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.
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?
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.
Mid-
You are going to sprain your brain if you keep this up.
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?
Perhaps some number theory may be appropriate here.Originally posted by midhvac
In this formula b = 6
a = (2 x 20^4) / b^6
So the answer is 6.8587
'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.
Ok, lets assume 'a' = 7, what is 'b'?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?
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?
You guys rock! Thanks! I've got a scientific calculator and the 1/6 power works.
Nah, I put an elastic support around my head, just in case.Originally posted by condenseddave
Mid-
You are going to sprain your brain if you keep this up.
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?
Let's put that elastic support to work...Originally posted by midhvac
Nah, I put an elastic support around my head, just in case.Originally posted by condenseddave
Mid-
You are going to sprain your brain if you keep this up.
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?
Nope. Using apropriate math: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?
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)
I think I am going into another field. I will never figure this stuff out!!!
You big bunch of math nerds.
Yea , bet they got pocket protectors too>)Originally posted by mattm
You big bunch of math nerds.
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
I guarantee you this will seperate the Dems from the Repubs right quick. We will always have the thinkers vs. the doers.
"And remember my sentimental friend......that a heart is not judged by how much you love, but by how much you are loved by others" - Wizard of Oz.
You've got the idea.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
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
And only the best pocket protectors... We're still trying to figure out where to put that Parker name on them...Originally posted by glennwith2ns
Yea , bet they got pocket protectors too>)Originally posted by mattm
You big bunch of math nerds.
Do me a favor-------------DON'T put it on there.Originally posted by Andy Schoen
And only the best pocket protectors... We're still trying to figure out where to put that Parker name on them...Originally posted by glennwith2ns
Yea , bet they got pocket protectors too>)Originally posted by mattm
You big bunch of math nerds.
Are you lost again, buttcheek?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.
It's not hard. Actually, to accomplish what Mid wants to accomplish, you spend fifty bucks on a ductulator that does this FOR you...Originally posted by ac rookie
I think I am going into another field. I will never figure this stuff out!!!