z₂ is equal to the negative of z₁.
Let's assume that the two non-zero complex numbers are represented in polar form as:
z₁ = r(cosθ₁ + i sinθ₁)
z₂ = r(cosθ₂ + i sinθ₂)
where r = |z₁| = |z₂| is the magnitude of both complex numbers, and θ₁ and θ₂ are their arguments.
From the given condition, we have:
arg(z₁) + arg(z₂) = π
Substituting the polar forms of z₁ and z₂ into the equation above, we get:
arctan(sinθ₁/cosθ₁) + arctan(sinθ₂/cosθ₂) = π
Simplifying this expression, we get:
θ₁ + θ₂ = π (Note that cosθ₁ and cosθ₂ are both positive because |z₁| = |z₂|, so we can use the arctan identity for the sum of two angles)
Rearranging this expression, we get:
θ₂ = π - θ₁
Substituting this into the polar form of z₂, we get:
z₂ = r(cos(π - θ₁) + i sin(π - θ₁))
z₂ = r(-cosθ₁ - i sinθ₁)
z₂ = -z₁
Therefore, z₂ is equal to the negative of z₁.
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Complete question is: z₁ and z₂ are two non-zero complex number such that |z₁|=|z₂| and argz₁ + argz₂ = π then z₂ equals to the negative of z₁.
A carpenter tosses a shingle off a 9.4 m high roof, giving it an initial horizontal velocity of 7.2 m/s.] How far does it move horizontally in this time
Answer:
Explanation:
Assuming negligible air resistance, the horizontal velocity of the shingle will remain constant and the vertical motion will be influenced by gravity.
We can use the kinematic equations of motion to determine the horizontal distance traveled by the shingle. The relevant equation is:
d = v * t
where d is the distance, v is the initial horizontal velocity, and t is the time of flight.
To find the time of flight, we can use the equation for the vertical displacement of an object under constant acceleration:
y = v0t + (1/2)at^2
where y is the vertical displacement, v0 is the initial vertical velocity (which is zero), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight. Solving for t, we get:
t = sqrt((2y)/a)
where sqrt means square root.
Substituting the given values, we have:
y = 9.4 m
a = -9.8 m/s^2
t = sqrt((2*9.4 m) / -9.8 m/s^2) = 1.45 s (using the positive root since time cannot be negative)
Now, we can use the horizontal velocity to find the distance traveled in this time:
d = v * t = 7.2 m/s * 1.45 s = 10.44 m
Therefore, the shingle moves a horizontal distance of 10.44 meters in this time.
Is this statement is correct ?? According to Newton's 4rd law, Action and reaction never start from the same point.
help me...
Explanation:
I'm sorry, but the statement you provided is incorrect. There is no such thing as Newton's 4th law. Newton's laws of motion consist of three laws, which are:
An object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
The acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass.
For every action, there is an equal and opposite reaction.
None of these laws state that action and reaction never start from the same point. However, it is true that the action and reaction forces act on different objects, not necessarily at the same point. This is because Newton's third law states that every action has an equal and opposite reaction, which means that when one object exerts a force on another object, the second object exerts an equal and opposite force back on the first object.
Which of the following does a scientist NOT need to calculate the age of something?
Amount of radioactive isotope within a sample
Half-life of radioactive isotope
Abundance on Earth
100g of the sample
Answer:
Abundance on Earth is not necessary for calculating the age of something using radioactive dating methods.
In contrast, the amount of radioactive isotope within a sample and its half-life are crucial for determining the age of the sample using radioactive dating methods. The amount of sample, such as 100g, is also important for determining the quantity of radioactive isotopes present, which is used in the calculation of the age of the sample.
What might happen if people did not have the rights established in Miranda v. Arizona
Answer:
If people did not have the rights established in Miranda v. Arizona, they could be subjected to police coercion and forced confessions without a lawyer present. This could lead to wrongful convictions and denial of due process, which are essential components of the American justice system
A 300 g football is kicked with an initial velocity of 140 m/s in a direction that
makes a 30° angle with the horizon. Find the peak height of the football.
