SOLUTION: I have to solve each problem then check my answer to be sure it is reasonable. Here's the problem:
A ten-gallon aquarium holding African cichlids is 3 inches higher than it is w
Question 34925: I have to solve each problem then check my answer to be sure it is reasonable. Here's the problem:
A ten-gallon aquarium holding African cichlids is 3 inches higher than it is wide. It's length is 21 inches, and its volume is 2730 cubic inches. What are the height and width of the aquarium?
I have set it up to look like this:
(x-7)~2 + (x+1)~2 + x~2 then I have gotten that figured out to x~2-14x+49+x~2+2x+1=x~2 that is where I get stuck after subtracting the x~2 to get it on the same side as the rest of the equation. Answer by mbarugel(146) (Show Source):
You can put this solution on YOUR website! Hello!
Let's call X to the width of the aquarium. We know that its height must be X+3. Also, its length is 21. Volume is calculated as width*height*length. So we get the following equation:
Now we can solve this quadratic equation using the standard procedure:
Quadratic equation (in our case ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=529 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 10, -13.
Here's your graph:
As you can see the two solution are 10 and -13. We can disregard the -13 because width can't be negative. So we conclude that the width of the aquarium is 10 inches. Therefore, its height must be 13 inches.
You can check that
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