<p>maximize its area, given the constraint that its perimeter equal 16?</p>
<p>I’m really not a fan of your username.</p>
<p>^hah. I thought you got banned again.</p>
<p>1x7=7
2x6=12
3x5=15
4x4=16</p>
<p>Since a square is technically a rectangle, 4x4 is ideal. Otherwise, a 3x5 is your second choice.</p>
<p>I hope you’re not planning on majoring in anything that requires… thought… in any capacity. Or more likely, this is some sort of spam question. </p>
<p>A 4x4 square…</p>
<p>I hate math.</p>
<p>Your two sets of constraints resolve into the following pseudo-numerical set</p>
<p>maximize x*y
x+y = 8 (where y<8 and x<8)</p>
<p>since there is a definite correlation between x and y, we can re-express either x or y in terms of the other</p>
<p>x = y-8 for example</p>
<p>then we would simply want the maximum for</p>
<p>y(y-8), or y^2-8y, where y is less than 8 (the implicit constraint of the second equation).</p>
<p>The maximum is obviously 4, therefore your solution is 4 by 4</p>
<p>Of course, use this set of logic only if you truly cannot figure out the problem via simple reasoning (which is fine), however if that is the case, you need a lot more practice…</p>
<p>thanks for all your help</p>
<p>No homework help allowed on CC.</p>
<p>Moderators please delete thread and warn the user.</p>
<p>Hmm, this seems more likely to be an SAT practice problem, as it requires more logic than numerical operations.</p>
<p>^ Not a SAT practice problem b/c it requires finding the maxima hence setting the derivative equal to zero.</p>
<p>It doesn’t necessarily require finding the critical points to solve the problem. Although now you mention it, it could very well be a Calculus question as well.</p>
<p>A calculus problem would include boarders around it, in that situation you have to do math (we did problems like that in BC). This you have to think for a half-second, that’s it. </p>
<p>Whenever you see a problem like this, it’s always a square.</p>
<p>Think of it like this, 10<em>10 > 9</em>11 > 8<em>12 > 7</em>13 > 6*14 and so on… But they all add to 20.</p>
<p>I had the weirdest connection when I saw this problem. For some reason I drew up Eratosthenes’ sieve and visualized the optimal border:fill ratio and realized that it was the less obvious reason why Eratosthenes used root as the iteration maximum. Reasoning does wonders…</p>
<p>(x + c)(x - c) = x^2 - c^2</p>
<p>If c is a real number, -c^2 is less than or equal to 0, so (x + c)(x - c) is greatest when c = 0. In other words, x*x is greater than the product of any other pair of numbers that add up to 2x.</p>
<p>I don’t think I did any calculus there, so it really could be an SAT question. It’s about the right difficulty too, obvious as it may be.</p>
<p>It actually sounds exactly like an SAT question, but it is not for the SAT I’m sure.</p>
<p>Yeah, I think it’s an elementary calculus problem, similar to deriving the formula for the volume of a sphere using triple integrals and spherical coordinates.</p>
<p>xy = A
2x + 2y = 16
x = 8 - y</p>
<p>y*(8-y) = A
8y - y^2 = A
A’ = 8 - 2y</p>
<p>y = 4
x = 4</p>
<p>idk that’s how I would approached it. But obviously there are easier solutions I see.</p>
<p>^^ You have the ability to make something that is actually nothing sounds like it’s something. Impressive.</p>
<p>^Referring to who?</p>
<p>You .</p>