Answer:
Explanation:
Assuming that air resistance is negligible, we can use the following kinematic equations to solve for the peak height:
v_f^2 = v_i^2 + 2ad
where v_f = 0 m/s (at the peak height) and a = -9.8 m/s^2 (acceleration due to gravity)
and
d = v_i t + (1/2)at^2
where d is the displacement or the peak height we want to find, v_i is the initial velocity, t is the time it takes to reach the peak height.
First, we need to resolve the initial velocity into its vertical and horizontal components:
v_i_x = v_i cos(30°) = 121.1 m/s
v_i_y = v_i sin(30°) = 70.0 m/s
Next, we can use the vertical component of the initial velocity to find the time it takes to reach the peak height:
v_f = v_i_y + at
0 m/s = 70.0 m/s + (-9.8 m/s^2)t
t = 7.14 s
Finally, we can use the time we found and the kinematic equation for displacement to find the peak height:
d = v_i_y t + (1/2)at^2
d = (70.0 m/s)(7.14 s) + (1/2)(-9.8 m/s^2)(7.14 s)^2
d = 247.5 m
Therefore, the peak height of the football is 247.5 meters.
It is fun to exercise outside, but you have to be careful when it's hot. What are two things you should always do when you exercise in the heat?
Answer:
When exercising in the heat, it's important to take precautions to prevent heat-related illnesses. Two things you should always do when exercising in the heat are:
1.Stay hydrated: Drink plenty of water before, during, and after your workout to avoid dehydration. Sip water frequently, even if you don't feel thirsty.
2.Take breaks and rest in the shade: If you start feeling dizzy, lightheaded, or excessively fatigued, take a break in a cool, shaded area. Resting can help your body cool down and prevent heat exhaustion or heat stroke.
Explanation:
hope its help <:
Student A has a mass of 95 kg and student B has a mass of 82 kg. If their centers of mass are
0.6 meters apart, what will be the gravitational force each student exerts on the other?
Round your answer to the nearest whole number.
Answer:
0 Newtons, to the nearest whole number
Explanation:
Using the formula attached to this answer,
F = (6.67 x 10-¹¹ • 95 • 82) / 0.6²
F = 5.19593 x 10-⁷ / 0.36
F = 1.4433 x 10-⁶ N
F = 0.000001443 N
To the nearest whole number
F = 0 N
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If you lift one load up one story, how much more work do you do lifting one load up
three stories?
Answer:
Explanation:
alot
If a 9 V battery is connect to a 4 ohm resistor, what is the current?
O2.3 A
O 36 A
O 0.44 A
5 A
Answer: Given data
The resistance of the first resistor is R1 = 4 ohm
The resistance of the second resistor is R2 = 5 ohm
The potential difference of the battery is V = 9 V
The resistors are connected in series. The expression for the equivalent resistance is given as:
The expression for the current in the 4-ohm resistor is given as:
Thus, the magnitude of the current flows through the 4-ohm resistor is 1 A.
Explanation:
Liam pulls a box with a horizontal force of 17 N over a distance of 19 m. What is the change in energy of the box after the 19 m?
So the change in energy of the box after being pulled by Liam over 19 m is 323 J.
What are some illustrations of energy change?Energy is capable of changing its forms. For instance, electrical energy transforms into thermal and light energy when a lightbulb is turned on. A automobile transforms the gasoline's molecular bonds' stored energy into a variety of other forms. Chemical energy is converted to light in the engine through a chemical reaction.
The work done on the box by Liam's force is:
work = force x distance x cos(theta)
where theta is the angle between the force and the direction of motion. Since the force is horizontal and the motion is also horizontal, theta is 0 degrees and cos(theta) is 1. Therefore, the work done on the box is:
work = 17 N x 19 m x 1 = 323 J
The change in energy of the box is equal to the work done on it, according to the work-energy principle. Therefore, the change in energy of the box is:
change in energy = work = 323 J
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A rocket takes off from a space station, where there is no gravity other than the negligible gravity due to the space station, and reaches a speed of 110 m/s in 10.0 s. If the exhaust speed is 1,600 m/s and the mass of fuel burned is 118 kg, what was the initial mass (in kg) of the rocket?
The initial mass of the rocket was 106 kg.
