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February 13, 2016
Posted by **Jin** on Wednesday, August 11, 2010 at 3:13pm.

Write the volume Vof the box as a function of x. Leave it as a product of factors, do not multiply out the factors.

V=

If we write the domain of the box as an open interval in the form (a,b), then what is a=?

a=

and what is b=?

I got V=x(18-2x)(2-2x)

and a=0

b=9

but it says that its not correct

- math -
**Reiny**, Wednesday, August 11, 2010 at 4:47pmYour equation V=x(18-2x)(2-2x) , which is correct, describes the volume for any given x

clearly V has to be a positive number.

notice that for x=9 and x=1, V is zero.

for all values of x between 1 and 9 , V is positive,

for x<1 and x > 9 , V is negative.

try a number between 1 and 9

Draw your conclusion from my hints.

- math -
**jai**, Thursday, August 12, 2010 at 5:58amthe equation you got is correct,, =)

first, note that x (which is the height of the box) cannot be negative, since there is no negative height,,

equating V to zero,

x=0, 1, 9

now, get some values in between (and if you want, get also a value greater than 9), and check if the dimensions will all be positive, and V will be positive as well,,

example,,

if x = 0.5, V = (0.5)(17)(1) = 8.5

if x = 4, V = (4)(10)(-6) = -240

if x = 10, V = (10)(-2)(-18) = 360

note that even if the volume that we got for x = 10 is positive, the length and width are negative, which cannot happen,,

therefore, domain is (0,1)

so there,, i hope i was able to help.. =)