To convert sinusoids to phasors in polar form, we need to first identify the amplitude and phase angle of the signal. For a sinusoid of the form A*cos(ωt + φ), the amplitude is A and the phase angle is φ. Once we have these values, we can represent the signal as a complex number in polar form, given by A*exp(jφ), where j is the imaginary unit.
Using this method, we can convert the following sinusoids to phasors in polar form:
(a) -20*cos(4t + 135°)
Amplitude: 20
Phase angle: -45° (subtract 180° from 135°)
Phasor in polar form: 20*exp(-j45°)
(b) 8*sin(20t + 30°)
Amplitude: 8
Phase angle: 30°
Phasor in polar form: 8*exp(j30°)
(c) 20*cos(2t) + 15*sin(2t)
To convert this to a single sinusoid, we can use the identity sin(x + y) = sin(x)cos(y) + cos(x)sin(y) and write:
20*cos(2t) + 15*sin(2t) = sqrt(20^2 + 15^2)*cos(2t + θ)
where cos(θ) = 20/sqrt(20^2 + 15^2) and sin(θ) = 15/sqrt(20^2 + 15^2). Therefore:
Amplitude: sqrt(20^2 + 15^2) = 25
Phase angle: θ = tan^-1(15/20) = 36.87°
Phasor in polar form: 25*exp(j36.87°)
In (a), we have a negative amplitude and a phase angle of 135°. To convert this to polar form, we need to subtract 180° from the phase angle to get it in the range of -180° to 180°. This gives us a phase angle of -45° and a positive amplitude of 20.
In (b), we have a positive amplitude and a phase angle of 30°. We can represent this as a complex number in polar form by multiplying the amplitude by the exponential of the phase angle, which gives us a phasor of 8*exp(j30°).
In (c), we have a sum of two sinusoids. To convert this to a single sinusoid, we can use the identity sin(x + y) = sin(x)cos(y) + cos(x)sin(y). This allows us to rewrite the signal as a single cosine wave with an amplitude of 25 and a phase angle of 36.87°. We can then represent this as a phasor in polar form by multiplying the amplitude by the exponential of the phase angle, which gives us a phasor of 25*exp(j36.87°).
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The sinusoid -20cos(4t + 135°) can be expressed in polar form as a phasor of 20exp(-j45°), whereas the sinusoid 8sin(20t + 30°) can be represented as a phasor of 8exp(j30°).
How to solveThe value of (a) is represented by a phase angle of 135° and a negative amplitude. In order to transform this into polar form, it is necessary to deduct 180 degrees from the phase angle so it can be within the limit of -180 degrees to 180 degrees.
We can determine a negative phase angle of 45 degrees and a 20-unit magnitude in the positive direction.
The value of (b) shows a constructive magnitude and a 30° angle of phase. A phasor of 8 multiplied by the exponential of the phase angle can be utilized to express this as a complex number in polar form, resulting in 8*exp(j30°).
In condition (c), we are presented with the addition of two sinusoidal waves. We can transform this into a solitary sinusoidal wave by applying the formula sin(x + y) = sin(x)cos(y) + cos(x)sin(y).
We can cleverly rework the signal to be expressed as a solitary cosine wave, possessing an amplitude of 25 and a phase angle measuring 36. 87°
Similarly, the combination of 20cos(2t) + 15sin(2t) can be represented by a single phasor of 25*exp(j36. 87°)
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HELP ME PLEASE!!!
One liter of water is cooled from 20°C to 3°C inside a refrigerator. What is the change in temperature in °F? K?
Answer:
Decrease of temperature by 62.6°F and 290.15°
Explanation:
First identify change in C: 17 degrees
now convert to Fahrenheit and Kelvin
Fahrenheit: 17 * (9/5) +32 = 62.6°
Kelvin: 17 + 273.15 = 290.15°
Please help with chem ASAP
Answer:
Imagine Dragon
Explanation:
These balls across yo face
Gottem
what is the equation for hydrogen peroxide
Answer:
H2O2
Explanation:
2 hydrogen, 2 oxygen wikipedia it
Answer:
hey!
