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

Q2) The number of people signed up for a bus trip increased from 32 to

Oduvanchick [21]

Answer:

45-32 = 13 / 32 *100= 40.625 round to the nearest percent is 41%

Step-by-step explanation: Brainlest plzzz

5 0

3 years ago

Can someone help me with this?

Lena [83]

day 5 has the highest visits and day 3 has the lowest visits

4 0

2 years ago

△RQP≅△ONM. Find the value of x. ( I WILL GIVE BRAINLIEST! PLS HELP!)<br><br> refer to attachment

zmey [24]

the answer is

x= 5/3

BTW thx for brainliest

5 0

2 years ago

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