9 is what percent of 25 in percentage 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

Zara has a collection of 4 marbles: an Aggie, a Bumblebee, a Steelie, and a Tiger. She wants to display them in a row on a shelf

KengaRu [80]

Answer:

Step-by-step explanation:

Oops I meant "there are 3! = 6 ways to permute ABTS that have TS."

3 0

3 years ago

For g(x)=x^2-x find g(x) when x=-2

torisob [31]

Answer:

$g(x) = 6$

Step-by-step explanation:

Begin with substuting the x variable with -2, we do this because the question has listed the value of x already.

Using the value of x, -2 we determine g(x).

g(x) = -2^2 + 2

Above is what the equation would look as, after you input the value of -2.

Using pemdas, (parantheses, exponents, multiplication, division, addition, subtraction) solve the equation.

-2^2 = 4

Think of it as -2 * -2, which is why -2^2 is 4.

Add 4 +2.

4 + 2 = 6.

Therefore, the value of g(x) = 6

6 0

3 years ago

Griffin ordered a pair of sneakers online. He had a $17 credit that he applied toward the purchase, and then he used a credit ca

MrMuchimi

Well it would be 63$ if we are not including tax because 80-17=63

4 0

3 years ago

RIP OpenStudy ;(

klemol [59]

First note that $\frac{2^n+1}{2^{n+1}} = \frac{2^n}{2^{n+1}} + \frac{1}{2^{n+1}} = \frac{1}{2} + \frac{1}{2^{n+1}}$

If you take limit, then you have $\lim_{n \to \infty}( \frac{1}{2} + \frac{1}{2^{n+1}})= \lim_{n \to \infty}( \frac{1}{2}) +\lim_{n \to \infty}(\frac{1}{2^{n+1}})=\frac{1}{2} +0= \frac{1}{2}$

3 0

3 years ago

Read 2 more answers