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2 years ago

Calculate the perimeter of the figure

Mathematics

2 answers:

Natasha_Volkova [10]2 years ago

7 0

Answer:

Step-by-step explanation:

4+4+4+4+4+4+8+8+18+18 = 76

motikmotik2 years ago

6 0

The answer is 46 because when you add all the numbers up you get 46

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Simplify the complex numbers using de Moivre's Theorem and match them with their solutions.

alexandr1967 [171]

For the numbers in $a+bi$ form, convert to polar form:

$1+i=\sqrt2\dfrac{1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)$

By DeMoivre's theorem,

$(1+i)^5=(\sqrt2)^5\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=4\sqrt2\dfrac{-1-i}{\sqrt2}=-4-4i$

$-1+i=\sqrt2\dfrac{-1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4}\right)$

$\implies(-1+i)^6=(\sqrt2)^6\left(\cos\dfrac{18\pi}4+i\sin\dfrac{18\pi}4\right)=8i$

$\sqrt3+i=2\dfrac{\sqrt3+i}2=2\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)$

$\implies2(\sqrt3+i)^{10}=2^{11}\left(\cos\dfrac{10\pi}6+i\sin\dfrac{10\pi}6\right)=2^{11}\dfrac{1-i\sqrt3}2=2^{10}(1-i\sqrt3)$

For the numbers already in polar form, DeMoivre's theorem can be applied directly:

$2\left(\cos20^\circ+i\sin20^\circ\right)^3=2\left(\cos60^\circ+i\sin60^\circ\right)=2\dfrac{1+i\sqrt3}2=1+i\sqrt3$

$2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)^4=2(\cos\pi+i\sin\pi)=-2$

At second glance, I think the 2s in the last two numbers should also be getting raised to the 3rd and 4th powers:

$\left(2(\cos20^\circ+i\sin20^\circ)\right)^3=8\left(\cos60^\circ+i\sin60^\circ\right)=4+4\sqrt3$

$\left(2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)\right)^4=16(\cos\pi+i\sin\pi)=-16$

4 0

3 years ago

2. What are the coordinates of point C?

KiRa [710]

Answer:

(3, -5)

Step-by-step explanation:

Can I please have brainliest?

4 0

3 years ago

Read 2 more answers

Janna drank 0.7 liter of water before soccer practice and 0.70 liter of water after practice compare the two decimals using grea

maria [59]

0.7 Liters and 0.70 Liters are the same amount.

You can think of them as fractions: 7/10 and 70/100. Both of these mean the same. 7/10 is the simplest form of the number.

When you put zeros to the right of any number that is to the right of the decimal point, it will not change the value of the number.

0.7 L = 0.70 L

5 0

3 years ago

85% as a fraction or mixed number

Sphinxa [80]

85/100 isnsvsisjdbbsbsjsjdjd

3 0

3 years ago

Read 2 more answers

HELP!! 70 points will be given!<br> Picture included

kkurt [141]

Answer: a) -13/16

Step-by-step explanation: Start by setting equations equal and rearrange X^3 - x^2 + 1 = 0. Visual inspection of graph shows x between -1 and -1/2. Start with x = 3/4 plug in and calculate: just a little too small. Try going halfway towards -1: x =-7/8 Plug in and the answer is very far from 0. Go halfway back towards -3/4: -13/16 and the equality is very close.

8 0

3 years ago