escribe verdadero o falso :
a) la primera derivada en la funcion de desplazamiento representa fisicamente la velocidad media.
b) al calcular la segunda derivada en la funcion de desplazamiento se determina la aceleracion instantanea.
c)al calcular la derivada de la funcion f(×)=2xa la n 4+12 resulta 8x4
d)la derivada de la funcion f(x)=2x a la n es f(x)=n2x a la n.​

Answers

Answer 1

By defining kinematics and derivative relations we can find which statements are true or false:

         a) False. The derivative is the instantaneous velocity.

        b) True. The second drift is the instantaneous acceleration.

        c) False the derivative is

        d) False the derivative is

a) The velocity is defined with the variation of the position with respect to time.

           \(v= \frac{dx}{dt}\)  

Wher x is the position and t the time.

In the change of the average velocity is the average value of the velocity in an interval

           \(v = \frac{v_f - v_o}{t}\)  

We can see that the derivative is the speed in a very small timet, that is, the speed instantaneous. Therefore the statement is False.

 

The prime derivative of the position is the instantaneous velocity, not the average velocity.

b) Acceleration is defined as the change in position with respect to time..

           \(a = \frac{dv}{dt}\)  

Let's use the chain rule.

          a = \(\frac{d}{dt} \frac{dx}{dt}\)  

          a = \(\frac{d^2 x}{dt^2}\)  

Therefore the second  derivative of the position is the instantaneous acceleration.

The statement is True.

Questions c and d ask the derivative of a function

             f (x) = 2 x aⁿ

c) derivative with respect  of x

            \(\frac{df}{dx} = 2 a^n\)

The answer is False.

d) derivative with respect to a.

            \(\frac{df}{da} = 2n \ x a^{n-1}\)

Answer d is false

In conclusion using the definition of kinematics and derivative relations we can find which statements are true.

        a) False. The derivative is the instantaneous velocity.

        b) True. The second drift is the instantaneous acceleration.

        c) False the derivative is:   \(\frac{df}{dx} = 2 a^n\)

        d) False the derivative is:   \(\frac{df}{da} = 2n \ x a^{n-1}\)

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Related Questions



2- A car on a straight highway goes in the positive direction for 8 km and then backs up for 3.6 km. What are the distance and displacement covered by the train?

Answers

Answer:

11.6km

4.4km in the negative direction

Explanation:

Distance is the total length of path covered and traveled by a body.

So, for this car on a straight line;

  Total distance  = 8km + 3.6km  = 11.6km

Displacement is the distance traveled along a path and the direction it takes.

It is a vector quantity with magnitude and directional attributes.

For this journey;

 Displacement  = 8km  - 3.6km  = 4.4km in the negative direction.

A stuntman sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 13.5 m/s, and the man is initially 3.55 m above the level of the saddle. Find a - What must be the horizontal distance between the saddle and limb when the man makes his move? Find b - How long is he in the air?

Answers

(a)  the horizontal distance between the saddle and limb when the man makes his move is approximately 11.386 meters.

(b)  the man is in the air for approximately 0.843 seconds.

To determine the horizontal distance between the saddle and limb when the man makes his move, we need to consider the horizontal velocity of the man when he drops from the tree limb.

Given:

Speed of the horse (constant velocity), v = 13.5 m/s

Vertical distance between the limb and saddle, h = 3.55 m

a) To find the horizontal distance, we can use the formula:

horizontal distance = horizontal velocity × time

Since the man drops vertically, his initial horizontal velocity is zero. The only horizontal velocity he will have is due to the motion of the horse.

The time taken by the man to fall can be determined using the equation for free fall:

h = (1/2) × g × t²

Where g is the acceleration due to gravity (approximately 9.8 m/s²) and t is the time.

Rearranging the equation, we get:

t = √(2h / g)

Substituting the given values:

t = √(2 × 3.55 / 9.8) ≈ 0.843 s

Now, we can find the horizontal distance:

horizontal distance = v × t

horizontal distance = 13.5 × 0.843 ≈ 11.386 m

Therefore, the horizontal distance between the saddle and limb when the man makes his move is approximately 11.386 meters.

b) The time the man is in the air can be calculated using the same equation for free fall:

t = √(2h / g)

Substituting the given value of h:

t = √(2 × 3.55 / 9.8) ≈ 0.843 s

Thus, the man is in the air for approximately 0.843 seconds.

