The volume of a cube is 500 cubic feet. What is the length of each edge of the cube?

Answer:

○ \(\displaystyle \frac{7 + 4i}{10}\)

Step-by-step explanation:

\(\displaystyle \frac{2 + 3i}{4 + 2i} → \frac{2 + 3i[4 - 2i]}{4 + 2i[4 - 2i]} = \frac{14 + 8i}{20} = \boxed{\frac{7}{10} + \frac{2}{5}i}\)

When dividing complex numbers, multiply the denominatour and numeratour by the conjugate of the denominatour. Then simply towards the end.

* Here is something you should know:

\(\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = i^4\: [every\:multiple\:of\:four]\)

I am joyous to assist you at any time.

Answer:

  7) perimeter = 16 units; area = 12 square units

  8) perimeter = 8 +√13 +√29 ≈ 17.0 units; area = 8 square units

Step-by-step explanation:

You want the perimeter and area of figures defined by their coordinates.

The figure is the brown rectangle in the attachment. It is seen to have a width of 2 units and a height of 6 units. The perimeter and area formulas are ...

  P = 2(W+H) = 2(2+6) = 16 . . . . units

  A = WH = (2)(6) = 12 . . . . square units

The perimeter of the figure is 16 units; the area is 12 square units.

The figure is the blue triangle in the attachment. It is seen to have a base length of 8 units, and a height of 2 units. Vertex T is 3 units from one end of the triangle, and 5 units from the other end.

The lengths of the sides can be found from the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

For side ST, its length is ...

  d = √((3 -0)² +(-2 -0)²) = √(9 +4) = √13 ≈ 3.606

For side TU, the side length is ...

  d = √((8 -3)² +(0 -(-2))²) = √(25 +4) = √29 ≈ 5.385

Side length SU can be seen to be 8 units with no calculation required.

The perimeter is the sum of the side lengths:

  ST +TU +UT = 3.606 +5.385 +8.000 = 16.991 ≈ 17.0 . . . . units

The area formula is

  A = 1/2bh

  A = 1/2(8)(2) = 8 . . . . square units

The perimeter of the figure is about 17.0 units; the area is 8 square units

The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Learn more about divergence of the vector this link:

https://brainly.com/question/30907324

#SPJ11

The probability that the sample proportion is greater than 0.24 is 0.9772

Given Data :

population proportion,  p = 0.31

sample size n = 179

μ = p = 0.31

σ = √p(1-p)/n =√( 0.31 (1-0.31 )/179 )= 0.0011

Let p be the sample proportion

p following normal distribution N (μ = 0.31 , σ = 0.0011 )

Here

z = (p - μ) / σ

Now

Now, We Have To Compute P (p > 0.24 )

Therefore,

p (p> 0.15 ) =1 - p( (p-μ )/σ < (0.24 -0.31)/0.0349 )

= 1-p(z < -2.0057) -----from z table

= 1 - 0.0228

=0.9772

Consequently, 0.9772 percent chance exists that the sample proportion will be higher than 0.24.

To learn more about probability click here:

https://brainly.com/question/28045837

#SPJ4

\(d^5\)

Recall the Law of Exponents:

\(\frac{a^m}{a^n} = a^{m -n}\\\)

Rewriting \(\frac{d^9}{d^4}\\\):

\(\frac{d^9}{d^4} \\ d^{9 -4} \\ d^5\)

Answer:

a)

x=4, y=-2

b)

x=2, y=2

c)

x=0, y=0

d)

x=1, y=1

e)

x=3, y=3

f)

x=4, y=4

Step-by-step explanation:

a) (x,-2) = (4,y)

x=4

y=-2

b) (3x, 4) = (6, 2y)

3x=6 => x=2

2y=4 => y=2

c) (2x-1, y + 2) = (-1,2)

2x-1 =-1 => x=0

y+2 = 2 => y=0

d) (2x + 4, y + 5) = (3x + 3,6)

2x+4 = 3x+3 => x=1

y+5 = 6 => y=1

e) (x + y,y + 3) = (6, 2y)

x+y = 6 => x+3 = 6 => x=3

y+3 = 2y => y=3

f) (x + y, x - y) - (8,0)​

x+y = 8 => 2x=8 => x=4

x-y = 0 => x=y => y=4

Answer:

b

Step-by-step explanation:

There are six different positive integers divisible by 4 that can be formed using each of the digits 1, 2, 3, and 4 at most once and no other digits: 12, 24, 32, 42, 43, and 124.

1. 12: 1 and 2

2. 24: 2 and 4

3. 32: 3 and 2

4. 42: 4 and 2

5. 43: 4 and 3

6. 124: 1, 2 and 4

The six different positive integers divisible by 4 that can be formed using each of the digits 1, 2, 3, and 4 at most once and no other digits are 12, 24, 32, 42, 43, and 124. To find these numbers, we begin by examining all the possibilities that can be formed using the digits 1, 2, 3, and 4. We can form 12, 24, 32, 42, 43 and 124 by combining different combinations of the digits. For example, 12 is made up of the digits 1 and 2. 24 is made up of 2 and 4. 32 is made up of 3 and 2. 42 is made up of 4 and 2.

Learn more about integer here

https://brainly.com/question/15276410

#SPJ4

Answer:

28

Step-by-step explanation:

4 x 77 / 11 x 1  =  308 / 11

308/11 = 28    11/11 = 1

the answer is 28 / 1

Hey there!

