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3 years ago

The slope of the line below is 2/5 and the y-intercept is (0, 4). What is the slope-intercept equation of the line?

Mathematics

1 answer:

atroni [7]3 years ago

3 0

Answer:5y=20+2x

Step-by-step explanation:

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Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form.

slava [35]

Answer:

After solving the power:

$\bold{2(cos60^\circ+isin60^\circ)}$

Rectangular form:

$\bold{1+i\sqrt3}$

Step-by-step explanation:

Given the complex number:

$2(cos20^\circ+isin20^\circ)^3$

To find:

The indicated power by using De Moivre's theorem.

The complex number in rectangular form.

Rectangular form of a complex number is given as $a+ib$ where a and b are real numbers.

Solution:

First of all, let us have a look at the De Moivre's theorem:

$(cos\theta+isin\theta )^n=cos(n\theta)+isin(n\theta )$

First of all, let us solve:

$(cos20^\circ+isin20^\circ)^3$

Let us apply the De Moivre's Theorem:

Here, n = 3

$(cos20^\circ+isin20^\circ)^3 = cos(3 \times 20)^\circ+isin(3 \times 20)^\circ\\\Rightarrow cos60^\circ+isin60^\circ$

Now, the given complex number becomes:

$2(cos60^\circ+isin60^\circ)$

Let us put the values of $cos60^\circ = \frac{1}{2}$ and $sin60^\circ = \frac{\sqrt3}{2}$

$2(\dfrac{1}{2}+i\dfrac{\sqrt3}2)\\\Rightarrow (2 \times \dfrac{1}{2}+i\dfrac{\sqrt3}2\times 2)\\\Rightarrow \bold{1 +i\sqrt3 }$

So, the rectangular form of the given complex number is:

$\bold{1+i\sqrt3}$

3 0

3 years ago

2.4 times (-8.3) how much would it equal

a_sh-v [17]

it would equal -19.92

4 0

3 years ago

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9. Which property is illustrated by (6 x 5) x 4 =6 x (5 x 4)?

Advocard [28]

For this case we have that by definition:

$(a * b) * c = a * (b * c)$

Indicates an example of the associative property of multiplication.

$(6 * 5) * 4 = 6 * (5 * 4)\\30 * 4 = 6 * 20\\120 = 120$

Similarly, we observe the associative property of multiplication

Answer:

associative property of multiplication

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4 years ago

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What is the slope of the line in this graph?

White raven [17]

Answer: 5/7. So B

Step-by-step explanation:

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3 years ago

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Two passengers leave the airport at Kansas City, Missouri. One flies to Los Angeles, California, in 4 hr and the other flies in

blsea [12.9K]

Answer:

Speed of plane to Los Angeles: 400 miles per hour

speed of plan to new York city: 460 miles per hour

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3 years ago

The slope of the line below is 2/5 and the y-intercept is (0, 4). What is the slope-intercept equation of the line?​

The slope of the line below is 2/5 and the y-intercept is (0, 4). What is the slope-intercept equation of the line?