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Your friend's 10.8 g graduation tassel hangs on a string from his rearview mirror. When he accelerates from a stoplight, the tassel deflects backward toward the rear of the car at an angle of 5.23 ∘ relative to the vertical.
A) Find the tension in the string holding the tassel.
B) At what angle to the vertical will the tension in the string be twice the weight of the tassel?

Answers

The tension in the string holding the tassel and the vertical will the tension in the string

T = 0.1953 NФ = 34.4 °

What is the tension in the string holding the tassel. ?

Generally, the equation for Tension is  mathematically given as

\(TCos\theta = mg\)

Therefore

\(TCos6.58^{o} = 19.8*10^{-3}*9.8\)

T = 0.1953 N

b).

Where

\(T* sin \theta = ma\)

\(0.1953*Sin6.58 \textdegree = 19.8*10^{-3}*a\)

a = 1.13 m/s^2

In conclusion

T* sinФ = ma

2msinФ = ma

2sinФ = a

\(sin\theta = \frac{a}{2}\)

\(\theta = sin^{-1}\frac{a}{2} \\\\\theta= sin^{-1}\frac{1.13}{2}\)

Ф = 34.4 °

In conclusion, The tension in the string holding the tassel and the vertical will the tension in the string

T = 0.1953 N

Ф = 34.4 °

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Please solve step by syep

Please solve step by syep

Answers

Answer:

0.258 +- 0.0162

Explanation:

First change the uncertainty to percentage uncertainty :

%uncertainty =uncertainty /estimated value *100

0.1/51.6 * 100=0.19%

Do the same for the rest you will get:

0.1%, 1%, 5%

Then add the %uncertainties

0.19% + 0.1% + 1% +5%=6.29%

Find density:

51.6/10 * 100 * 0.20 = 0.258

Change the %percentage uncertainty to absolute uncertainty :

Absolute uncertainty = %uncertainty * the answer

6.29/100 * 0.258 = 0.0162

Answer = 0.258 +- 0.0162

After rounding:

0.26 +- 0.02

Raju completes one round of a circular track of diameter 200m in 30s. Calculate
a. The distance travelled by Raju
b. The magnitude of displacement travelled by Raju at the end of 30 s.

Answers

Explanation:

Given:

Diameter = 200 m

Radius, r = 200/2 = 100 m

Time taken, t = 30 seconds

Formula to be used:

Distance traveled, = circumference of circle = 2πr

Answer:

Putting all the values, we get

Distance traveled = 2πr

Distance traveled = 2 × 22/7 × 100 Distance traveled = 4400/7 Distance traveled = 628.57 m

So, the distance traveled by Raju is 628.57 m.

Now, magnitude of the displacement,

At the end of 30 seconds, Raju will come to starting position or initial position, so displacement is zero.

A candle is placed in front of a concave mirror as it is shown . State the image characteristics (SALT)

Answers

As a result, the picture behind the mirror is virtual, upright, and enlarged.

What does SALT in concave mirrors stand for?

You will find that the properties of an image (SALT) created in a concave mirror depend on the object's position. A) if the item is larger than C. Size, attitude, and location are all important considerations.

The image will be true, but reversed and much reduced. To obtain a crisp flame image, move the burning candle towards the mirror while moving the screen away from it. The size of the inverted picture grows.

Concave mirrors may create both physical and virtual images. A virtual and enlarged picture is produced when the item gets closer to the mirror. When the item is placed further away from the mirror,.

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True or False: a projectile accelerates only in the y (vertical) direction. The "x," or
horizontal acceleration is equal to zero.

Answers

Answer:

True

Explanation:

Assuming no wind resistance, there will be no horizontal acceleration, because there will be no forces acting on it.

An object is attached to a trolley with a 0.80 kg mass, which is then pushed into an identical trolley at a speed of 1.1 m / s. The two trolleys couple together and move at a speed of 0.70 m / s after the collision. Calculate the mass of the object.

Answers

The mass of the object is approximately 0.457 kg.