Your answer is that the equation for Hydrogen Peroxide is [tex]H_{2}[/tex][tex]O_{2}[/tex]
Explanation:
Its formed when [tex]H_{2}[/tex]O and [tex]O_{2}[/tex] react chemically together!
HOPE THIS HELPED!
Im gonna ride it do it just how you like it and after that let's do it?
what is the answer of this.
Answer:
the hell?
Explanation:
How many grams of carbon is needed to react with hydrogen gas to produce 59.8 grams of acetylene (C2H2)?
Answer:
[tex]55.1657[/tex] grams/mol of carbon is needed to react with hydrogen gas to produce 59.8 grams of acetylene (C2H2)
Explanation:
The molecular weight of acetylene is 26.04 g/mol
Molecular weight of carbon is equal to 12.011 g/mol
Two carbon atom produces one acetylene molecule.
Thus, 2 * 12.011 g/mol of carbon is used to produce 26.04 g/mol of acetylene,
Amount of carbon required to produce 59.8 grams of acetylene
[tex]\frac{2*12.011}{26.04} * 59.8 \\= 55.1657[/tex]grams/mol
[tex]55.1657[/tex] grams/mol of carbon is needed to react with hydrogen gas to produce 59.8 grams of acetylene (C2H2)
Every ________ will have its own unique set of quantum numbers.
Select the correct answer below:
A. atom
B. shell of electrons
C.proton
D. individual electron
Answer:
D. individual electron
Explanation:
Every individual electron will have its own unique set of quantum numbers.
What are quantum numbers?
Quantum numbers are the numbers which describe the values of conserved quantities with respect to the dynamics of a quantum system.They correspond to the Eigen values of operators which commute with the Hamiltonian quantities.
The Hamiltonian quantities can be known with precision simultaneously with the system's energy.Quantum numbers can take values of discrete sets of integers or even half-integers even though they can approach infinity in some cases.
They can specifically describe energy levels of electrons, and can also explain angular momentum,spin,etc.These are used to describe the path of an electron in an atom ,when the quantum numbers of all atoms are combined they must comply with the Schrodinger equation.
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5.
Given: C2H5C1
P1: 951.72 kPa
P2: 362.29 kPa
T1: 653.34 K
Wanted: kelvins?
Answer: The final temperature is 248.7 K
Explanation:
To calculate the final temperature of the system, we use the equation given by Gay lussac Law. This law states that pressure of the gas is directly proportional to the temperature of the gas at constant volume.
Mathematically,
[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]
where,
[tex]P_1\text{ and }T_1[/tex] are the initial pressure and temperature of the gas.
[tex]P_2\text{ and }T_2[/tex] are the final pressure and temperature of the gas.
We are given:
[tex]P_1=951.72kPa\\T_1=653.34K\\P_2=362.29kPa\\T_2=?[/tex]
Putting values in above equation, we get:
[tex]\frac{951.72}{653.34}=\frac{362.29}{T_2}\\\\T_2=248.7K[/tex]
Thus the final temperature is 248.7 K
mass-mass problem:
If 25.0 grams of carbon dioxide are used in photosynthesis how many grams of glucose (C6H12O6) could be Produced according
to the following equation : 6CO2 + 6H2O → C6H12O6 + 602
Answer:
17.05 g of glucose
Explanation:
The equation of the reaction is given as;
6CO2 + 6H2O → C6H12O6 + 602
From the equation;
6 mol of CO2 produces 1 mol of C6H12O6
Converting to masses;
CO2:
Mass =Number of moles * Molar mass
Mass = 6 mol * 44 g/mol = 264 g
C6H12O6:
Mass = Number of moles * Molar mass
Mass = 1 mol * 180 g/mol = 180 g
This means 264g of CO2 produces 180g of C6H12O6
25g of CO2 would produce x g of C6H12O6
264 = 180
25 = x
x = 25 * 180 / 264
x = 17.05 g
1) Write the symbol and charge for each individual ion
2) Balance the charge so that they equal to zero
3)Write the formula based on how many of each ion you used in step 2
11) Beryllium and Phosphorus
12) cesium and Sulfur
13) Lithium and phosphorus
14) fluorine and rubidium
15) Francium and oxygen
Answer:
I'm pretty sure these are correct
11) Be 2+ and P 3- Formula is Be3P2
12) Cs 1+ and S 2- Formula: Cs2S
13) Li 1+ and P 3- Formula: Li3P
14) Rb 1+ and F 1- Formula: RbF
15) Fr 1+ and O 2- Formula: Fr2O
Explanation:
You do the criss-cross method where the charge on one ion becomes the amount on the second
How do parasites affect their hosts?
