Which of these forms should you use to file your tax return? W-2 form

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

4 years ago

PLEASE HELP ME!!!!! Factor completely b^4 − b^3 + b − 1

Afina-wow [57]

b^4 − b^3 + b − 1
=(b^4 − b^3) + (b − 1)
= b^3(b - 1) + (b - 1)
=(b - 1)(b^3 + 1)

7 0

4 years ago

Complete the equation of the line through [1,4] and [2,2]

son4ous [18]

First find the slope of the line so change in y over change in x so 4-2/1-2 which is 2/-1 so -2 is your slope then plug that as well as a point from above to find your y intercept so y=mx+b 2=-2(2)+ b then you have 2=-4+b then add 4 to each side and you find b is six then you make ur equation from your slope and y int(b) y=-2x+6

6 0

3 years ago

Y = 8x + 6, x = 5 plz help i can get admin if i solve this

RoseWind [281]

Answer:

y = 46

Step-by-step explanation:

I'm assuming you wanted to solve for y.

x = 5

y = 8(5) + 6

y = 40 +6

y = 46

8 0

3 years ago

Does (-6)2 have a value less than zero?

masha68 [24]

Answer:

yes it does, -6x2= -18

Step-by-step explanation:

8 0

3 years ago