Question

Help!!

Answer 1

from this I can create these two equations, i think
40 = 2hw^2
60 = 2w^2 + 6hw

but when I try to sub them into each other Im getting problems.. please help :/

Answer 2

when I substitute them into each other I get w^3 - 30w + 60 = 0 and I normally would do trial and error till i find one factor and then divide that factor into the equation and factor the new equation but i cannt find a factor :/

Answer 3

@hartnn @myininaya @wio @RadEn @ganeshie8 @KingGeorge

Answer 4

Yes that is what I am getting too.
This is a cubic equation.
Evaluate the expression f(w) = (w^3 - 30w + 60) for a few values of w
w = 1; f(1) = 1 - 30 + 60 = +31
w = 2; f(2) = 8 - 60 + 60 = +8
w = 3; f(3) = 27 - 90 + 60 = -3
w = 4; f(4) = 64 - 120 + 60 = +4

So it changes sign between w=2 and w=3 and so there is a root in between 2 & 3
And there is a root between w = 3 & 4

Answer 5

so do I keep plugging in different values between 2&3 as well as 3&4 for w until i find the root?

Answer 6

I will do a binary search. 2, 2.5 and 3.
If it changes sign between 2.5 and 3 then 2.75 and so on until f(w) gets close to 0.

Answer 7

im at 2.5555 and it keeps getting closer to 0 but not quite xD

Answer 8

Try 2.558

Answer 9

close, that's -0.00207

Answer 10

Yes that is one solution. Another one is near 3.73

Answer 11

but dont you need it to be exactly 0?

Answer 12

Well we are allowed to round off answers to the second or third decimal place.

Answer 13

Sometimes roots are irrational numbers.

Answer 14

ive never done a question like this before >.< dumb teacher gave me this for h-w.. ok ill rounds it off to the nearest 3 decimals

Answer 15

This equation happens to have irrational roots. So we have to round it off at some point.

Answer 16

kk ill keep playing with it lol

Answer 17

You may have two sets of dimensions satisfying the given conditions.

Answer 18

Meaning two sets of l, w and h.

Answer 19

but is that possible? I mean there is only one aquarium?

Answer 20

Yes it is possible. In fact if the cubic equation had three positive roots then three sets of aquarium dimensions will satisfy the given condition. But this one has two positive roots and one negative root and hence two sets of aquarium dimensions.

Answer 21

i got 2.558 and 3.730 as two possible values of w which satisfies the equation. shouldnt there be one more since the equation has a w^3 in it?

Answer 22

The third one is negative at -6.288

Answer 23

oh and since the other root is negative and it isnt possible for an aquarium to have a negative root then we wont include it as a possible dimention for the aquarium?

Answer 24

Yes.

Answer 25

Also put the two values of w you got into the equation and find length and height. If any one them gives a ridiculous value say height is 0.1 feet or something you can throw out that set of dimensions too. But otherwise give both set of dimensions as answer to the problem.

Answer 26

ok can check to see if all the dimensions look gud? it wont take me long to find h and l now

Answer 27

w=2.558 , l= 5.116 , h= 3.057
and
w=3.73 , l=7.46 , h= 1.438

looks good to me :)

Answer 28

Yeah. Sometimes math will give all possibilities but we will have to make a call on whether it is practical. Here both looks reasonable dimensions. I will use those numbers and see if the volume and surface area computes to the numbers given in the problem. This is one way to verify that your answers are correct. Don't sweat if it does not exactly computes to an integer because there will be some difference due to rounding off which gets maginified when you multiply three dimensions to get volume and two dimensions to get surface area.

Answer 29

ok! thx so much for your help :)

Answer 30

you are welcome.