# Maths

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#1
how do i make x the subject in this formula:

V = 4XQUBED-(2L-2W)X SQUARD +XLW/
V EQUALS FOUR EX DOUBLED MINUS BRAKET TWO EL MINUS TWO DOUBLEU BRAKET CLOSED EX SQUARD PLUS EX EL W

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16 years ago
#2
wtf is dubed
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16 years ago
#3
(Original post by Naz1)
how do i make x the subject in this formula:

V = 4XQUBED-(2L-2W)X SQUARD +XLW/
V EQUALS FOUR EX DUBED MINUS BRAKET TWO EL MINUS TWO DOUBLEU BRAKET CLOSED EX SQUARD PLUS EX EL W

V = 4 x³ - (2l-2w) x² + xlw

It is quite difficult to make x the subject, you need to use the 3rd orde equivalent of the "quadratic" formula, which has one real answer (which is probably the one you want, seeing as the equation looks physical)
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16 years ago
#4
wrong. can't be bothered to try again.
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16 years ago
#5
(Original post by elpaw)
V = 4 x³ - (2l-2w) x² + xlw

It is quite difficult to make x the subject, you need to use the 3rd orde equivalent of the "quadratic" formula, which has one real answer (which is probably the one you want, seeing as the equation looks physical)
What is that formula? Do you know that one exists?
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16 years ago
#6
(Original post by mik1a)
What is that formula? Do you know that one exists?
yes i do know it exists. i dont know the formula off the top of my head
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16 years ago
#7
It is, errm, rather difficult to do that any other way apart from using the formula. I suspect that using the cubic formula will throw out some horrible answer though.
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16 years ago
#8
(Original post by mik1a)
V/x = (2x - L)(2x + w)
= 4x² + (2w + 2L)x + Lw

a = 4
b = (2w - 2L)
c = Lw

x = ( -b +/- sqroot (b² - 4ac) ) / 2a
= 2L - 2w +/- sqroot ( (2w-2L)² - 4*4*Lw) / 2*4
= 2L - 2w +/- sqroot ( 4w² + 4L² - 24Lw ) / 8

more or less
you cant use the quad formula, because the RHS has to be 0, and yours is V/x
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16 years ago
#9
And when you multiply out the brackets the constant term has to be +LW not -LW (as your factorisation suggests). All in all, that's a bad piece of maths.
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16 years ago
#10
(Original post by mik1a)
What is that formula? Do you know that one exists?
There are general formulas for cubics and quartics, but not for any higher order equations.
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16 years ago
#11
Here's the formula - it's not nice.
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16 years ago
#12
(Original post by chrisbphd)
It is, errm, rather difficult to do that any other way apart from using the formula. I suspect that using the cubic formula will throw out some horrible answer though.
ive used mathematica and it's a horrible answer. im trying to format it and post it. (and thats only the real answer! the imaginaries are worse!)
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16 years ago
#13
(Original post by chrisbphd)
Here's the formula - it's not nice.
Sorry, I should add that a is the coefficient of x cubed, b is the coefficient of x squared, c is the coefficient of x and d is the constant term. It is only valid for a(x^3)+b(x^2)+cx+d=0
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16 years ago
#14
(Original post by chrisbphd)
Here's the formula - it's not nice.
uh-oh spaghetti o's
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16 years ago
#15
(Original post by Naz1)
how do i make x the subject in this formula:

V = 4XQUBED-(2L-2W)X SQUARD +XLW/
V EQUALS FOUR EX DUBED MINUS BRAKET TWO EL MINUS TWO DOUBLEU BRAKET CLOSED EX SQUARD PLUS EX EL W

i assume this is the coursework for finding max vol of box so u want to first differentiate and the max for cetain values of l and w will be when it equals 0
differentiate:
v/x=12x^2-(2l-2w)+LW
when this equals 0,
however, i think u may have gone wrong sumwhere

but u can use quad formula to find values of x for certain ls and ws
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#16
(Original post by elpaw)
you cant use the quad formula, because the RHS has to be 0, and yours is V/x
Thank you
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16 years ago
#17
(Original post by chrisbphd)
Here's the formula - it's not nice.
*shudders*

Who on earth came up with that!
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16 years ago
#18
mathematica gives the real answer as:

x = 2(l-w)/3 + (2^(1/3))*(-4(l -w)²+3lw)/(3(-16 l³ - 27 V + 66 l²w - 66 lw² + 16 w³ + √(4(-4(l-w)²+ 3 lw)³ + (-16 l³ - 27V + 66 l²w - 66 lw² +16 w³)²))^(1/3)) - (1/(3*2^(1/3))) ((-16 l³ - 27 V + 66 l²w - 66 lw² + 16 w³ + √(4(-4(l - w)² + 3 lw)³ + (-16 l³ - 27 V + 66 l²w - 66 lw² + 16 w³)²))^(1/3))))
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16 years ago
#19
(Original post by chrisbphd)
Here's the formula - it's not nice.
I wonder how you'd prove that. Completing the cube?
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#20
(Original post by elpaw)
mathematica gives the real answer as:

x = 2(l-w)/3 + (2^(1/3))*(-4(l -w)²+3lw)/(3(-16 l³ - 27 V + 66 l²w - 66 lw² + 16 w³ + √(4(-4(l-w)²+ 3 lw)³ + (-16 l³ - 27V + 66 l²w - 66 lw² +16 w³)²))^(1/3)) - (1/(3*2^(1/3))) ((-16 l³ - 27 V + 66 l²w - 66 lw² + 16 w³ + √(4(-4(l - w)² + 3 lw)³ + (-16 l³ - 27 V + 66 l²w - 66 lw² + 16 w³)²))^(1/3))))

Are you sure thats the only way i can make X the subject & how about this one:
SIMPLIFY IT, THEN MAKE X THE SUBJECT
V=(L-2X)*(W-2X)*X
0
X
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