El número de llegadas al servicio de urgencias de un hospital es de 2 cada 15 min. Si se supone que

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

Find the area of the isosceles triangle. please help thanks

fiasKO [112]

Answer:

1080 m^2 Don't submit m^2 in your answer.

Step-by-step explanation:

Givens

The catch is to find h

To do that, use a^2 + b^2 = c^2

a b and c are in the same 1/2 triangle.

a = 48/2 = 24 m

b = h = ?

c = 51 meters

Solution

a^2 + b^2 = 51^2 Substitute for b^2 = h^2

24^2 + h^2 = 51^2 Expand 24^2 and 51^2

576 + h^2 = 2601 Subtract 576 from both sides

h^2 = 2601 - 576

h^2 = 2025 Take the square root of both sides

h = 45

Area

Area = 1/2 b * h

Area = 1/2 48 * 45

Area = 1080

Remark

Notice that to find h you only use 1/2 of 48 because that is the base of the right triangle.

To find the area, you need to use all of 48 because 48 is the full length of the base.

5 0

3 years ago

Use set notation to write the members of the following set, or state that the set has no members. Odd numbers between 2 and 82 t

adell [148]

Let the set of all Odd multiples of 9 between 2 and 82 be denoted by D, then, using set-builder notation,

$D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}$

The odd multiples of 9, $m$ , in the range $2\le m \le 82$ form the set

$\{9,27,45,63,81\}$

Each member of the set is a term of the arithmetic progression

$U_n=18n+9$

where the values of $n$ range from 0 to 4, or $0\le n\le 4$

Putting these facts together, we get the result

$D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}$

Learn more about set-builder notation here: brainly.com/question/17238769

3 0

2 years ago

Shawndra said that it is not possible to draw a trapezoid that is a rectangle, but it is possible to draw a square that is a rec

ICE Princess25 [194]

Shawndra is correct

She made two statements, and both are true:

1. It is not possible to draw a trapezoid that is a rectangle.

This is true because a trapezoid<span> is a quadrilateral that has exactly one pair of parallel sides, whereas a rectangle is a parallelogram (i.e. it has two pairs of parallel sides)</span>

2. It is possible to draw a square that is a rectangle.

This is true because a rectangle refers to any parallelogram with right angles. A square is also a parallelogram (has two pairs of opposite sides) with right angles. In fact, all squares are rectangles; only that they are a special kind of rectangle, where all the sides are equal in length.

8 0

3 years ago

Read 2 more answers

If two lines are perpendicular, which statement must be true?

Kryger [21]

Answer:

Their slopes are opposites

8 0

2 years ago