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vagabundo [1.1K]

3 years ago

13

12-sqrt(-8) Complex number notation

1 answer:

andrey2020 [161]3 years ago

4 0

Answer:

The complex number notation of 12-sqrt(-8) is 12 - 2.828i

Step-by-step explanation:

Given:

12-sqrt(-8)

To Find:

The complex number notation of 12-sqrt(-8)

Solution:

12-sqrt(-8) can be $12-\sqrt{(8}$

where $\sqrt{8}$ can be written as

$\sqrt {4 \cdot 2 \cdot -1}$

Now using the below radical rule which states that

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

Then,

$\sqrt {4 \cdot 2 \cdot (-1)}$

=> $\sqrt {4} \cdot \sqrt {2} \cdot \sqrt { -1}$

=> $2 \cdot \sqrt {2} \cdot \sqrt {-1}$ -----------------(1)

Also we know that

$\sqrt {-1}= i$ ---------------------(2)

substituting (2) in (1)

we get

=> $2 \cdot \sqrt {2} \cdot i$

=> $2i \cdot \sqrt {2}$

=> $2i \cdot 1.414$

=> 2.828i

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Solve by quadratic equation

Ymorist [56]

<h2>Question :</h2>

$\tt \dfrac{x+2}{x-2} + \dfrac{x-2}{x+2} = \dfrac{5}{6}$

<h2>Answer :</h2>

$\large \underline{\boxed{\bf{x = \dfrac{\pm 2\sqrt{119}}{7}}}}$

<h2>Explanation :</h2>

$\tt : \implies \dfrac{x+2}{x-2} + \dfrac{x-2}{x+2} = \dfrac{5}{6}$

$\tt : \implies \dfrac{(x+2)(x+2) + (x-2)(x-2)}{(x-2)(x+2)} = \dfrac{5}{6}$

$\tt : \implies \dfrac{(x+2)^{2} + (x-2)^{2}}{(x-2)(x+2)} = \dfrac{5}{6}$

<u>Now, we know that</u> :

$\large \underline{\boxed{\bf{(a+b)^{2} = a^{2} + b^{2}+ 2ab}}}$
$\large \underline{\boxed{\bf{(a-b)^{2} = a^{2} + b^{2} - 2ab}}}$
$\large \underline{\boxed{\bf{(a+b)(a-b) = a^{2} - b^{2}}}}$

$\tt : \implies \dfrac{x^{2}+2^{2}+ 2 \times x \times 2 + x^{2}+2^{2} - 2 \times x \times 2 }{x^{2}-2^{2}} = \dfrac{5}{6}$

$\tt : \implies \dfrac{x^{2}+ 4 + \cancel{4x} + x^{2}+ 4 - \cancel{4x}}{x^{2}-4} = \dfrac{5}{6}$

$\tt : \implies \dfrac{x^{2} + x^{2} + 4 + 4}{x^{2}-4} = \dfrac{5}{6}$

$\tt : \implies \dfrac{2x^{2} + 8}{x^{2}-4} = \dfrac{5}{6}$

<u>By cross multiply</u> :

$\tt : \implies (2x^{2} + 8)6= 5(x^{2}-4)$

$\tt : \implies 12x^{2} + 48 = 5x^{2}-20$

$\tt : \implies 12x^{2} + 48 - 5x^{2} + 20 = 0$

$\tt : \implies 7x^{2} + 68 = 0$

$\tt : \implies 7x^{2} + 0x + 68 = 0$

<u>Now, by comparing with ax² + bx + c = 0, we have</u> :

a = 7
b = 0
c = 68

<u>By using quadratic formula</u> :

$\large \underline{\boxed{\bf{x = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}}}}$

$\tt : \implies x = \dfrac{-(0) \pm \sqrt{(0)^{2} - 4(7)(68)}}{2(7)}$

$\tt : \implies x = \dfrac{0 \pm \sqrt{0 - 1904}}{14}$

$\tt : \implies x = \dfrac{\pm \sqrt{- 1904}}{14}$

$\tt : \implies x = \dfrac{\pm \sqrt{2\times 2\times 2\times 2\times 7\times 17}}{14}$

$\tt : \implies x = \dfrac{\pm \cancel{2} \times 2\sqrt{7\times 17}}{\cancel{14}}$

$\tt : \implies x = \dfrac{\pm2\sqrt{119}}{7}$

$\large \underline{\boxed{\bf{x = \dfrac{\pm 2\sqrt{119}}{7}}}}$

Hence value of $\bf x =\dfrac{\pm 2\sqrt{119}}{7}$

5 0

3 years ago

Read 2 more answers

Isabella painted her bedroom. She used 2 gallons of paint and finished in 8 hours. At what rate did Isabella paint the room?

GrogVix [38]

Answer: " \frac{1}{4} gal /hr ; or, write as: " 0.25 gal/hr. " .

_______________

Step-by-step explanation:

_______________

This is a "unit rate" problem;

that is: we want to solve for a particular quantity per [single] unit.

_______________

→ in this case, per single "hour" ;

_______________

So we convert:

_______________

" 2 gal per 8 hours" ; to the correct number of:

_?_ gal per [single] hr.

_______________

{<u>Note</u>: "gal" refers to: "gallon(s)" ;

"hr" refers to: "hour(s)" .}.

_______________

→ " $\frac{2 gal}{ 8 hr} = [\frac{2}{8}]$ gal / hr. " ;

_______________

→ " { $\frac{2}{8} =$ [2÷2] / [8÷2] = 1/4 ;

_______________

So, the answer is:

→ " $\frac{1}{4} gal /hr$ " ;

_______________

or: write as decimal:

→ " $\frac{1}{4}$ = (1 ÷ 4) = 0.25 " ;

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write the answer as:

_______________

→ " 0.25 gal/hr. "

_______________

Or, when we had:

→ "2/8" gal/hr ;

_______________

Use calculator:

→ " $\frac{2}{8}$ = "2 ÷ 8" ;

= " 0.25 gal/ hr.

_______________

So: The correct answer is:

_______________

" \frac{1}{4} gal /hr ; or, write as: " 0.25 gal/hr. " ;

_______________

Hope this is helpful to you!

Best wishes in your academic endeavors—

and within the "Brainly" community!

_______________

6 0

3 years ago

I really need help with this can someone please help me with these questions thanks

ehidna [41]

See the attachment for answers and solving.

8 0

4 years ago

is social media company conducted research on the number of our high school students are on social media and the hours of leaf t

vekshin1

Answer:

8.5 hours

Step-by-step explanation:

Draw a line of best fit to predict

4 0

3 years ago

A tortoise and a hare are competing in a race around a 1600-meter track. The arrogant hare decides to let the tortoise have a 78

Sindrei [870]

I am presuming that the question is who won or by how much did the winner win.

distance equals rate times time, or d = r*t
For the Hare d = 1600 and r = 10
1600 = 10 t
Divide both sides by 10
t = 160
The hare finished in 160 seconds

For the tortoise d = 1600 - 780 = 820 (due to the head start) and r = 5.3
820= 5.3 t
Divide both sides by 5.3
t = 154.72 (rounded to the hundredths place)

The tortoise won by 5. 28 seconds (160-154.72)

6 0

4 years ago

Read 2 more answers