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irina [24]
3 years ago
15

Solve using demoivres theorem

Mathematics
1 answer:
pashok25 [27]3 years ago
3 0
It's difficult to make out, but I think the task is to expand

(\sqrt3-i)^4

Write the number in polar form first:

\sqrt3-i=2e^{-i\pi/6}

By DeMoivre's theorem, you have

(\sqrt3-i)^4=\left(2e^{-i\pi/6}\right)^4=2^4e^{-i4\pi/6}=16e^{-i2\pi/3}

and converting back to Cartesian form, this number is equivalent to

16\left(\cos\dfrac{2\pi}3-i\sin\dfrac{2\pi}3\right)=16\left(-\dfrac12+-\dfrac{\sqrt3}2\right)=-8(1+i\sqrt3)
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A 20% apple juice drink is mixed with a 100% apple juice drink. The function f(x)=(2)(1.0)+x(0.2)2+x models the concentration of
luda_lava [24]

Answer:

17.5

Step-by-step explanation:

Given that:

20% apple juice drink is mixed with a 100% apple juice drink.

f(x)=\dfrac{(2)(0.1)+x(0.2)}{2+x}

represents the concentration of apple juice in the drink when x gallons of 20% drink are added to 2 gallons of pure juice.

Also, given that 6 gallons of 20% drink are added to the 2 gallons of pure juice.

To find:

The concentration of apple juice in the drink = ?

Solution:

Given the function:

f(x)=\dfrac{(2)(0.1)+x(0.2)}{2+x}

and

x=6\ gallons

f(x)=\dfrac{(2)(0.1)+6(0.2)}{2+6}\\\Rightarrow f(x)=\dfrac{0.2+1.2}{8}\\\Rightarrow f(x)=\dfrac{1.4}{8}\\\Rightarrow f(x)=\bold{0.175}

In percentage, the concentration 17.5.

7 0
3 years ago
Find the square root of these numbers to the nearest tenth. 72 = 32 = 481 =
larisa86 [58]
Squrt of 72 is  8.49

squrt of 32 is  5.66

squrt of 481 is 21.93
4 0
3 years ago
Read 2 more answers
a hardware factory produces 3.6 •10^5 bolts in 2400 minutes. what is the factory rate of production in bolts per minute​
Ainat [17]
10^5=100,000
100,000*3.6
360,000
360,000/2400

I believe it’s 150 bolts per minute
5 0
3 years ago
If ΔΡQR
frozen [14]

Answer:

If y varies directly as x^3 and y=36 when x=7, find y if x=4? (Round answer to the nearest hundredth) , find y if x=4 x = 4 . (Round off your answer to the nearest hundredth.)

Step-by-step explanation:

6 0
3 years ago
Simplify the expression below:
kifflom [539]

Answer:

C. -7x^2 - 28

Step-by-step explanation:

Firstly simplify the bracket before doing anything;

4x(3x - 7) = 12x^2 - 28x

then go back to the question and substitute the expression(12x^2 - 28x) on the bracket and then work out the question;

12x^2 - 28x -19x^2...then group the values with the same exponent of x,

(12x^2 - 19x^2) - 28x

; -7x^2 - 28x

6 0
3 years ago
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