_____ are both ways of preserving current energy resources.

Find the cube roots of 27(cos 327° + i sin 327° ). Write the answer in trigonometric form.

Sati [7]

Answer:

$z^{\frac{1}{3} }= -0.978 + i\cdot 2.836$ , $z^{\frac{1}{3} }= -1.967 - i\cdot 2.265$ , $z^{\frac{1}{3} }= 2.945 - i\cdot 0.571$

Explanation:

The cube root of the complex number can determined by the following De Moivre's Formula:

$z^{\frac{1}{n} } = r^{\frac{1}{n} }\cdot \left[\cos\left(\frac{x + 2\pi\cdot k}{n} \right) + i\cdot \sin\left(\frac{x+2\pi\cdot k}{n} \right)\right]$

Where angles are measured in radians and k represents an integer between $0$ and $n - 1$ .

The magnitude of the complex number is $27$ and the equivalent angular value is $1.817\pi$ . The set of cubic roots are, respectively:

k = 0

$z^{\frac{1}{3} } = 3\cdot \left[\cos \left(\frac{1.817\pi}{3} \right)+i\cdot \sin\left(\frac{1.817\pi}{3} \right)]$

$z^{\frac{1}{3} }= -0.978 + i\cdot 2.836$

k = 1

$z^{\frac{1}{3} } = 3\cdot \left[\cos \left(\frac{3.817\pi}{3} \right)+i\cdot \sin\left(\frac{3.817\pi}{3} \right)]$

$z^{\frac{1}{3} }= -1.967 - i\cdot 2.265$

k = 2

$z^{\frac{1}{3} } = 3\cdot \left[\cos \left(\frac{5.817\pi}{3} \right)+i\cdot \sin\left(\frac{5.817\pi}{3} \right)]$

$z^{\frac{1}{3} }= 2.945 - i\cdot 0.571$

5 0

3 years ago

All but one statement could describe a scientific theory. That is:

murzikaleks [220]

D is the wrong answer. New information does often completely change the theory. Its hard to change something and leave the major theory intact.

8 0

3 years ago

Read 2 more answers

When the liquid line is restricted, the supply of refrigerant to the metering device is reduced. What is the effect on suction p

Nimfa-mama [501]

Answer:

The suction pressure decreases and the superheat increases when the liquid line is restricted and the supply of refrigerant to the metering device is reduced.

Explanation:

1. The five components of refrigeration are:

Fluid refrigerant
Compressor
Condenser coil
Evaporator coil
Expansion device.

The compressor limits the vapor released by the refrigerant. This

causes a rise in pressure (in refrigerant), which then pushes the

vapor into the coils on the outside of the refrigerator.

2. Now when the cooler air meets the warm gas present in the coils, it

gets converted into liquid form.

3. Thus, when the liquid form is at high pressure, the refrigerant then

cools down as it flows through the coils placed in the fridge ( in both

freezing and normal sections).

4. The refrigerant also absorbs the warm air present in the fridge, which

causes it to evaporate and flow back through the compressor and the

cycle repeats in the same form.

Thus, when the liquid line is restricted and the supply of refrigerant to the metering device is reduced it causes a decrease in suction pressure and an increase in superheat.

Learn more about refrigeration here:

<u>brainly.com/question/9046279</u>

#SPJ4

8 0

2 years ago

According to the rayleigh criterion, what is the shortest object we could resolve at the 25.0 cm near point with light of wavele

Blizzard [7]

Answer:

$6.71 *10^{-5}$ rad

Explanation:

∅ = $\frac{1.22*wavelength}{D}$ = $\frac{1.22*550 * 10^{-9} }{25 * 10^{-2} }$

∅ = $6.71 *10^{-5}$ rad

The minimum resolvable angle = $6.71 *10^{-5}$ rad

7 0

3 years ago

What evidence is there that the Universe began in a big bang?<br><br>

NeTakaya

Answer: For me personally i have a Biblical faith and first of all there is evidence that looks convincing that the big bang made the universe, but man wants answers and God in the Bible says he created the universe for us it is hard to believe it but i have faith.

5 0

3 years ago

Read 2 more answers