algebra and up end up with:

b=(2x20^4/a)all raised to the 1/6

You need a scientific calculator to get what b is. That is, 46656.07 ^1/6

plug in all the numbers and the answer is 6.

Is this what you were asking?

[Andy Schoen]

Originally posted by midhvac
In this formula b = 6

a = (2 x 20^4) / b^6
So the answer is 6.8587

Perhaps some number theory may be appropriate here.

'a' in this example is equal to exactly 320,000 / 46,656 or approximately 6.85871056241426611796982167352538 (using Microsoft calculator )

'a' is considered a 'rational' number because it can be wriiten as a fraction, i.e., x / y where x and y are integers.

Originally posted by midhvac

If I already knew that a = 6.8587, and b was the unknown, how would I solve that problem so that the answer to b didn't come out in exponential form. I mean, so that the answer would come out as "6" instead of something to the something power?

Ok, lets assume 'a' = 7, what is 'b'?

b = (320,000 / 7)^(1/6)

where 'b' is approximately 5.979643919487405903197485402773 (again using Microsoft calculator)

In this case, 'b' is an irrational number. There is no fraction, x / y, that can define 'b' where x and y are integers. Think about it! No integer numbers whatsoever. Raising this expression to the 1/6th power causes this to occur.

Mmmmm... so does this help?

[midhvac]

You guys rock! Thanks! I've got a scientific calculator and the 1/6 power works.

[midhvac]

Originally posted by condenseddave
Mid-

You are going to sprain your brain if you keep this up.

Nah, I put an elastic support around my head, just in case.

[midhvac]

Hey! Wait a minute! Why are we using 1/6? Is it because the answer to b is 6? So I have to know the answer before I can work the problem?

[Andy Schoen]

Originally posted by midhvac

Originally posted by condenseddave
Mid-

You are going to sprain your brain if you keep this up.

Nah, I put an elastic support around my head, just in case.

Let's put that elastic support to work...

Using your calculator, solve the following:

x^3 = x * x * x = -27

or x = (-27)^(1/3)

A little figuring will show that 'x' must equal -3, i.e., -3 * -3 * -3 = -27

Why does the calculator fail to figure this out?

[Andy Schoen]

Originally posted by midhvac
Hey! Wait a minute! Why are we using 1/6? Is it because the answer to b is 6? So I have to know the answer before I can work the problem?

Nope. Using apropriate math:

a = (2 x 20^4) / b^6

a = 320,000 / b^6

b^6 = 320,000 / a

(b^6)^(1/6) = (320,000 / a)^(1/6)

b = (320,000 / a)^(1/6)

[ac rookie]

I think I am going into another field. I will never figure this stuff out!!!

[mattm]

You big bunch of math nerds.

[glennwith2ns]

Originally posted by mattm
You big bunch of math nerds.

Yea , bet they got pocket protectors too>)

[midhvac]

Thanks again Andy. I got it now. The reason for my questions was that I was trying to figure out how the different ductulator formulas work so I could use my scientific calculator to do them, or plug them into an Excel spreadsheet application. Somebody else here was asking about the formulas a while back, but nobody knew them. I found a formula that calculates the pressure drop per 100' when the cfm and duct diameter are known:

pd = (.109136 x CFM^1.9)/dia^5.02

But I wanted to know how to find the diameter when CFM and pd are known. With your help, I've got it now. My $8.99 Casio scientific calculator won't allow me to use a decimal point in a fractional exponent, so I couldn't do ^1/5.02. So I just changed it from a fraction to a decimal equivalent of .1992

dia = (.109136 x CFM^1.9/pd)^.1992

[Steve Wiggins]

I guarantee you this will seperate the Dems from the Repubs right quick. We will always have the thinkers vs. the doers.

[Andy Schoen]

Originally posted by midhvac
But I wanted to know how to find the diameter when CFM and pd are known. With your help, I've got it now. My $8.99 Casio scientific calculator won't allow me to use a decimal point in a fractional exponent, so I couldn't do ^1/5.02. So I just changed it from a fraction to a decimal equivalent of .1992

dia = (.109136 x CFM^1.9/pd)^.1992

You've got the idea.

If I'm reading your equation correctly (I really should look it up), you can get precise answers doing the following on your Casio:

calculate A:

A = CFM^1.9

next B:

B = .109136 x A /pd

next C:

C = LN(B) this is the natural log of B (I'm assuming the Casio has log functions)

next D:

D = C / 5.02

finally E:

E = exp(D) this is the e^x function which is inverse to the natural log

[Andy Schoen]

Originally posted by glennwith2ns

Originally posted by mattm
You big bunch of math nerds.

Yea , bet they got pocket protectors too>)

And only the best pocket protectors... We're still trying to figure out where to put that Parker name on them...

[condenseddave]

Originally posted by Andy Schoen

Originally posted by glennwith2ns

Originally posted by mattm
You big bunch of math nerds.

Yea , bet they got pocket protectors too>)

And only the best pocket protectors... We're still trying to figure out where to put that Parker name on them...

Do me a favor-------------DON'T put it on there.

[condenseddave]

Originally posted by Steve Wiggins
I guarantee you this will seperate the Dems from the Repubs right quick. We will always have the thinkers vs. the doers.

Are you lost again, buttcheek?

[condenseddave]

Originally posted by ac rookie
I think I am going into another field. I will never figure this stuff out!!!

It's not hard. Actually, to accomplish what Mid wants to accomplish, you spend fifty bucks on a ductulator that does this FOR you...