2nd order differential equation...anyone?

[Aliensanctuary]

Using Aubrey's link to the Excel Tank Calculator worksheet, I can see that the tank must be longer than 20 feet since it is supposed to be a 10,000 gallon tank. I'd like to compare Robert's solution to the Excel worksheet, but I forgot how to do the arc-cos or inverse cos.

With this info I can determine how much water a tank of gas in a generator connected to a submersible pump will pump into the tank, and, how much water a tenant uses if I were down there to measure the change in water depth, or, check for leaks in the system.

Although we live in a small town now, we did live at the property off the grid for about 10 years. Since that time I installed a water-wheel pump which worked very well at keeping the tank full to overflowing. It's no longer in use, so the tenants have to use the generator down at the creek to pump water into the tank.

I am humbled to be in the presence of mathematical greatness.

[Robert]

2 hours ago, Aliensanctuary said:

I'd like to compare Robert's solution to the Excel worksheet, but I forgot how to do the arc-cos or inverse cos.

In Excel place the following command in a cell: =ACOS()

 

[Robert]

2 hours ago, Aliensanctuary said:

 

I am humbled to be in the presence of mathematical greatness.

Not I, but Christ.  I do not want to glory in my abilities, although my fallen nature loves it.

I was told by my 3rd grade elementary teacher that I would never understand math...never!  I failed high school algebra because I wasn't the least bit interested.  "Who uses this stuff?"

 Too busy with my head in the clouds.  

Robert

[Robert]

Really, it's a bit more complicated than I originally thought. My original equation is only true for the following inequality: 0<=X<=4 

If X is greater than 4 (i.e., more than half full) then we need a second formula.  The inequality then becomes 4<=x+4<=8  

Here's what the second formula looks like: 

V = 8Pi + 20[16*arcCosine(X/4) - X[(4+x)(4-X)]^1/2]

This would be best used in an Excel format.  

 

 

 

[Robert]

Okay, I used excel.  See format:

 

[Robert]

Per your specs "X" (cell: F3) is a vertical, linear distance between and including 0 to 8 ft., i.e., [0,8].

Here are what the cells I3, I4 and I5 look like, respectively:

=IF(F3<4,7.4805*20*16*ACOS((4-F3)/4)-(4-F3)*SQRT(F3*(8-F3)),"")

=IF(F3=4,7.4805*20*0.5*PI()*F3*F3,"")

=IF(F3>4,20*7.4805*(16*((PI()/2)-ACOS(F4/4))+F4*SQRT(16-F4*F4)+8*PI()),"")

BTW, cell F4 is hidden.  The data there is: =IF(F3>4,F3-4)

 

[Robert]

On 6/18/2016 at 1:07 PM, Robert said:

=IF(F3>4,20*7.4805*(16*((PI()/2)-ACOS(F4/4))+F4*SQRT(16-F4*F4)+8*PI()),"")

When X > 4 ft

 

[Robert]

On 6/18/2016 at 9:55 AM, Robert said:

I failed high school algebra because I wasn't the least bit interested.  "Who uses this stuff?"

Anyway, I was one of those who had no use for advanced math.  One reason was my teachers never gave me a practical reason to learn the stuff.  Things change.  Now I analyze electronic drawings for component level repair.  For this one needs algebra, trigonometry and some basic calculus (including differential equations).  

Here's a sample of what I do:

 

On this unit I needed to know the phase shift and amplitude of the output of op-amp AO1.  The below is the computation:

[Outta Here]

Well then....you SHOULD remember that stuff. 

[Robert]

4 hours ago, Aubrey said:

Well then....you SHOULD remember that stuff. 

Yes, but why take it if you aren't going to use it?  Because that's how colleges make money.  They sell info....

At the end of the day "cramming, memorizing, regurgitating, and forgetting" just doesn't make it....

[Outta Here]

Well, I took it because I enjoyed it. I don't use it in my daily work. I've been a substitute teacher, after-school caregiver, babysitter, accountant, tax preparer, lawn mower, homeschooler, robotics club mentor, Pathfinder leader, Sunday School teacher, Sabbath School teacher, caregiver for elderly and stroke victims, College Algebra instructor and a lunch lady. The only time I ever needed to know Calculus was when I helped my kids do their homework. Now...one of them WILL use it on a daily basis (my actuary daughter, and the other WILL use it on an ocassional basis (my draftsman son). I'd say the best use of my Associates in Math was to encourage others to stay the course....you never can tell where your education will take you.

