• Which expression is equivalent to 2(8n)

Answer: C. cos(Pi) + isin(Pi)

Step-by-step explanation:

The value of subtraction of two given complex numbers z₁ and z₂ is cos(π) + isin(π).

A complex number is an element of a number system that includes real numbers and a specific element labeled i sometimes known as the imaginary unit, and which obeys the equation i² = 1. Furthermore, every complex number can be written as a + bi, where a and b are both real values.

We know that cos(π - x) = - cosx, sin(π - x) = sinx, cos(π/4) = 1/√2 = sin(π/4), cos(π/2) = 0, sin(π/2) = 1, cos(π) = - 1, sin(π) = 0.

Given that z₁ = √2[cos(3π/4) + isin(3π/4)] = √2[cos(π - π/4) + sin(π - π/4)] = √2[- cos(π/4) + sin(π/4)] = √2[- 1/√2 + 1/√2] = √2[0] = 0

and z₂ = cos(π/2) + isin(π/2) = 0 + i × 1 = 1

Now, z₁ - z₂ = 0 - 1 = - 1 = - 1 + i × 0 = cos(π) + isin(π)

Therefore, the value of subtraction of two given complex numbers z₁ and z₂ is cos(π) + isin(π).

Learn more about complex numbers here -

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Answer:

[tex]\frac{1}{9}[/tex]    

Answer:

p > -3

Step-by-step explanation:

This is an alternating p-series.  It is absolutely convergent if│an│converges.  1 / nᵖ⁺³ converges if the exponent is greater than 1.

p + 3 > 1

p > -2

The series is conditionally convergent if │an│diverges.  1 / nᵖ⁺³ diverges if the exponent is greater than 0 and less than or equal to 1.

0 < p + 3 ≤ 1

-3 < p ≤ -2

Combining these two, we get p > -3.

Answer:

The equations for each situation are

A = 36 + 6t

B = 21 + 9t

After 3 years, Tree A is taller.

Step-by-step explanation:

From the question,

Tree A was 36 inches tall and Tree B was 21 inches tall at the time of planting; and

Tree A grew by 6 inches per year and Tree B grew by 9 inches per  year after planting.

For Tree A,

Given a period of t years after planting, the height would have increased by 6t

∴ A = 36 + 6t

For Tree B,

Given a period of t years after planting, the height would have increased by 9t

∴ B = 21 + 9t

To determine, which tree is taller after 3 years,

t = 3

For Tree A

A = 36 + 6t

A = 36 + 6(3)

A = 36 + 18

A = 54 inches

For Tree B

B = 21 + 9t

B = 21 + 9(3)

B = 21 + 27

B = 48 inches

Hence, After 3 years, Tree A is taller.

9514 1404 393

Answer:

  a = {1, 2, 3}, b = (2, 4, 7}, c = (-3/14, -3/7, 5/14}

Step-by-step explanation:

For the above vectors, ...

  a × b = a × c = (2, -1, 0)

__

Here, c is found to be a scaled version of (a×(a×b)).

Answer:

take a look ...........

5x² + 2x - 3 < 0

5x² + 2x < 3

x² + 2/5 x < 3/5

Complete the square on the left side:

x² + 2/5 x + 1/25 - 1/25 < 3/5

(x + 1/5)² - 1/25 < 3/5

(x + 1/5)² < 16/25

Take the square root of both sides, keeping in mind that √(x²) = |x| for all x.

√((x + 1/5)²) < √(16/25)

|x + 1/5| < 4/5

This means

-4/5 < x + 1/5 < 4/5

-1 < x < 3/5

Answer:

Step-by-step explanation:

Because the area of a triangle you have to divide by 2 and then you get the area right so we multiply 80 x 2 = 160 is the area of the square which you divide by 2 but we are not going to do that. now we have to get 2 lengths with 12 difference so we have to just do trial and error method.

Answer:

its b

Step-by-step explanation:

took the test on edge

Answer:

9 by adding all the three cards

Answer:

The final balance is $1,692.94.

The total compound interest is $392.94.

Step-by-step explanation:

1,300 x 0.045=___ x 6

Answer:

26,676population

Step-by-step explanation:

Population in 2010 = 24,700

If it grows yearly by 1%, increment per year is expressed as:

1% of 24,700

= 1/100×24700

= 247 populations

After 8years, population increase will be 247×8 = 1976 population

Statesville population in 2018 will be expressed as;

Population in 2010+increase after 8years

= 24700+1976

= 26,676 population

Hence statesville population in 2018 will be 26,676population

Answer:

x = -3

Step-by-step explanation:

f(x) = x + 3

0 = x + 3

-x = 3

x = -3

Answer:

4 becuase 40+14 = 54 so 50+4= 54 too

Step-by-step explanation:

Answer:

It will take her 318 minutes.

Step-by-step explanation:

26.5 times 12 equals 318

Answer:

25.84 divide by 4 Is 6.46.

Answer:

x = amount of 100% acid solution (pure acid, no water)

y = amount of 10% acid solution (acid + water)

both amounts are in liters

Step-by-step explanation:

Answer:

all really all you have to do is do 8 divided by 19 and then whatever that number that you get from that attractive from your highest number that you have in your question which is 11000

The answer to the equation is [tex]n=5[/tex]

First, you must add 0.8n on both sides.

[tex]0.6n+7=10[/tex]

Then, subtract 7 from both sides.

[tex]0.6n=3[/tex]

Finally, divide both sides by 0.6

[tex]n=5[/tex]

Answer:

root 85

decimal 9.21

slope 9/2

Step-by-step explanation:

didnt know which one you wanted fully

Answer: The trip should take 3.5 hours.

Step-by-step explanation: To find the time, divide the distance by the rate. In this case, 210/60 = 3.5.

Answer:

3.5 hours or specifically, 3 hours and 30 minutes

Step-by-step explanation:

We know that the car can be driven 60 miles per hour. The goal is 210 miles. If you divide 210 miles by 60, the result is 3.5. The whole number 3 in 3.5 will represent the hours taken which means 3 hours. The 0.5 will also represent the minutes. 0.5 = 1/2, 1/2 of an hour = 30 minutes.

Answer:

.77

Step-by-step explanation:

the 7 is repeating so you can put a dash above the second 7