What is the rectangular form of 12(cos(Pi) + isin(Pi))?

12
-12
12 + i
–12 + i

Answer:

$69.21

Step-by-step explanation:

Since the box has a square base the length and breadth of the box will be equal. Let it be [tex]x[/tex]

Let h be the height of the box

V = Volume of the box = [tex]620\ \text{cm}^3[/tex]

[tex]x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}[/tex]

Now surface area of the box with an open top is given

[tex]s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}[/tex]

Differentiating with respect to x we get

[tex]\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}[/tex]

Equating with zero

[tex]0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74[/tex]

Double derivative of the function

[tex]\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0[/tex]

So, x at 10.74 is the minimum value of the function.

[tex]h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37[/tex]

So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.

The total area of the sides is [tex]4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2[/tex]

The area of the base is [tex]x^2=10.74^2=115.35\ \text{cm}^2[/tex]

Cost of the base is $0.40 per square cm

Cost of the side is  $0.10 per square cm

Minimum cost would be

[tex]230.7\times 0.1+0.4\times 115.34=\$69.21[/tex]

The minimum cost of the box is 69.21 dollars.

Answer:

Unitary cost (per pound)= $0.682

Step-by-step explanation:

Giving the following information:

Total cost= $3.75

Total pounds= 5.5 pounds

To calculate the unitary cost of each pound, we need to use the following formula:

Unitary cost= total cost / total pounds

Unitary cost per pound= 3.75 / 5.5

Unitary cost per pound= $0.682

Answer:

0.49 49

=

49      this is a fraction

99

Step-by-step explanation:

Let

XXX

x

=

0.49

¯¯¯¯

49

then

XXX

100

x

=

49.49

¯¯¯¯

49

and

XXX

99

x

=

100

x

−

x

=

49

XXX

x

=

49

99

Answer:

2

Step-by-step explanation:

y=mx+n m is slope

y-6=2(x+3) so y=2x+12  m=2 is slope.

Allison's average driving speed in miles per hour is 65.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

130 miles = 2 hours

Divide 2 on both sides.

130/2 miles = 1 hour

65 miles = 1 hour

Thus,

The average speed is 65 miles per hour.

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Answer:

The number is 2

Step-by-step explanation:

To attempt this question, we need to represent the number with (x).

Let the number be x

Five more than the number is:

5 + x

Seven-halves means 1/2 × 7 = 7/2

Mathematically, the question is saying:

5 + x = 7/2 × x

5 + x = 7x/2

Cross multiply;

2(5 + x) = 7x

10 + 2x = 7x

We collect like terms;

10 = 7x - 2x

10 = 5x

x = 10/5

x = 2

The number represented by x is 2

We want to convert the given sentence into an equation, and then solve it. We will see that the number is 2.

We start with the sentence:

"Five more than a number is equal to seven-halves of the number"

if we define x as the number, we can write:

5 + x = (7/2)*x

Now we can solve this equation for x, we will get:

5 + x = (7/2)*x

5 = (7/2)*x - x = (7/2 - 1)*x

5 = (7/2 - 2/2)*x = (5/2)*x

(2/5)*5 = x

2 = x

So the number is 2.

If you want to learn more about linear equations, you can read:

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Answer:

no puedo alludar te perdón

Answer:

12m by 3m

Step-by-step explanation:

lol please mark brainliest

Answer:

10

Step-by-step explanation:

you do the one plus the nine which gives you 11 then subtract 2 which gets you 9 then add 4 which gets you 13 then minus 3 which gets you 10.

Answer:

The density is 8.5 g/cm³

Step-by-step explanation:

The density formula is density = mass/volume

When we plug our numbers into the formula, we get:

Density = 2210 / 260

We can then solve and get our answer 8.5 g/cm³

It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 . The density is 8.5 g/cm³.

Suppose that a finite amount of substance is there having its properties as:

The mass of substance = m kg

The density of substance = d kg/m³

The volume of that substance = v m³

Then, they are related as:

[tex]d = \dfrac{m}{v}[/tex]

It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 .

density = mass/volume

When we substitute our numbers into the formula, we get:

Density = 2210 / 260

Density = 8.5 g/cm³

It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 . The density is 8.5 g/cm³

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Answer:

The probability that the device fails during its first hour of operation is 0.625.

Step-by-step explanation:

The joint density function of the lifetimes of the two components, both measured in hours, is:

[tex]f(x,y)=\frac{x+y}{8};\ 0<x<2,\ 0<y<2[/tex]

Compute the probability that the device fails during its first hour of operation as follows:

[tex]P[(X<1)\cup (Y<1)]=1-\int\limits^{2}_{1} {\int\limits^{2}_{1} {\frac{x+y}{8}} \, dx } \, dy[/tex]

                                  [tex]=1-\int\limits^{2}_{1} {\frac{x^{2}+2xy}{16}}|^{2}_{1} \, dy\\\\=1- \int\limits^{2}_{1}[{\frac{4+4y}{16}-\frac{1+2y}{16}}] \, dy\\\\=1-\int\limits^{2}_{1}{\frac{3+2y}{16}}\, dy\\\\=1-[\frac{3y+y^{2}}{16}]^{2}_{1}\\\\=1-0.375\\\\=0.625[/tex]

Thus, the probability that the device fails during its first hour of operation is 0.625.