The mass of the object attached to the trolley can be calculated using the principle of conservation of momentum. Since the two trolleys couple together and move as a single system after the collision, the total momentum before and after the collision should be the same. Given the mass of one trolley is 0.80 kg and the initial speed is 1.1 m/s, the momentum before the collision is 0.80 kg * 1.1 m/s = 0.88 kg·m/s. After the collision, the total mass is the sum of the two trolleys, and the final speed is 0.70 m/s.

Using the momentum equation, the mass of the object can be calculated as follows:

Total momentum before collision = Total momentum after collision

0.88 kg·m/s = (0.80 kg + mass of the object) * 0.70 m/s

Solving for the mass of the object, we get:

0.88 kg·m/s = (0.80 kg + mass of the object) * 0.70 m/s

0.88 kg·m/s = 0.56 kg + 0.70 kg * mass of the object

0.88 kg·m/s - 0.56 kg = 0.70 kg * mass of the object

0.32 kg = 0.70 kg * mass of the object

Dividing both sides by 0.70 kg, we find:

mass of the object = 0.32 kg / 0.70 kg = 0.457 kg

The two trolleys collide and couple together, the total momentum before the collision is equal to the total momentum after the collision according to the principle of conservation of momentum.

The momentum of an object is defined as the product of its mass and velocity. In this case, the mass of one trolley is known (0.80 kg) and the initial speed is given (1.1 m/s), allowing us to calculate the momentum before the collision.

After the collision, the two trolleys move together at a new speed (0.70 m/s). By setting the initial momentum equal to the final momentum and solving for the unknown mass of the object, we can find its value.

In the calculation, we subtract the masses of the two trolleys from the total mass in order to isolate the mass of the object.

Dividing the difference in momentum by the product of the known mass and the new speed, we obtain the mass of the object. In this case, the mass of the object is approximately 0.457 kg.

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Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 450 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 50 centimeters to 80 centimeters

Answers

The work done in stretching the spring from 50 cm to 80 cm is 67.5 J.

Hooke's Law

Hooke's law states that the force applied to an elastic material is directly proportional to its extension, provided its elastic limit is not exceeded.

To calculate the amount of work done by Hooke's law, first, we need to find the force constant of the spring.

Formula:

F = ke................. Equation 1

Where:

F = Force appliedk = Spring constante = extension

make k the subject of the equation

k = F/e................ Equation 2

From the question,

Given:

F = 450 Ne = 30 cm = 0.3 m

Substitute these values into equation 2

k = 450/0.3k = 1500 N/m.

Finally, To find the work done in stretching the spring from 50 cm to 80 cm, we use the formula below.

W = ke²/2........... Equation 3

Where:

W = Work donek = spring constante = extension

Also, From the question,

Given:

e = (80-50) = 30 cm = 0.3 mk = 1500 N/m

Substitute these values into equation 3

W = 1500(0.3²)/2W = 67.5 J.

Hence, The work done in stretching the spring from 50 cm to 80 cm is 67.5 J.

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Which type of energy is the "waste energy" generated when energy is used?

Answers

Answer:

thermal energy

Explanation:

In a typical electric power generation plant, input fuel is used to create electricity while excess thermal energy (in the form of steam) is wasted in the process.

Calculate the height of stairs a 60 kg student would have to run in order to burn off 1 Calorie of food energy, which is the equivalent of 4190 Joules.

Answers

The height of stairs a 60 kg student would have to run in order to burn off 1 Calorie of food energy will be 7.1 meters.

What is potential energy?

The potential energy is due to the virtue of the position and the height. The unit for the potential energy is the joule.

Given data;

Mass of student,m = 60 kg

Energy,E = 4190 J

Height of stairs,h=?

The potential energy is mainly dependent upon the height of the object. The potential energy is found as;

Potential energy = mgh

E=mgh

h=E/mg

h= 4190 J / (60 kg× 9.81  m/s²)

h = 7.1 metre

Hence the height of the stairs will be 7.1 meters.

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paleomagnetism shows at equal distances from the mor, the polarity of the earth's magnetism in the rock is the same. T/F

Answers

False, Paleomagnetism, is the study of glamorous fields recorded in jewels, deposition, or archeological accoutrements . Geophysicists who specialize in paleomagnetism are called paleomagnetists.