[Aliensanctuary]

Quote

Now I analyze electronic drawings for component level repair.  For this one needs algebra, trigonometry and some basic calculus (including differential equations).  

That sounds like a fun job.

I studied for a year to be a laser technician, which is mainly about electronics, but lost interest in that as a career so I dropped out. I've always been interested in math and science, but not sports.

[Robert]

On 6/18/2016 at 1:07 PM, Robert said:

=IF(F3<4,7.4805*20*16*ACOS((4-F3)/4)-(4-F3)*SQRT(F3*(8-F3)),"")

=IF(F3=4,7.4805*20*0.5*PI()*F3*F3,"")

=IF(F3>4,20*7.4805*(16*((PI()/2)-ACOS(F4/4))+F4*SQRT(16-F4*F4)+8*PI()),"")

Really, you need just two "If" statements. The middle one can be deleted. Then change the last to this:

=IF(F3=>4,20*7.4805*(16*((PI()/2)-ACOS(F4/4))+F4*SQRT(16-F4*F4)+8*PI()),"

 

[Robert]

See:  https://www.yahoo.com/style/lot-people-having-trouble-math-161950574.html

[Bravus]

I'm about to teach a series of classes for teachers of junior high science who want to be senior high science teachers. One of the challenges is that this kind of math really should be second nature, as it is to me... and in some cases it isn't.

[Gregory Matthews]

I came up with the wrong answer of 3.

[Outta Here]

That's an easy one. Get it...one. LOL (I crack myself up sometimes.)

[Gregory Matthews]

Well, I suppose I could respond by stating that I would edit it by taking the "p" out of woman.  But it I were to do that you might  just laugh harder. 

 

[Outta Here]

I don't understand. To be honest, I don't understand a lot of the things you post. I don't mean to be rude, but I think it best for me to simply not respond to your posts, Greg. If you don't see a response from me, it's because I no longer will see your words.

[Robert]

11 hours ago, Aubrey said:

That's an easy one. Get it...one. LOL (I crack myself up sometimes.)

Apparently 60% can't get it....Anyway.

[Gregory Matthews]

Aubrey,  I took no offense at your post.  My response was simply joining with you in a good laugh, I thought.

Well, my wife tells me that I have a dry sense of humor that people sometimes do not understand.

[Gregory Matthews]

Now I am confused!  I think that  my response about taking the "p" out of women was placed in the wrong thread.  It was in response to a typo where I had spelled "woman" with a "p" inserted in the word.  Someone commented on my typo.  Perhaps it was Aubrey.  Perhaps it was someone else.  In what I considered to be the same spirit as the person who commented on my typo, I responded with a post to the effect that I could remove the "p"" from women, and meant the word that I had misspelled.

Somehow things did not work out exactly as I thought they were going down.

I can understand how Aubrey might be confused.  So, was I. 

 

 

 

[Robert]

22 hours ago, David Geelan said:

I'm about to teach a series of classes for teachers of junior high science who want to be senior high science teachers. One of the challenges is that this kind of math really should be second nature, as it is to me... and in some cases it isn't.

Agreed...In fact college algebra and trigonometry should be second nature too....Maybe not higher math, but at least the basics.

I've asked young people in college "what is the square root of 4?"  They reply "2".  Then I asked "is that your final answer"?  Then they look at me bewildered.

The answer, of course, is it has two roots: +2 and -2.

Should be basic....

[Gregory Matthews]

And the cube root of 8 is only +2.

[Gregory Matthews]

I have figured out the problem Aubrey mentioned.

Last Saturday I posted a comment in a new thread that I titled "The Latest Scam."   In my comment I made a typo and I wrote "wopman" instead of the word "woman" which I intended to write.

Pam caught it and posted a response that informed me of my typo error.

Having some fun with Pam, I responded with a post about taking the "p"' out of women.  But somehow my response was posted in this thread, rather than the Latest Scam thread.  I do not know how it happened.

As it was posted directly under a post made by Aubrey, she was confused, as was I when I read her response.

I am sorry that it happened.  She had every right to be confused.  As she has blocked my posts, she may not read my post here. But, for the rest of you, who may have been just as confused as she,  this is my story.