All categories

3 years ago

Simplify and write as a decimal.

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

6 0

11.9

i just got it right on a quiz so yeah

You might be interested in

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

Reasoning If 1/2 of 1 is 1/2 what is 1/2 of 2,3 and 4

hichkok12 [17]

Answer:

half of 2 is 1, half of 3 is 1.5,half of 4 is 2.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Why is a circle not a polygon

Goryan [66]

Because a polygon is a shape that has equal sides and no curves.

4 0

3 years ago

Read 2 more answers

If multiplying by 1/4 makes a positive number smaller then what does dividing by 1/4 do to the value of the number? Explain your

Free_Kalibri [48]

Hello,

If multiplying by 1/4 makes a positive number smaller then dividing by 1/4 makes the number its being dividing to see how many times 1/4 can be put into that number. For Example,

2 / 1/4 = 8

1/4 can go into 2 eight times!

Hope This Helps!

5 0

3 years ago

RUDIKE [14]

$4680
Since 18% is 18/100 you just have to multiply the $842.4 by the reciprocal of that to find your answer
Reciprocal of 18/100 is 100/18
842.4* 100/18 equals 84240/18
84240/18 equals 4680

3 0

3 years ago