What is the initial mass of the rocket?We can use the principle of conservation of momentum to solve this problem.
The momentum of the rocket before takeoff is zero, since it is at rest, and the momentum after takeoff is the product of the mass of the rocket and its velocity.
However, during the takeoff, the rocket ejects a mass of fuel at a certain velocity, which creates a backward force (thrust) that propels the rocket forward.
This thrust can be calculated using the equation:
Thrust = (mass flow rate) x (exhaust velocity)
mass flow rate = (mass of fuel burned) / (burn time)
The mass of the rocket at any given time can be calculated using the equation:
mass = (initial mass) - (mass of fuel burned)
Using these equations, we can solve for the initial mass of the rocket:
Calculate the thrust:
Thrust = (118 kg / 10.0 s) x 1600 m/s = 1,888 N
Calculate the mass of the rocket at the end of the burn:
mass(end) = (initial mass) - (mass of fuel burned) = (initial mass) - 118 kg
Use the principle of conservation of momentum to find the initial mass:
momentum before = momentum after
0 = (mass(end) + 118 kg) x 110 m/s
mass(end) = -118 kg / 110 m/s = -1.07 kg/s
mass(end) = (initial mass) - 118 kg
(initial mass) = mass(end) + 118 kg
(initial mass) = (-1.07 kg/s x 10.0 s) + 118 kg
(initial mass) = 106 kg
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A 0.5kg wooden block is placed on top of a 1.0kgwooden block. The coefficient static friction between the two blocks is 0.35. The coefficient of kinetic friction between the lower block and the level table is 0.20 wht is the maximum horizontal force that can be applied to the lower block
A block of 0.5 kg is placed on top of another wooden block which weighs 1.0 kg. The coefficient of static friction between the two blocks is 0.35, whereas the coefficient of kinetic friction between the lower block and the level table is 0.20.
To calculate the maximum horizontal force that can be applied to the lower block, we need to determine the limiting frictional force between the two blocks.
Since the upper block is not moving, the force of static friction is acting on it. We can calculate this force as follows:
`F_static = friction coefficient * normal force`
where, normal force = weight of upper block = 0.5 kg * 9.81 m/s^2 = 4.905 N
`F_static = 0.35 * 4.905 = 1.718 N`
Therefore, the static frictional force acting on the upper block is 1.718 N.
Now, we need to find the maximum force that can be applied to the lower block before it starts moving. This force is equal to the force of static friction acting on the lower block.
Since the upper block is not moving, the force of static friction acting on the lower block is equal to the force of static friction acting on the upper block.
`F_static(lower block) = F_static(upper block) = 1.718 N`
This means that the maximum horizontal force that can be applied to the lower block is 1.718 N.
However, if the applied force exceeds this value, the lower block will start moving and the force of kinetic friction will be acting on it, which is equal to:
`F_kinetic = friction coefficient * normal force`
`F_kinetic = 0.20 * 4.905 = 0.981 N`
Hence, if the applied force exceeds 1.718 N, the lower block will start moving and the force of kinetic friction will act on it, which is 0.981 N.
Therefore, the maximum horizontal force that can be applied to the lower block is 1.718 N.
Answer:
Explanation:
To determine the maximum horizontal force that can be applied to the lower block without causing the blocks to move, we need to calculate the maximum static friction force between the two blocks. This force is given by:
F_friction = coefficient of static friction * normal force
where the normal force is the force perpendicular to the surface of contact between the blocks. Since the blocks are resting on a level table, the normal force acting on the lower block is equal to the weight of both blocks, which is:
N = (m1 + m2) * g
where m1 is the mass of the lower block, m2 is the mass of the upper block, and g is the acceleration due to gravity (9.81 m/s^2).
Plugging in the given values, we have:
N = (1.0 kg + 0.5 kg) * 9.81 m/s^2 = 14.715 N
The maximum static friction force is then:
F_friction = 0.35 * 14.715 N = 5.15025 N
Therefore, the maximum horizontal force that can be applied to the lower block without causing the blocks to move is 5.15025 N. If a greater force is applied, the blocks will start to move and the kinetic friction force will take effect, which is given by:
F_kinetic = coefficient of kinetic friction * normal force
where the coefficient of kinetic friction is 0.20 in this case.
