Eqn using 4 points: [-6.1√(55b-hb)]+[6.1√(90b-hb)] = [-8.3√(35b-hb)]-[8.3√(45b-hb)]

KeatonBuddy

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Eqn using 4 points: [-6.1√(55b-hb)]+[6.1√(90b-hb)] = [-8.3√(35b-hb)]-[8.3√(45b-hb)]

THE EQUATION ----> [-6.1√(55b-hb)]+[6.1√(90b-hb)] = [-8.3√(35b-hb)]-[8.3√(45b-hb)] Solve for b and h
 
THE EQUATION ----> [-6.1√(55b-hb)]+[6.1√(90b-hb)] = [-8.3√(35b-hb)]-[8.3√(45b-hb)] Solve for b and h

You have one non-linear equation and two unknowns. Non-trivial unique solution does not exist.

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33
 
You have one non-linear equation and two unknowns. Non-trivial unique solution does not exist.

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33


ok, well i was trying to create an equation for a graph with the points A(35, 1.52), B(45, 7.62), C(55, 12.73), D(90, 21.08) and it looked like a radical equation so i put the points into a[√b(x-h)]-k and tried to use systems to solve for the unknowns. Am i doing something wrong? Please reply if i am making a mistake.
 
I am trying to create an equation for a graph with the points A(35, 1.52), B(45, 7.62), C(55, 12.73), D(90, 21.08) and it looked like a radical equation so i put the points into a[√b(x-h)]-k and tried to use systems to solve for the unknowns. Am i doing something wrong? Please reply if i am making a mistake.
The best-fit-line according to excel is:

y = -0.0058*x2 + 1.0837*x - 29.302 (R2 = 1)
 
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I am trying to create an equation for a graph with the points A(35, 1.52), B(45, 7.62), C(55, 12.73), D(90, 21.08) and it looked like a radical so i put the points into a[√b(x-h)]-k and tried to use systems to solve for the unknowns. Am i doing something wrong? Please reply if i am making a mistake.

Well, Subhotosh Khan gave you a "line of best fit" (which is actually a quadratic equation), although this doesn't pass exactly through any of the four points. You can easily create a quadratic (or cubic or any n-degree polynomial) that does pass exactly through all four points. But, as was also mentioned, there's no one unique equation by which you can derive the "original" function that created these points. Given the decimal nature of the values, creating a radical equation seems like a reasonable thing to do too. You said you "tried" to use a system of equations to solve it. You have four equations and four unknowns, so it's solvable (although "no solution" might be the answer). Where did you run into difficulties? Please share your work with us, even if you know it's wrong. Thank you.
 
Well, Subhotosh Khan gave you a "line of best fit" (which is actually a quadratic equation), although this doesn't pass exactly through any of the four points. You can easily create a quadratic (or cubic or any n-degree polynomial) that does pass exactly through all four points. But, as was also mentioned, there's no one unique equation by which you can derive the "original" function that created these points. Given the decimal nature of the values, creating a radical equation seems like a reasonable thing to do too. You said you "tried" to use a system of equations to solve it. You have four equations and four unknowns, so it's solvable (although "no solution" might be the answer). Where did you run into difficulties? Please share your work with us, even if you know it's wrong. Thank you.

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here is what i tried too do, its a little messy so please forgive me but yea... the green is that final equation. what i was thinking was to put the coefficients into the square roots then squaring both sides until all the square roots where gone then just solving for b or h. Is that right?
 

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