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2 years ago

What is the definition of voyage

Mathematics

1 answer:

Alla [95]2 years ago

4 0

Answer:

The definition of voyage is

Step-by-step explanation:

Voyage- A long journey involving travel by see or in space

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Assume z = x + iy, then find a complex number z satisfying the given equation. d. 2z8 – 2z4 + 1 = 0

kodGreya [7K]

Answer: complex equations has n number of solutions, been n the equation degree. In this case:

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i11,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i101,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i191,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i281,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i78,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i168,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i258,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i348,75°}$

Step-by-step explanation:

I start with a variable substitution:

$Z^{4} = X$

Then:

$2X^{2}-2X+1=0$

Solving the quadratic equation:

$X_{1} =\frac{2+\sqrt{4-4*2*1} }{2*2} \\X_{2} =\frac{2-\sqrt{4-4*2*1} }{2*2}$

$X=\left \{ {{0,5+0,5i} \atop {0,5-0,5i}} \right.$

Replacing for the original variable:

$Z=\sqrt[4]{0,5+0,5i}$

or $Z=\sqrt[4]{0,5-0,5i}$

Remembering that complex numbers can be written as:

$Z=a+ib=|Z|e^{ic}$

Using this:

$Z=\left \{ {{{\frac{\sqrt{2}}{2} e^{i45°} } \atop {{\frac{\sqrt{2}}{2} e^{i-45°} }} \right.$

Solving for the modulus and the angle:

$Z=\left \{ {{\sqrt[4]{\frac{\sqrt{2}}{2} e^{i45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i45}} } \atop {\sqrt[4]{\frac{\sqrt{2}}{2} e^{i-45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i-45}} }} \right.$

The possible angle respond to:

$RAng_{12...n} =\frac{Ang +360*(i-1)}{n}$

Been "RAng" the resultant angle, "Ang" the original angle, "n" the degree of the root and "i" a value between 1 and "n"

In this case n=4 with 2 different angles: Ang = 45º and Ang = 315º

Obtaining 8 different angles, therefore 8 different solutions.

3 0

3 years ago

Plz help please<br><br> Is the relation shown in the arrow diagram a function?

SSSSS [86.1K]

Answer:

The answer is A

Step-by-step explanation:

In order for it to be a function every x value has to have a different y value or every input has to have a different output.

4 0

3 years ago

Read 2 more answers

Roberto has $200 in spending money. He wants to buy some video games that cost $25.50 each. Write and solve an inequality to fin

Veseljchak [2.6K]

Answer:

f(x) = 25.50x Roberto can buy 7 video games

Step-by-step explanation:

Each game is $25.50 which in math means it has an "x"

So if x=1 then 25.50x says that 1 video game is $25.50

Set up the equation:

200 = 25.50x (divide both sides by 25.50 to isolate the x)

200/25.50 = 7.84

x = 7.84

You can't have 0.84 of a video game, so Roberto can only buy 7 of them.

3 0

3 years ago

Read 2 more answers

vivi is a drummer for a band. she burns 756 calories while drumming for 3 hours. she burns the same number of calories each hour

Airida [17]

Answer:

252 cph

Step-by-step explanation:

756 divide by 3 is 252

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2 years ago

Find two consecutive integers whose sum is -29

LuckyWell [14K]

Example:

The sum of two consecutive integers is -15. What is the product of the two integers?

x = 1st consecutive integer

x + 1 = 2nd consecutive integer {consecutive integers increase by 1}

x + x + 1 = -15 {the sum of two consecutive integers is -15}

2x + 1 = -15 {combined like terms}

2x = -16 {subtracted 1 from each side}

x = -8 {divided each side by 2}

x + 1 = -7 {substituted -8, in for x, into x + 1}

-8 and -7 are the two consecutive integers

Their product is 56.

8 0

3 years ago