Solve Formula For h

[mathdad]

Solve the formula given for h.

V = 40h^2•sqrt{(96/h) - 0.608}

(V)^2 = [40h^2•sqrt{(96/h) - 0.608}]^2

V^2 = 1600h^4[(96/h) - 0.608]

V^2 = 153,600h^3 - 93,388.8h^4

V^2 = h^3(153,600 - 93,388.8h)

I am stuck here. How can I possibly isolate h?

 

[Dr.Peterson]

I don't know! You're right to observe that this is a fourth degree equation for which no obvious factorization is possible.

Here is what WolframAlpha does with it: https://www.wolframalpha.com/input/?i=solve+for+x:+V+=+40x^2•sqrt{(96/x)+-+0.608}

No, you aren't expected to do that!

If this is from a book and I were helping you in person, I would be checking whether you copied something wrong, or the instructions say something other than to solve algebraically.

 

[mathdad]

I don't know! You're right to observe that this is a fourth degree equation for which no obvious factorization is possible.

Here is what WolframAlpha does with it: https://www.wolframalpha.com/input/?i=solve+for+x:+V+=+40x^2•sqrt{(96/x)+-+0.608}

No, you aren't expected to do that!

If this is from a book and I were helping you in person, I would be checking whether you copied something wrong, or the instructions say something other than to solve algebraically.

Thanks. I don't feel so bad now.

 

[Otis]

Did you make up the exercise in this thread?

\(\;\)

 

[mathdad]

Did you make up the exercise in this thread?

\(\;\)

1. I am not that smart to create my own questions.

2. This question was found online at algebra.com in the UNANSWERED category.

3. Stop making assumptions about me, a person you do not know outside of the site.

4. I am 54 years old and have no time to waste your time here.

 

[Dr.Peterson]

This illustrates a reason for the first rule in our submission guidelines: From where does your question come?

If you indicate that it is not from the textbook you have been generally referring to, and in fact that there is no evidence it can be solved, we can know not to take it too seriously - and also not to wonder if you made it up. Some students are not aware that a random equation probably can't be solved!

It takes no time at all to make up a problem; what's a little harder is to make up one that can be solved. You do that by starting with the solution and working backward; this can actually be a good thing to do for your own practice.

But you might want to stop making assumptions about the reasons for asking a question. Sometimes it's just a question! Relationships can be better maintained by assuming the best rather than the worst, in both directions.

 

[mathdad]

This illustrates a reason for the first rule in our submission guidelines: From where does your question come?

If you indicate that it is not from the textbook you have been generally referring to, and in fact that there is no evidence it can be solved, we can know not to take it too seriously - and also not to wonder if you made it up. Some students are not aware that a random equation probably can't be solved!

It takes no time at all to make up a problem; what's a little harder is to make up one that can be solved. You do that by starting with the solution and working backward; this can actually be a good thing to do for your own practice.

But you might want to stop making assumptions about the reasons for asking a question. Sometimes it's just a question! Relationships can be better maintained by assuming the best rather than the worst, in both directions.

The question comes from algebra.com. It is not from the Sullivan textbook or any other textbook. I make great effort to post questions exactly as they printed in the books or online. I actually go out of my way to be professional and on track.

 

[Otis]

... This question was found online at algebra.com in the UNANSWERED category.

Please do not copy unanswered questions from other math forums.

By the way, the 'Unanswered' section at algebra.com is for tutors.

... Stop making assumptions about me ...

I did not assume; I asked you to tell me. You seem offended by tutors' follow-up questions.

That, or you're making assumptions about our questions. Either way is not good.