4/11 of 77

= 4/11 * 77/1

= 4(77) / 11(1)

= 77(4) / 1(11)

= 77 + 77 + 77 + 77 / 11

= 154 + 154 / 11

= 308 / 11

= 28

Therefore, your answer is: 28

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

6

Step-by-step explanation:

Sin = adjacent ÷ hypotenuse

Sin 45 = x ÷ 9

0.71 = x ÷ 9

0.71 × 9 = x

x = 6.36

~6.

hope it helps. :)

ANSWER = 8460x (5y-23)(2x+13)

                                 60

Answer:

x = 600 pages

Step-by-step explanation:

Let the total books pages be x

Given that

Hank had read = 25% of x

25% of x = 150

=>  

Multiplying both sides by 4

=> x = 150 * 4

=> x = 600 pages

Step-by-step explanation:

There you go.

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

45x+6y=15

-x+18y = 11

let's use elimination, the other way is by substitution,  either way works but, it looks to me like elimination would be easy with the  'y'

3(45x+6y=15)

135x + 18y = 45 ( subtract  2nd eq.  from 1st )

-( -x+18y = 11 )

136x +0y =34

x = 34 /136

x = 1 /4

there is X

plug that back into either of the 1st or 2nd equations to solve for y

- 1/4 + 18 y = 11

18y = 11 1/4

18y = 45/4

y = 45/4 *  1/18

y = 45/ 72

the fractions seem  "difficult"  but that's just what the given problem finds

sent a message if you don't "get it"    :)

Answer:

Step-by-step explanation:

You make 4 into 4/1 and then raise it to 8/2. then you divide across, if im right.

Answer:

4 is the same things as 4/1. and we know that dividing by a fraction is the same thing as multiplying by its reciprocal. so 5/2 times 1/4. just multiply straight across and you get 5/8

Step-by-step explanation:

The number of liters of paint needed will be A divided by 8.

We have,

To calculate the amount of paint needed, we need to consider the coverage rate of the paint, which is given as 1 liter of paint covering 8 square meters.

This means that 1 liter of paint is sufficient to cover an area of 8 square meters.

To determine the total amount of paint needed for a specific area, we divide the total area (in square meters) by the coverage rate (8 square meters per liter).

This calculation gives us the number of liters required to cover the entire area.

For example,

Let's say we have a wall with an area of 32 square meters.

To calculate the amount of paint needed, we divide 32 by 8:

Number of liters needed

= 32 / 8

= 4

So, in this case, we would need 4 liters of paint to cover the entire 32 square meters of the wall.

This approach can be applied to any given area to calculate the required amount of paint based on the given coverage rate.

Thus,

The number of liters of paint needed will be A divided by 8.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Let's transform the equation into slope intercept form first ~

that is ~

now, equate the equation with general equation of line in slope intercept form (that is : y = mx + c) where, m = slope of the line and c = its y - intercept.

So, we get the value of m (slope) as ~

where as the value of c (y - intercept) is ~

I hope it helps ~

Step-by-step explanation:

False!

the correct equation should be ( x - 3)² + 2

3 units shifted to the right and 2 units upward.

also you can expand the equation to find the axis of symmetry to be sure. :)

Answer:

Open

Step-by-step explanation:

The <, > signs will have an open circle and the greater than or equal to or less than or equal to will be a be a closed circle.

Hope this helps and I hope u have an Amazing day!!

To determine the vertices of image U′V′W′ after a 180° counterclockwise rotation, we can apply the following transformation rules:

Using these rules, we can find the vertices of image U′V′W′ as follows:

Therefore, the vertices of image U′V′W′ after a 180° counterclockwise rotation are U′(0, -2), V′(1, -3), and W′(3, -3).

So, the answer is option (b) U′(0, −2), V′(1, −3), W′(3, −3).

The next term is -88.7

The value of du becomes 4 by integration.

According to the statement

we have given a two statement which are u - 4x and  u = x + 1.

And we have to find the value of du by the use of integration.

An Integral assigns numbers to functions in a way that describes the data.

So,

From u  - 4x

here du becomes by derivative

du - 4dx/du

du = 4dx/du.  -(1)

And in u = x + 1.

here du becomes

du = dx/du  -(2)

by comparing both terms from equation (1) and (2) we get the value of du

du = 4.

the value of du is 4.

So, The value of du becomes 4 by integration.

Learn more about INTEGRATION here https://brainly.com/question/19053586

#SPJ4

Answer:

thank u so much dost pls give me extra free point Pls mark as a brilliant pls dost

Answer:

20 counters/box

Step-by-step explanation:

Missing counters(m)= 8

Total number of counters available (t-m)= 132

Required number of counters(t):

=(t-m) + m

= 132 + 8 = 140

Total number of boxes(tB) = 7( 6 full and one with eight missing)

Total Counters/Boxes= t/tB

= 140/7

= 20

\(a = \frac{1}{2} h(b1 + b2)\)

take h 4½ to the left

\( \frac{2a}{h} = b1 + b2\)

take b2 to the left

\(b1 = \frac{2a}{h} - b2\)

\(b2 = \frac{2a}{h} - b2\)

Answer:

ummm -34x-14=46

Step-by-step explanation:

Answer:

2 + 2x = 262x = 24x=12 3.

Step-by-step explanation:

i think its right

Answer:

gkekwjrjwitkciviewjfjic