A stuntman of mass 55 kg is to be launched horizontally out of a spring- loaded cannon. The spring that will launch the stuntman has a spring coefficient of 266N / m and is compressed 5 m prior to launching the stuntman. If friction and air resistance can be ignored, what will be the approximate velocity of the stuntman once he has left the cannon?
The approximate velocity of the stuntman, once he has left the cannon, is 11 m/s.
StepsWe can use the conservation of energy, where the potential energy stored in the compressed spring is converted into the kinetic energy of the stuntman as he is launched out of the cannon.
The potential energy stored in the spring is given by:
PE = (1/2)kx²
where k is the spring constant and x is the distance the spring is compressed.
PE = (1/2)(266 N/m)(5 m)² = 3325 J
This potential energy is then converted into kinetic energy:
KE = (1/2)mv²
where m is the mass of the stuntman and v is his velocity.
3325 J = (1/2)(55 kg)v²
v² = (2*3325 J) / 55 kg
v² = 121 m²/s²
v = √(121 m²/s²) = 11 m/s
Therefore, the approximate velocity of the stuntman, once he has left the cannon, is 11 m/s.
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1 Suppose the displacement of particle P from origin at time t is given by x(t)=t²-6t find the average velocity and acceleration of p over the time interval 1 <=t<=3 sec
Answer:
-2 m/s and the average acceleration is 2 m/s².
Explanation:
To find the average velocity of particle P over the time interval 1<=t<=3 sec, we need to use the following formula:
average velocity = (final displacement - initial displacement) / (final time - initial time)
In this case, the initial time is 1 sec and the final time is 3 sec. Therefore, the initial displacement is:
x(1) = 1² - 6(1) = -5
And, the final displacement is:
x(3) = 3² - 6(3) = -9
Now, we can substitute the values in the formula:
average velocity = (-9 - (-5)) / (3 - 1) = -2 m/s
To find the average acceleration of particle P over the time interval, we need to use the following formula:
average acceleration = (final velocity - initial velocity) / (final time - initial time)
We know that the initial time is 1 sec, the final time is 3 sec, and the initial velocity is the velocity at time t=1 sec. Therefore, the initial velocity is:
v(1) = 2t - 6 = 2(1) - 6 = -4 m/s
We also know that the final velocity is the velocity at time t=3 sec. Therefore, the final velocity is:
v(3) = 2t - 6 = 2(3) - 6 = 0 m/s
Now, we can substitute the values in the formula:
average acceleration = (0 - (-4)) / (3 - 1) = 2 m/s²
Therefore, the average velocity of particle P over the time interval 1<=t<=3 sec is -2 m/s and the average acceleration is 2 m/s².
460miles per hour with the wind nd 420 per hour gainst the wind
The speed of the wind is 20 miles per hour.
To solve this problem, we can use the formula:
Speed = Distance/Time
Let's assume that the speed of the wind is x miles per hour.
With the wind, the plane travels at a speed of 460 miles per hour. This means that its speed relative to the ground is the sum of its airspeed and the speed of the wind:
460 = Airspeed + x
Against the wind, the plane travels at a speed of 420 miles per hour. This means that its speed relative to the ground is the difference between its airspeed and the speed of the wind:
420 = Airspeed - x
We can solve this system of equations to find the airspeed of the plane:
460 = Airspeed + x
420 = Airspeed - x
Adding the two equations gives:
880 = 2Airspeed
Dividing both sides by 2 gives:
Airspeed = 440 miles per hour
Now that we know the airspeed of the plane, we can find the speed of the wind by substituting this value into one of the equations we obtained earlier:
460 = Airspeed + x
460 = 440 + x
x = 20
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Explain how a balloon is able to keep its shape?
Answer:
It depends on how they are made.
Explanation:
Rubber balloons are not always spherical in shape. When filled with air, the inflation forms a balance between the balloon material, including its shape and thickness and its elasticity and the pressure of the air. That’s what determines its shape. Although a sphere is often the shape, it could be tubular, offset, and most other shapes.
