Select the correct answer.

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

3 years ago

Find the domain of fg. f(x)=x+2 g(x)=1/x+2 a. all real numbers b. all real numbers, except 2 c. all real numbers, except -2 d. (

sleet_krkn [62]

Answer:

all real numbers

Step-by-step explanation:

the domain will always be all real numbers

6 0

3 years ago

What is Quantum theory?

Mariana [72]

Answer:

a theory of matter and energy based on the concept of quanta, especially quantum mechanics.

Step-by-step explanation:

there really is no step by step explanation :)

8 0

3 years ago

Write 12/15 in the simplest form

victus00 [196]

If you would like to know what is 12/15 in the simplest form, you can calculate this using the following step:

12/15 simplifies to 4/5 (the common factor of 12 and 15 is 3, so you can divide both numbers by 3).

The result is 4/5.

5 0

2 years ago

Read 2 more answers

Solve ( x - 2)( x + 7) =0

lara31 [8.8K]

Answer:

x = 2 or

x = -7

Step-by-step explanation:

(x - 2)(x + 7) = 0

x - 2 = 0

Add 2 to both sides

x - 2 + 2 = 2 + 0

x = 2

OR

x + 7 = 0

Subtract 7 from both sides

x + 7 - 7 = 0-7

x = -7

Therefore

x = 2 or

x = -7

6 0

3 years ago