heres a question i dunt get how to solve, the width of a square based storage 3m less than its height. THe tank has a capacity of 20m^3. If the deimension are integer value in metres, what are they?
$\displaystyle w = h-3$width of a square based storage 3m less than its height. THe tank has a capacity of 20m^3.
area of base, $\displaystyle B = (h-3)^2$
$\displaystyle V = Bh = h(h-3)^2 = 20$
$\displaystyle h^3 - 6h^2 + 9h - 20 = 0$
rational root theorem ... possible positive integer roots {1, 2, 4, 5, 10, 20}
go for it.
Hmm, good question. I don't know if I can answer that in general, but I'll tell you the key words for this problem.
"square base" - this means that the length and width are equal.
"width... 3m less than its height" - this is great because we can now relate the width to the height.
"capacity of 20m^3" - we got the volume of the container now.
Now I think how do I put this together and use it. Well the volume of a box is the L*W*H, length times width times height. We know this equals 20. So the length and width of the base are the same as we said before, so we can say W*W*H=20. Now the width is 3 meters less than the height. Write that out just like it sounds. W = H-3. Now you can substitute this in and you got your answer.
I don't know if that helps at all, but my advice is look for all the key info given. Write down the numbers given and what they pertain to. The hardest part usually will be making some kind of substitution, so look for some kind of relation that you can use to make a substitution.