the opposite of an equation

[hyb]

hi


I have an equation...


X = (-Y / 179 + 2) * Y * 182.0444


Now what is the corresponding


Y = ?

Thank you!

 

[hyb]

I tried with

Y = sqrt{181 * X / 182.0444}

but it doesn't seem to be correct

 

[JeffM]

hi


I have an equation...


X = (-Y / 179 + 2) * Y * 182.0444 That is an equation; there is no rule that y be expressed in terms of x. That is simply a convention.


Now what is the corresponding


Y = ?

Thank you!

Before I try to answer your question, I need some information to ensure that an answer will be meaningful to you. (Please read Read Before Posting.)

Are you studying first year algebra? What methods do you know for solving quadratic equations? If you are not studying algebra now, have you ever studied it, and what is the context of this equation?

Is this the equation that you are starting from

\(\displaystyle x = 182.0444y\left(\dfrac{- y}{179} + 2\right)\)?

Are there any constraints on x? For example, does x have to be non-positive?

 

[hyb]

Before I try to answer your question, I need some information to ensure that an answer will be meaningful to you. (Please read Read Before Posting.)

Are you studying first year algebra? What methods do you know for solving quadratic equations? If you are not studying algebra now, have you ever studied it, and what is the context of this equation?

Is this the equation that you are starting from

\(\displaystyle x = 182.0444y\left(\dfrac{- y}{179} + 2\right)\)?

Are there any constraints on x? For example, does x have to be non-positive?

Er...actually I studied some algebra...(too) MANY years ago... and seldom used it since then, so re-starting to solve a simple problem like this is a little painful


x should be comprised between 1 and 32767

for example, the result when x = 29046 should be (rounded) y = 120...

 

[JeffM]

Er...actually I studied some algebra...(too) MANY years ago... and seldom used it since then, so re-starting to solve a simple problem like this is a little painful


x should be comprised between 1 and 32767

for example, the result when x = 29046 should be (rounded) y = 120...

Er...actually I studied some algebra...(too) MANY years ago... and seldom used it since then, so re-starting to solve a simple problem like this is a little painful


x should be comprised between 1 and 32767

for example, the result when x = 29046 should be (rounded) y = 120...

A further question. Do you just want an answer or do you want to know how to get answers to such problems?

I am going to do the best I can but I am still not sure I understand the problem because you did not answer all my questions.

\(\displaystyle x = 182.0444y\left(\dfrac{-y}{179} + 2\right) \implies -179x = 182.0444y(y - 179 * 2) \implies -\left(\dfrac{179}{182.0444}\right)x = y^2 - 2 * 179y \implies\)

\(\displaystyle \dfrac{-179x}{182.0444} + 179^2 = y^2 - 2 * 179y + 179^2 = (y - 179)^2\implies \pm \sqrt{179^2 - \dfrac{179x}{182.0444}} = y - 179 \implies\)

\(\displaystyle y = \sqrt{32041 - \dfrac{179x}{182.0444}} + 179.\)

Now the answer above cannot be right because there is no real value of y that corresponds to x = 32767. Moreover

\(\displaystyle \sqrt{32041 - \dfrac{179 * 29046}{182.0444}} + 179 \approx \sqrt{32041 -28650.25} + 179 = \sqrt{3480.75} + 179 \approx 59 + 179 = 238.\)

Let's go back to your original equation. (Or what I think is your original equation).

\(\displaystyle x = 182.0444y\left(\dfrac{-y}{179} + 2\right)\ and\ y = 120 \implies\)

\(\displaystyle x = 182.0444 * 120\left(\dfrac{-120}{179} + 2\right) \approx 182.0444 * 120(-0.67 + 2) = 182.0444 * 120 * (1.33) \approx 29054.3 \ne 29046.\)

Something is wrong with the original equation.

 

[hyb]

A further question. Do you just want an answer or do you want to know how to get answers to such problems?

I am going to do the best I can but I am still not sure I understand the problem because you did not answer all my questions.

\(\displaystyle x = 182.0444y\left(\dfrac{-y}{179} + 2\right) \implies -179x = 182.0444y(y - 179 * 2) \implies -\left(\dfrac{179}{182.0444}\right)x = y^2 - 2 * 179y \implies\)

\(\displaystyle \dfrac{-179x}{182.0444} + 179^2 = y^2 - 2 * 179y + 179^2 = (y - 179)^2\implies \pm \sqrt{179^2 - \dfrac{179x}{182.0444}} = y - 179 \implies\)

\(\displaystyle y = \sqrt{32041 - \dfrac{179x}{182.0444}} + 179.\)

Now the answer above cannot be right because there is no real value of y that corresponds to x = 32767. Moreover

\(\displaystyle \sqrt{32041 - \dfrac{179 * 29046}{182.0444}} + 179 \approx \sqrt{32041 -28650.25} + 179 = \sqrt{3480.75} + 179 \approx 59 + 179 = 238.\)

Let's go back to your original equation. (Or what I think is your original equation).

\(\displaystyle x = 182.0444y\left(\dfrac{-y}{179} + 2\right)\ and\ y = 120 \implies\)

\(\displaystyle x = 182.0444 * 120\left(\dfrac{-120}{179} + 2\right) \approx 182.0444 * 120(-0.67 + 2) = 182.0444 * 120 * (1.33) \approx 29054.3 \ne 29046.\)

Something is wrong with the original equation.

Maybe, but that's not important...I mean, I elaborated the first equation since I had to get an approximate value i.e.

take a number between 0 and 179 and convert it into a number between 0 and 32767

where the numbers close to 0 (1..2..3) are multiplied by 2 but progressively become multiplied by 1 when we reach 179
i.e. there is a slope on the increment. And I came up with that "wrong" solution, that gave me a good approximation of what I needed.

Then I neeed the reverse...always approximate.


I reiterate that I'm not into math since a long time, so I hope my explanation could be clear to you...
Many thanks anyway! Because according to what I wrote above, 29054.3 is a good approximation of 29046 for my purposes.