They help their hosts by consuming or using their cells.
They help their hosts by growing in size.
O They harm their hosts by growing in size.
They harm their hosts by using their hosts as a food source.
What is a song that gets you in a mood? ;)
Answer:
Uhm- s-- money- feelings- die? But, slowed -w-
Explanation:
Explain why a halogen bulb has a longer bulb life than a traditional incandescent bulb filled with argon.
Answer:
The halogen bulb lasts longer because the filament lasts longer. It can have twice the life of an incandescent and use the same amount or slightly less (10%) electricity.
Explanation:
45 grams of ammonia, NH3, in 0.75 L of solution.
The diagram shows movement of thermal energy
In which areas of the diagram does conduction occur?
W and X
X and Z
Y and Z
Z and W
Answer:
Y AND Z
HOPE IT HELPS THANK ME LATER.
Answer:
B. Y and Z
Explanation:
Solid sodium combines with solution of magnesium fluoride to form sodium fluoride solution and magnesium metal.
Solid sodium combines with solution of magnesium fluoride to form sodium fluoride solution and magnesium metal is adding hydrochloric acid into form magnesium chloride solution and hydrogen gas. A solution could be copper oxide is combined with solid carbon. This forms copper metal and carbon dioxide gas.
____Na3PO4+____CaCI2 --->____NaCI+ ____Ca(PO4)2
Answer:
3CaCi2 + 2Na3PO4 → Ca3(PO4)2 + 6NaCi
Explanation:
how does a allergy develop?
PLEASE HELP!
Answer: im not fully sure but from what i rememeber Allergies develop when your immune system mistakenly identifies a thing such as pollen, mold or food as harmful then your body reacts to it
Explanation:
magnesium__ + sulfuric acid goes to form magnesium sulfate+ water + carbon dioxide
Answer:
carbonate
Explanation:
this is because when carbonates react with acid they form carbon dioxide and water and respective metal oxide
After the shuttle disaster, an unknown compound residue was removed from a piece of the debris. Upon analysis, it was found to contain 2.61 g of carbon, 6.09 g of nitrogen, and 1.31 g of hydrogen. What is its empirical formula?
Answer:
The final empirical formula is [tex]C_2 N_5 H[/tex]
Explanation:
Given
The amount of carbon, nitrogen and hydrogen in a given compound is as follows
C:N:H
[tex]2.61 : 6.09 : 1.31[/tex]
On simplifying the ration values we get
[tex]\frac{2.61}{1.31} : \frac{6.09}{1.31} : \frac{1.31}{1.31}[/tex]
So the final ratio is
[tex]2 : 5 : 1[/tex]
The final empirical formula is [tex]C_2 N_5 H[/tex]
What type of energy transformation happens during photosynthesis?
(select the BEST answer choice
thermal --> radiant
chemical --> radiant
chemical --> thermal
radiant --> chemical
Answer:
radiant - chemical is the best answer
i really need help with this
Answer:
the process shown here is endocytosis.
Explanation:
endocytosis is a process of taking something inside the cell..
