Physics, 09.11.2019 06:31, kbar7555

Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3737 ft by 2020 ft. the resulting piece of cardboard is then folded into a box without a lid. find the volume of the largest box that can be formed in this way. b. suppose that in part (a) the original piece of cardboard is a square with sides of length s. find the volume of the largest box that can be formed in this way. a. to find the objective function, express the volume v of the box in terms of x.

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answered: Cocco

a) The volume of the largest box that can be formed is 1,393.53 ft^3 .

b) The maximum volume of the box: $\frac{2s^3}{27}$

Explanation:

a) Length of the card board = l = 37 ft

Width of the card board= b = 20ft

Squares with sides of length x are cut out of each corner of a rectangular cardboard to form a box.

Now, length of the box = L = 37 -2x

Breadth of the box ,B= 20- 2x

Height of the box ,H= x

Volume of the box ,V= L × B × H

$\frac{dV}{dx}=\frac{(37 -2x)(20-2x)x}{dx}$

$\frac{dV}{dx}=\frac{d(740x-114x^2+4x^3)}{dx}$

$\frac{dV}{dx}=740-228x+12x^2$

Putting , $\frac{dV}{dx}=0$

0=740-228x+12x^2

x = 4.1537 , 14.846

$\frac{d^2V}{(dx)^2}=-228+24x$

When , x = 4.1537 , $\frac{d^2V}{(dx)^2}$ (maxima)

The volume of the largest box that can be formed:

$(27 -2x)(15-2x)x = (37 -2\times 4.1537 )(20-2\times 4.1537 )\times 4.1537$

V=1,393.53 ft^3

The volume of the largest box that can be formed is 1,393.53 ft^3 .

b) Original piece of cardboard is a square with sides of length s.

Length of the card board = l = s

Squares with sides of length x are cut out of each corner of a rectangular cardboard to form a box.

Now, length of the box = L = s -2x

Height of the box ,H = x

Volume of the box ,V= L × L × H

$=\frac{dV}{dx}=\frac{(s -2x)(s-2x)x}{dx}$

$\frac{dV}{dx}=\frac{d((s-2x)^2x)}{dx}$

$\frac{dV}{dx}=(s-2x)^2+x(2(s-2x)(-2))$

$\frac{dV}{dx}=(s-2x)^2-8x(s-2x)$

$\frac{dV}{dx}=O$

$x=\frac{s}{6},\frac{s}{2}$

$\frac{d^2V}{(dx)^2}=2(s-2x)(-2)-8(2-2x)+16x$

When , $x=\frac{s}{6} , \frac{d^2V}{(dx)^2}$ (maxima)

The maximum volume of the box:

$V_{max}=(s-2x)^2x=(s-2\times \frac{s}{6})^2\times \frac{s}{6}=\frac{2s^3}{27}$

answered: Guest

another example of kinetic energy would be,

kinetic energy > moving energy

answer > letter choice (c), a hammer falling off a table.

hope that ! : )

answered: Guest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$