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

Please help me I need help with my test review I can’t figure out m<1 and m<2

aksik [14]

Answer:

m1=12 and m2=168

Step-by-step explanation:

$m1 + m2 = 180 \: (straight \: angle) \\ then \\ x - 12 + 7x = 180 \\ 8x - 12 = 180 \\ 8x = 180 + 12 = 192 \\ x = 192\div 8 \\ x = 24\\ hence \\ m1 = 24 - 12 = 12 \\ m2 = 7 \times 24 = 168.$

6 0

4 years ago

Can one of yall help me on this please.

ser-zykov [4K]

Answer:

Answer

3.0/5

Brainly User

There are 128 ounces in 1 gallon

1,5gallons= 192 ounces

Scott = 3 oz per lid

192 divided by 3 = 64 lids of detergent

Nikki = 4oz per lid

192 divided by 4 = 48 1/2 lids

64 - 48.5 = 15.5 lids more

Step-by-step explanation:

7 0

3 years ago