A metal filament Lamp rated at 750w, 100v into be connected in series with a capacitor across a 230v, 60hz supply. Calculate the capacitance required
Answer : 0.00885 farads or 8.85 microfarads
Explanation: To calculate the capacitance required, we can use the following formula:
C = 1 / [2 * pi * f * ((V^2 - Vlamp^2)/P)]
where:
C = capacitance in farads (F)
pi = 3.14159...
f = frequency in hertz (Hz)
V = voltage in volts (V)
P = power in watts (W)
Vlamp = voltage of the lamp in volts (V)
Using the given values, we have:
C = 1 / [2 * pi * 60 * ((230^2 - 100^2)/750)]
C = 1 / [2 * 3.14159 * 60 * ((230^2 - 100^2)/750)]
C = 1 / [113.09724]
C = 0.00885 farads (F)
Therefore, the capacitance required is approximately 0.00885 farads or 8.85 microfarads.
a metal block of density 900kg weight 60newton in air find it's weight when it is immersed in paraffin wax of density 800kg
Answer:
We can use the concept of buoyancy to solve this problem.
The weight of the metal block in air is equal to the force of gravity acting on it, which is given as 60 Newtons. When the block is immersed in paraffin wax, it displaces a certain volume of wax equal to its own volume, and experiences an upward force due to buoyancy that partially cancels out the force of gravity acting on it.
The buoyant force acting on the block is given by the formula:
buoyant force = weight of fluid displaced
= density of fluid x volume of fluid displaced x acceleration due to gravity
The weight of the metal block in the paraffin wax is then equal to the difference between the weight of the block in air and the buoyant force acting on it.
Let's calculate the volume of the metal block first:
density of metal block = 900 kg/m³
weight of metal block in air = 60 N
acceleration due to gravity = 9.81 m/s²
weight of metal block = density of metal block x volume of metal block x acceleration due to gravity
volume of metal block = weight of metal block / (density of metal block x acceleration due to gravity)
= 60 N / (900 kg/m³ x 9.81 m/s²)
= 0.006536 m³
Now, let's calculate the weight of the metal block in the paraffin wax:
density of paraffin wax = 800 kg/m³
buoyant force = density of fluid x volume of fluid displaced x acceleration due to gravity
= 800 kg/m³ x 0.006536 m³ x 9.81 m/s²
= 51.02 N
weight of metal block in paraffin wax = weight of metal block in air - buoyant force
= 60 N - 51.02 N
= 8.98 N
Therefore, the weight of the metal block when it is immersed in paraffin wax of density 800 kg/m³ is 8.98 Newtons.
Bob travels 60km north turns around and travels 20km south what is his total distance travelled? what is his displacement
Explanation:
Total distance travelled is 60 + 20 = 80 km
He went 60....then turned around and headed back 20 km
so his displacement ( distance from starting point) is 60 - 20 = 40 km
13 Which of these fitness events happened LAST? OA. PE becomes part of American school curriculum. OB. Title IX forbids gender discrimination in sports. O C. The YMCA opens a gym in America. O D. The adjustable plate-loaded barbell is invented.
The answer is A. PE becomes part of American school curriculum.
Title IX, which forbids gender discrimination in sports, was enacted in 1972.
The YMCA opened its first gym in America in Boston in 1851.
The adjustable plate-loaded barbell was invented in the late 1940s by a man named George Snyder.
Physical Education (PE) has been a part of American school curriculums for well over a century, with the first school gymnasiums being built in the 1800s.
What is an american school curriculum?
The American school curriculum is the set of educational standards and guidelines used by schools in the United States to structure their academic programs. The curriculum typically includes courses in core academic subjects such as English, math, science, and social studies, as well as elective courses in areas such as the arts, foreign languages, and physical education.
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Select in the ticker-timer a frequency of 25 Hz or 50 Hz. Determine the period of the ticker-timer.
Answer:
The period of a ticker-timer is the time interval between two consecutive dots made by the ticker.