Answer:

y = 8º

y = 8º  

Step-by-step explanation:

Given:

(10x - 61)º  

(18y + 5)º

(x + 10)º

Find:

x and y

Computation:

(10x - 61) + (x + 10) = 180

11x - 51 = 180

11x = 231

x = 21º

(10x - 61)º   = (18y + 5)º      [Vertical opposite angle]

10x - 61 = 18y + 5

10x - 18y = 66

5(21) - 9y = 33

y = 8º

Answer: x=60

Step-by-step explanation:

x+22+x+6+x−28=180

Step 1: Simplify both sides of the equation.

x+22+x+6+x−28=180

x+22+x+6+x+−28=180

(x+x+x)+(22+6+−28)=180(Combine Like Terms)  22+6=28 and then 28-28=0

3x=180  

3x=180

Step 2: Divide both sides by 3.

3x/3 = 180/3

x=60

hope this was helpful.

Answer:

$1

Step-by-step explanation:

i hope i read it right

Answer:

1

Step-by-step explanation:

cuz half of 2 is 1

417

Step-by-step explanation:

I hope this helps :)

Answer:

Being proportional between two entities, refers to the 'Constant of Proportionality' that would be fixed between them which establishes a relationship between them when multiplied or divided.

If we considered it on a graph, the 'Constant Of Proportionality' may take any real values between the coordinate pairs x and y [x,y]. As even 0 is a real number, it will surely be a constant of proportionality when multiplied since its product would result in itself (0). Hence, both x and y turns 0.

As the coordinates of the origin are always (0,0), the graph  (Or the slope) would surely pass through the origin.

Example :

If we consider a graph such that x=y.

And if we multiply or divide any real number (a) between them.

ax=ay

As a is a variable, and can take the value of 0, the graph can pass through the origin as x and y nullify becoming the coordinates of the origin.

Answer:

6/53

Step-by-step explanation:

Answer:

45 Degrees

Step-by-step explanation:

Compare to its other side

Answer:

[tex]m=\frac{-14}{11}[/tex]

General Formula and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Point (9, -5)

Point (-2, 9)

Step 2: Find slope m

Answer:

Between 2.25 and 2.5

Step-by-step explanation:

The square root of 6 is 2.4494.... which is closer to 2.5

Answer:

1,232 ft/min (feet per minute)

Step-by-step explanation:

14 miles = 73,920 feet

1 hour = 60 minutes

73, 920 / 60 = 1,232 feet/minute

Answer:

13. 1/4x

14. -2/4x or -1/2x

15 1/3x or 2/6x

16. Zero

Step-by-step explanation:

13. goes up once and goes to the side 4 times

14. goes down twice and goes to the side 4 times

15. goes up one time and three to the side

16. zero slope, the line is horizontal

Answer:

13. 1/4

14. -1/2

15 1/3

16. Zero

Step-by-step explanation:

Answer:

A) 7 and 8

Step-by-step explanation:

root of 7 is 2.64575..... then when u multiply by 3

3*2.64575=7.93725

Answer: The answer would be -5w-1

Step-by-step explanation:

Answer:

xcgvb                     vgjbnnnnnnnnnn vbjn bvh

Step-by-step explanation:

Answer:

8 Hours.

Step-by-step explanation:

Answer:

= -56.22

Step-by-step explanation:

have a great day

pls mark as brainliest!

hope this helped!

Answer:

-56.22

just calculated it (:

Answer:

5/7

Step-by-step explanation:

You find a slope by using the equation y2-y1/x2-x1.

In this case: 15-5/21-7

10/14

5/7

Since S is closed, you can use the divergence theorem, which says

[tex]\displaystyle\iint_S \vec F(x,y,z) \cdot \mathrm d\vec S=\iiint_R \mathrm{div}\vec F(x,y,z)\,\mathrm dV[/tex]

where R is the interior of the surface S.

We have

div F (x, y, z) = ∂/∂x (0) + ∂/∂y (y) + ∂/∂z (-z) = 1 - 1 = 0

so the flux would be 0.

In this exercise we have to calculate the flux by the divergent theorem:

The flux would be ZERO

Since S is closed, you can use the divergence theorem, which says:

[tex]\int\limits\int\limits_s {F(x,y,z} \, ds= \int\limits \int\limits\int\limits_R {divF(x, y, z)} \, dv[/tex]

where R is the interior of the surface S. We have:

[tex]\nabla F (x, y, z) = 1-1= 0[/tex]

so the flux would be ZERO.

See more about vectorial calculus at : brainly.com/question/6960786