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3 years ago

Why is 0 not an identity for subtraction? explain

Mathematics

1 answer:

ki77a [65]3 years ago

5 0

When zero is added to or subtracted to a number, the number is not affected.

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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.

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Answer would be: B.) 3/8 cup

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. Kyle is 24 years older than his daughter Hannah. Kyle is 48 years old. How old is Hannah?

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Suppose your dean of admissions is considering surveying high school seniors about their perceptions of your school to design be

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Answer and explanation:

Advantages of telephone interviews:

They are more convenient than face to face interviews

They are alot more cost-effective

There is a wider geographical access as you can reach people in other countries too

Disadvantages of telephone interviews:

Questions become has limited complexity as opposed to face to face interviews

It may be somewhat intrusive for customers and there could also be interference from noise in the background. Also bad connection issues.

Advantages of internet survey:

Increased geographical access leading to high response rate.

Alot more convenient and flexible than face to face interviews

Low cost advantages

Disadvantages of internet survey:

Inability for individuals who are not online to participate

Non response bias

Limited complexity of questions, usually close ended questions

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Which statement below compares the decimals correctly?

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