If the frequency of the ticker-timer is 25 Hz, then it makes 25 dots in one second. Therefore, the period of the ticker-timer can be calculated as:
Period = 1/frequency = 1/25 Hz = 0.04 seconds
If the frequency of the ticker-timer is 50 Hz, then it makes 50 dots in one second. Therefore, the period of the ticker-timer can be calculated as:
Period = 1/frequency = 1/50 Hz = 0.02 seconds
So, the period of the ticker-timer is 0.04 seconds for a frequency of 25 Hz and 0.02 seconds for a frequency of 50 Hz
Explanation:
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When heal flows between systems Entropy
Answer: increases
Explanation:
Please HELP me answer these three questions!! (show work)
Answer:
2) 42.6
3) 1500000 m
4) no he will not be late, it will take 3s
Explanation:
#2:
Formula for average velocity:
⇒ [tex]v=\frac{d}{t}[/tex]
Substitute
⇒ [tex]\frac{2560}{60}[/tex]
⇒ [tex]42.6[/tex]
#3:
1st convert 60km to m/s (correct si unit must always come first)
to convert kilometer to meter, multiply by 1000 (prefix 'kilo' = 1000)
60 km x 1000 = 60000 m
use the formula for speed, distance, & time
60000 = d/25
to find displacement just multiply the speed and time together
60000 x 25
1500000m is the displacement
#4:
s = d/t
given are displacement and speed/velocity
d = 25m
v = 8.5 m/s
to find the time just divide displacement by speed
8.5 = 25/t
25/8.5
≈ 3 seconds
so he will not be late for class.
A block of mass m1=3.0kg rests on a frictionless horizontal surface. A second block of m2=2.0kg hangs from an ideal cord of negligible mass that runs over an ideal pulley and then is connected to the first block . the blocks are released from rest . determine the displacement of the velocityA block of mass m1=3.0kg rests on a frictionless horizontal surface. A second block of m2=2.0kg hangs from an ideal cord of negligible mass that runs over an ideal pulley and then is connected to the first block . the blocks are released from rest . Determine how far has block 1 moved during the 1.2-s interval? A) 13.4 m B) 2.1m C) 28.2m D) 7.6mA block of mass m1=3.0kg rests on a frictionless horizontal surface. A second block of m2=2.0kg hangs from an ideal cord of negligible mass that runs over an ideal pulley and then is connected to the first block . the blocks are released from rest . determine the displacement of the velocityA block of mass m1=3.0kg rests on a frictionless horizontal surface. A second block of m2=2.0kg hangs from an ideal cord of negligible mass that runs over an ideal pulley and then is connected to the first block . the blocks are released from rest . Determine how far has block 1 moved during the 1.2-s interval?
To solve this problem, we can use the conservation of mechanical energy principle. When the blocks are released from rest, the potential energy of the system is converted to kinetic energy. Since the surface is frictionless, the mechanical energy of the system is conserved.
Using the principle of mechanical energy conservation, we can write:
m1*g*h = (m1+m2)*v^2/2
where m1 is the mass of the first block, m2 is the mass of the second block, g is the acceleration due to gravity, h is the height that the second block falls, and v is the velocity of the system after the blocks have moved a distance x.
The displacement of the first block can be found by using the time it takes the system to reach this velocity. The time t can be found using the formula:
x = (1/2) * a * t^2
where a is the acceleration of the first block.
The acceleration of the first block is equal to the acceleration of the system, which can be found by using the equation:
m1*a = m2*g - m1*g
Substituting the value of a in the previous formula, we get:
x = (1/2) * (m2*g - m1*g) * t^2 / m1
Substituting the values we get:
x = (1/2) * (2.0 kg * 9.81 m/s^2 - 3.0 kg * 9.81 m/s^2) * (1.2 s)^2 / 3.0 kg
x ≈ 7.6 m
Therefore, the correct answer is D) 7.6 m.
(a) Find the frequency ratio between the two frequencies fi =256 Hz and f2 = 320 Hz. (b) Add the interval of a fifth to f2 to obtain fs, and find the frequency ratio fs/fi. (c) Find the frequency of f3.
(a) The frequency ratio between the two frequencies fi = 256 Hz and f2 = 320 Hz is:
[tex]\frac{f_2}{f_i} = \frac{320}{256} = \frac{5}{4} = 1.25[/tex]
So the frequency ratio is 1.25.
