Is the book answer wrong?

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michaelcaba

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I am stumped. I have a book that gives an answer to a practice problem, but it does not seem possible that the book is correct.

Here is the problem: Y^3= 3(Y^3 + t)/m. Rearrange so that Y is the subject of the formula. (By way of note, the Y^3 is "Y to the third power.")

How do you rearrange so that Y is the subject, that is, Y= ?????

Thank you

Mike
 
Hello, and welcome to FMH! :)

I would first multiply by \(m\) and then distribute the 3 on the right to get:

[MATH]mY^3=3Y^3+3t[/MATH]
[MATH]mY^3-3Y^3=3t[/MATH]
[MATH](m-3)Y^3=3t[/MATH]
[MATH]Y^3=\frac{3t}{m-3}[/MATH]
[MATH]Y=\sqrt[3]{\frac{3t}{m-3}}[/MATH]
 
A different approach using numbers:

The equation Y³= 3(Y³+ t)/m holds true if we let Y = 6, t = 72, m = 4.
Check: LHS = 6³ = 216 RHS = 3(216 + 72)/4 = (3/4)(288) = 216 = RHS

Rearrange equation to isolate 6 on the LHS:
Remove ÷ 4 from RHS by shifting it to LHS and reversing the operation to × 4:
6³ = 3(6³ + 72)/4
6³ × 4 = 3 × 6³ + 3 × 72

Remove + 3 × 6³ from RHS by shifting it to LHS and reversing the operation to
- 3 × 6³:
6³ × 4 - 3 × 6³ = 3 × 72

Take out 6³ as a common factor:
6³(4 - 3) = 3 × 72

Remove × (4 - 3) from LHS by shifting it to RHS and reversing the operation
to ÷(4 - 3):
6³ = (3 × 72)/(4 - 3)

Remove power 3 from LHS by shifting it RHS and reversing the operation to ∛:
6 = ∛[(3 × 72)/(4 - 3)]
Check that LHS = RHS
LHS = 6
RHS = ∛[216/1] = ∛(6³) = 6 = LHS

Since Y = 6, t = 72, m = 4 it follows:
Y = ∛[3t/(m - 3)]
 
Jomo said:
Can we not supply full answers to students?
Click to expand...
Only if necessary, but in most cases it is better to let the student work from hints. It's called the "Socratic method" of teaching. The idea is to help the student by asking leading questions or hints to improve the student's knowledge of the subject as well as their ability with critical thinking.

But there are instances that this does not work well. For example, when teaching Physics there are a number of types of problems in, say, static equilibrium, that simply have to be demonstrated before the student can grasp the concept. Ideally this would be done directly in the classroom but that doesn't always work. It depends on how well the student and instructor work together. If there is a lack of comprehension between student and instructor then it is good for a student to find a tutor that can explain the solution step by step.

Here, and on the other Forums I work with, we don't want to make a habit of just giving out answers because that damages our relationship with the associated schools. If I find a student is using us to cheat I close the thread and try to contact the school where the student attends. This can only be done rarely but I think it's a good policy.

-Dan
 
Last edited:
topsquark said:
Only if necessary, but in most cases it is better to let the student work from hints. It's called the "Socratic method" of teaching. The idea is to help the student by asking leading questions or hints to improve the student's knowledge of the subject as well as their ability with critical thinking.

But there are instances that this does not work well. For example, when teaching Physics there are a number of types of problems in, say, static equilibrium, that simply have to be demonstrated before the student can grasp the concept. Ideally this would be done directly in the classroom but that doesn't always work. It depends on how well the student and instructor work together. If there is a lack of comprehension between student and instructor then it is good for a student to find a tutor that can explain the solution step by step.

Here, and on the other Forums I work with, we don't want to make a habit of just giving out answers because that damages our relationship with the associated schools. If I find a student is using us to cheat I close the thread and try to contact the school where the student attends. This can only be done rarely but I think it's a good policy.

-Dan
Click to expand...
Dan,
I agree with everything you said. I do have one question and that is what was so special about this problem where we could not guide the student to the desired results?
Steven
 
Jomo said:
Dan,
I agree with everything you said. I do have one question and that is what was so special about this problem where we could not guide the student to the desired results?
Steven
Click to expand...
I'm confused. Who said we shouldn't have, in this thread?

In my mind, the important thing in this thread is that the OP specifically pointed out that the book's answer seemed wrong, but showed neither what that answer was, not why it seemed wrong. As a result, it was impossible to answer that central aspect of the question. And a full answer, while perhaps justified by the fact that they had an answer from the book, didn't help in correcting whatever the student's issue was.

I would probably have asked for the missing information and provided a hint.
 
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