Convert 6.03 m to km using Dimensional Analysis
Explanation:
[tex]6.03 \: m \times \frac{1 \: km}{1000 \: m} = 0.00603 \: km[/tex]
Please help: A complete moon cycle is how many weeks
Answer:
29.5 days
Explanation:
its 29.5 days i hope it helps
Answer:
The Moon takes 27.3 days to orbit Earth, but the lunar phase cycle (from new Moon to new Moon) is 29.5 day
I need help with this question ASAP
Answer:
True
Explanation:
Asexual reproduction does not involve sex cells or fertilization . Only one parent is required, unlike sexual reproduction which needs two parents. As a result, the offspring are genetically identical to the parent and to each other.
1. Which of the following is the most important function of the microscope?
A. measuring specimen
B. magnification of the specimen
C. photographing the specimen
D. locating and viewing the specimen
image or
Which two ways the nervous and endocrine systems interact?
Answer:
Along with the nervous system, the endocrine system coordinates the body's functions to maintain homeostasis during rest and exercise. The nervous and endocrine systems also work together to initiate and control movement, and all the physiological processes movement involves.
Explanation:
A gas in a piston starts out with a volume of 156 mL, a temperature of 28.1° C, and a pressure of 1.12 atm. If it ends with a volume of 312 mL and a temperature of 87.2° C, what is the new pressure?
Answer:
0.67atm is the new pressure of the gas
Explanation:
To find one condition of a gas when pressure, volume and absolute temperature change we must use combined gas law:
[tex]\frac{P_1V_1}{T_1} =\frac{P_2V_2}{T_2}[/tex]
Where P is pressure, V is volume and T is absolute temperature of 1, initial state and 2, final state of the gas.
Replacing:
P₁ = 1.12atm
V₁ = 156mL
T₁ = 28.1°C + 273.15K = 301.25K
P₂ = ?
V₂ = 312mL
T₂ = 87.2°C + 273.15 = 360.35K
1.12atm*156mL / 301.25K = P₂*312mL / 360.35K
P₂ = 0.67atm is the new pressure of the gas
You start with 2.5g of magnesium and add it to 400mL of CO2 at 23 o C and 1atm. How many grams of magnesium oxide will be formed?
Answer:
0.664 g are formed by the reaction.
Explanation:
First of all, we determine the reaction:
Mg + CO₂ → MgO + CO
We need to determine the moles of the CO₂ by the Ideal Gases Law.
We convert to L, the volume → 400 mL = 0.4L
T° → 23°C + 273 = 296K
P . V = n . R .T
n = P . V / R .T
n = (1 atm . 0.4L) / (0.082 . 296K) → 0.0165 moles
Moles of Mg → 2.5 g . 1mol / 24.3g = 0.103 moles
As ratio is 1:1, CO₂ is the limiting reactant.
For 1 mol of Mg, we need 1 mol of gas
Then, for 0.103 moles of Mg, we need 0.103 moles of gas, but we only have 0.0165 moles.
If we see the product side, ratio is also 1:1
0.0165 moles of CO₂ must produce 0.0165 moles of MgO.
We convert the moles to mass → 0.0165 mol . 40.3 g /1mol = 0.664 g
How does fertilizer affect nitrogen cycle
Cuando se usa demasiado fertilizante para las plantas una parte de ese nitrógeno no vuelve a la atmósfera y a cambio contamina el medio ambiente
Explanation:
the nitrogen cycle is a natural process that adds nitrogen to the soil. however the use of fertilizer has increased the amount of usable nitrogen in the soil
Dona is attempting to make an electromagnetic to pick up old nails in her driveway. Which of these materials would be best to us for the core to make the strongest electromagnetic to pick up the most nails?
Answer:
The materials would be best to us for the core to make the strongest electromagnetic to pick up the most nails is described below in detail.
Explanation:
Use a couple of wire strip-pers to exclude some centimeters of insulation from every end of the cable. Skillfully cover the cable around the nail. The more cable you enclose around the nail, the more effective your electromagnet will be. Compose certain that you leave sufficient of the cable unwrapped so that you can connect the battery.