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3 years ago

What is the value of x in the equation shown below 0.75x + 3 = 6(x - 3)

Mathematics

1 answer:

EleoNora [17]3 years ago

7 0

Answer: x=4

Step-by-step explanation: 0.75x+3=6(x−3)

0.75x+3=(6)(x)+(6)(−3)

0.75x+3=6x+−18

0.75x+3=6x−18

0.75x+3−6x=6x−18−6x

−5.25x+3−3=−18−3

−5.25x /−5.25 =− 21 /−5.25

x=4

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Answer:

After solving the power:

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Step-by-step explanation:

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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:

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First of all, let us solve:

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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:

$\bold{1+i\sqrt3}$

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