(b) Adding the interval of a fifth to f2 = 320 Hz gives:
fs = f2 * (3/2) = 320 * (3/2) = 480 Hz
The frequency ratio fs/fi is:
[tex]\frac{f_s}{f_i} = \frac{480}{256} = \frac{15}{8} = 1.875[/tex]
So the frequency ratio is 1.875.
(c) To find the frequency of f3, we need to add the interval of a fourth to f2:
f3 = f2 * (4/3) = 320 * (4/3) = 426.67 Hz
Therefore, the frequency of f3 is 426.67 Hz.
A loudspeaker of mass 15.0 kg is suspended a distance of h = 1.00 m below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of l = 2.70 m .
1. What is the tension T in each of the cables?
Use 9.80 m/s2 for the magnitude of the free-fall acceleration.
Answer:
To solve the problem, we use the equations of equilibrium to find the tension in each cable holding up the loudspeaker. Since the loudspeaker is in equilibrium, the sum of the forces acting on it is zero. The weight of the loudspeaker is calculated first, and then we use trigonometry to find the horizontal and vertical components of the tension in one of the cables. We then apply the equation of equilibrium in the y direction to find the tension in each cable. The final answer is that the tension in each cable is approximately 81.1 N, which balances the weight of the loudspeaker.
___
Given:
Mass of loudspeaker (m) = 15.0 kg
Distance from ceiling (h) = 1.00 m
Length of cable (l) = 2.70 m
Acceleration due to gravity (g) = 9.80 m/s^2
Weight of loudspeaker:
Fg = mg
Fg = (15.0 kg)(9.80 m/s^2)
Fg = 147 N
Horizontal and vertical components of tension in one cable:
sinθ = h/l
sinθ = 1.00 m / 2.70 m
θ = sin^(-1)(1.00/2.70)
θ ≈ 21.6°
T_x = T sinθ
T_y = T cosθ
where T is the tension in the cable.
Equation of equilibrium in y direction:
ΣF_y = 2T cosθ - Fg = 0
Solving for T:
2T cosθ = Fg
T = Fg / (2 cosθ)
Plugging in the values:
T = (147 N) / (2 cos(21.6°))
T ≈ 81.1 N
Describe the change to the graph of Y= X +3 when Y=2X -3 is graphed 
Answer: a stretch of 2
Explanation: because it 2 (x) - 3
it the frequency of a wave is increased it’s
and
will decrease but its
will stay the same.
Answer:
Wavelength will decrease but frequency will stay the same.
Explanation:
The higher the frequency, the shorter the wavelength. The relationship between wavelength and frequency is called an inverse relationship, because as the frequency increases, the wavelength decreases.
However, the frequency usually remains the same because it is like a driven oscillation and maintains the frequency of the original source. If v changes and f remains the same, then the wavelength λ λ must change. Since v = f λ v = f λ , the higher the speed of a sound, the greater its wavelength for a given frequency.
Which type of marco molecules help a cell break down food?
Answer: Each macromolecule is broken down by a specific enzyme. For instance, carbohydrates are broken down by amylase, sucrase, lactase, or maltase. Proteins are broken down by the enzymes pepsin and peptidase, and by hydrochloric acid. Lipids are broken down by lipases.
Explanation:
Hope this will help
What factors would create an ideal circuit?
An ideal circuit is a theoretical representation of an electrical circuit, where all components are perfect and all parameters such as resistance, capacitance, and inductance are zero.
The ideal circuit also has no energy losses, making it an ideal electrical system. To create an ideal circuit, the following factors must be considered:
1. Perfectly Conductive Wires: The wires and other conductors used in the circuit should be perfect conductors, which means the resistance should be zero. This will ensure that no energy is lost in the form of heat.
2. Zero Inductance: Inductance is a property of a circuit which causes a voltage drop when current flows through it. The ideal circuit should have no inductance so that the current can flow freely.
3. Zero Capacitance: Capacitance is a property in which electric charge builds up when current passes through it. To create an ideal circuit, the capacitance should be zero.
4. Zero Impedance: Impedance is the opposition to the flow of current in an electrical circuit. The ideal circuit should have zero impedance so that the current can flow freely.
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