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3 years ago

300,719,287,824 + 297,789,000,086

Mathematics

1 answer:

sammy [17]3 years ago

4 0

Answer:

598508287910

Step-by-step explanation:

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

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

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

What is the equation of the given line in the point-slope form

Genrish500 [490]

First using the given two points we can find the slope (m) of the line

$Slope = m = \frac{Rise}{Run} \\ \\ 
m= \frac{4-1}{3-0} \\ \\ 
m=1$

Thus the slope of given line is 1.

Using slope and a point (0,1) we can write the equation in point slope form as

y - 1= 1(x-0)
y - 1 = x

The above equation is the point-slope form of the equation.

4 0

3 years ago

Evaluate Each Expression. (Show Your Work.)

Anna11 [10]

Answer:

1. 8^2

2. 3^4

3. 5^3

Step-by-step explanation:

1)8×8 = 64

2)3×3×3×3=81

3)5×5×5=125

3 0

3 years ago

Find the midpoint of the segment with the following endpoints (-10,-1) and (-6,7)

Gala2k [10]

Answer:

(-8 , 3)

Step-by-step explanation:

(x1 , y1) (x2 , y2) = (-10 , -1) (-6 , 7)

$\frac{-6-10}{2}$ , $\frac{7-1}{2}$ -6 is going to be my x1 and -10 my y1

7 is going to be my x2 and -1 my y2

(-8 , 3)

7 0

3 years ago

-7x - 2y = 19<br> 4x + y = -12<br> Solve the system

nalin [4]

-7x - 2y = 19

4x + y = -12

Set y equal to each other (opposite signs are fine and you could also set x equal instead of y)

-7x - 2y = 19

8x + 2y = -76

Add equations together

x = -52

Plug x value into an equation

4(-52) + y = -12

Solve for y

-208 + y = -12

y = 196

Hope this helps! ;)

4 0

3 years ago