If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides $12-2x$ and $16-2x$ , and a height of x.

So, the volume will be given by the product of the dimensions, i.e.

$(12-2x)(16-2x)x = 4x^3-56x^2+192x$

The derivative of this function is

$12x^2-112x+192$

and it equals zero if and only if

$12x^2-112x+192=0 \iff x = \dfrac{14\pm 2\sqrt{13}}{3}$

If we evaluate the volume function at these points, we have

$f\left(\dfrac{14-2\sqrt{13}}{3}\right) = \dfrac{64}{27}(35+13\sqrt{13})> f\left(\dfrac{14-2\sqrt{13}}{3}\right) = -\dfrac{64}{27}(13\sqrt{13}-35)$

So, the maximum volume is given if you cut a square with side length

$x=\dfrac{14-2\sqrt{13}}{3}\approx 2.7$

5 0

3 years ago

What Is the perfect square of 9x-1

Maksim231197 [3]

(9x - 1)² = <em>81x² - 18x + 1</em>

6 0

3 years ago

What does 2/5 divided by 5 equal

ivanzaharov [21]

2/5 divided by 5 equals 0.08

4 0

4 years ago

Read 2 more answers

E=300-10 (30)<br> How to solve it step by step

Zepler [3.9K]

Answer:

Step-by-step explanation:

e = 300-10(30)

e = 300 - 300

e = 0

6 0

4 years ago