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Musya8 [376]
3 years ago
13

Which list shows these numbers in order from least to greatest?

Mathematics
1 answer:
ira [324]3 years ago
3 0

Answer:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15...

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 23 in. by 13 in. by
faltersainse [42]

Answer:

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is 361.19 in^3.

Step-by-step explanation:

Given that the dimensions of a cardboard is 23 in by 13 in.

Let the side of the square be x in.

Then the length of the box= (23-2x) in

and the width of the box =(13-2x) in

and height = x in.

The volume of the box is = length ×width × height

                                         =[(23-2x)(13-2x)x] in^3

                                         =(299x-72x² +4x^3) in^3

∴V=299x-72x² +4x³

Differentiating with respect x

V'= 299-144x+12x²

Again differentiating with respect x

V''= -144+24x

To find the dimensions, we set V'=0

∴299-144x+12x²=0

Applying Sridharacharya formula that is the solution of a quadratic equation ax²+bx+c is x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Here a=12, b=-144 , c=299

\therefore x=\frac{-(-144)\pm\sqrt{(-144)^2-4.12.299}}{2.12}

\Rightarrow x= 9.33, 2.67

If  we take x=9.33 in, then the width of the box [13-(2×9.33)] will negative.

∴x = 2.67 in

If at x = 2.67, V''<0 , then the volume of the box will be maximum or V''>0 then volume of the box will be minimum.

V''|_{x=2.67}=-144+(24\times 2.67)=-79.92

Therefore  at x = 2.67, the volume of the box maximum.

The length of the box =[23-(2×2.67)] in

                                    =17.66 in

The width of the box =[13-(2×2.67)] in

                                  =7.66 in

The height of the box= 2.67 in

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is =(17.66×7.66×2.67) in^3

                                                            =361.19 in^3

8 0
3 years ago
For the Christmas dance ,the dance committee needs three hours of music. Each song is an average of 3.5 minutes . how many song
GREYUIT [131]
An hour is 60 minutes

there are three hours so 
60*3=180

how many times will 3.5 go into 180 so 
180/3.5=51.43 or rounded up you get 52 songs (if they're good, they'll play 52 average songs and one half legnth songs)
so they will need 52 songs

3 0
3 years ago
Read 2 more answers
What is the value of x? (Use only the digits 0 - 9 and the decimal point, if needed, to write the number.)
GREYUIT [131]

Answer:

5.34

Step-by-step explanation:

X + 12.66 = 18

-12.66 -12.66

X = 5.34

3 0
2 years ago
Read 2 more answers
What slope is perpendicular to x + 4y = 12
myrzilka [38]
Solve for the equation. The. Divide by 4 on both sides. And whatever you get for the slope. Write the opposite which will give you the perpendicular slope. For example: 1/4x is perpendicular to -4x
6 0
3 years ago
Which equation will solve the following word problem? News Center 13 has just released tomorrow's weather forecast. The high tem
WARRIOR [948]

Answer:

low temperature= high temperature/2 or X= 74/2

Step-by-step explanation:

The low is 37 btw

6 0
3 years ago
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