Certain glamorous minerals in jewels can record the direction and intensity of Earth's glamorous field at the time they formed. This record provides information on the once geste of the geomagnetic field and the once position of monumental plates. The record of geomagnetic reversals saved in stormy and sedimentary gemstone sequences provides a time- scale that's used as a geochronologic tool.

substantiation from paleomagnetism led to the reanimation of the international drift thesis and its metamorphosis into the ultramodern proposition of plate tectonics. Apparent polar wander paths handed the first clear geophysical substantiation for international drift, while marine glamorous anomalies did the same for seafloor spreading. Paleomagnetic data continues to extend the history of plate tectonics back in time, constraining the ancient position and movement of mainland and international fractions( topographies).

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HI PLEASE HELP?A speed skater skates 1.5 km in 78 s. What is her speed in km/h?Need a Hint?57 km/h61 km/h65 km/h68 km/h

Answers

The speed of skater can be given as,

\(v=\frac{d}{t}\)

Here, v is the speed, d is the distance travelled and t is the time taken.

Substitute the known values,

\(\begin{gathered} v=\frac{1.5\text{ km}}{(78\text{ s)(}\frac{1\text{ h}}{60\text{ min}})(\frac{1\text{ min}}{60\text{ s}})_{}} \\ \approx68\text{ km/h} \end{gathered}\)

Thus, the speed of skater is approximately 68 km/h.

A cubic box is completely filled with 2800 g of water. What is the length of one side of the box, in meters?
m
Explain your reasoning.
Since the density of water is
cm3 is
g/cm3, then the volume of 2800 g of water is
cm on each side. Converting [ cm to meters, the cube is
Proy
13 of 15
⠀⠀⠀
Next
cm³. A cubic box with a volume of [
m on each side.

A cubic box is completely filled with 2800 g of water. What is the length of one side of the box, in

Answers

The density of water is approximately 1 g/cm^3. Therefore, the volume of 2800 g of water would be 2800 cm^3 because density is mass/volume, and so volume is mass/density.

Since this volume is inside a cubic box, the length of each side of the cube (a, for instance) could be found by taking the cubic root of the volume. This is because the volume of a cube is calculated by a^3 (length of one side cubed). Hence, a = cube root of 2800 cm^3 ≈ 14.1 cm.

Converting centimeters to meters (as 1 meter is equal to 100 centimeters), we get approximately 0.141 meters.

So the filled cubic box has a side length of approximately 0.141 m.

Where is the near point of an eye for which a spectacle lens of power +2 D is prescribed for reading purpose?

Answers

The near point of a human eye is about a distance of 25 cm.

The closest distance that an object may be viewed clearly without straining is known as the near point of the eye.

This distance (the shortest at which a distinct image may be seen) is 25 cm for a typical human eye.

The closest point within the accommodation range of the eye at which an object may be positioned while still forming a focused picture on the retina is also referred to as the near point.

In order to focus on an item at the average near point distance, a person with hyperopia must have a near point that is further away than the typical near point for someone of their age.

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Harmonic Motion Basics

10. Calculate the period of a pendulum that has a length of 68 cm.​

Answers

The period of the pendulum with a length of 68 cm is 1.65 seconds.

What is period of the pendulum?

The period of a pendulum is the time taken for one complete back-and-forth swing or oscillation. It is the time taken for the pendulum to move from its highest point (the point of maximum displacement) to its lowest point and back again to the highest point. The period of a pendulum depends on its length and the acceleration due to gravity.

The period of a pendulum can be calculated using the formula:

T = 2π√(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.81 m/s²).

Converting the length of the pendulum to meters:

L = 68 cm = 0.68 m

Substituting the values into the formula:

T = 2π√(0.68 m / 9.81 m/s²)

Simplifying:

T = 2π√(0.0694 s²)

Calculating the square root:

T = 2π x 0.263 s

Simplifying:

T = 1.65 s

Therefore, the period of the pendulum with a length of 68 cm is 1.65 seconds.

What is an acceleration of the pendulum?

An acceleration of a pendulum refers to the rate at which its velocity changes as it swings back and forth. The acceleration of a pendulum is not constant but rather varies as the pendulum swings, with the greatest acceleration occurring at the endpoints of its swing, where it changes direction.The acceleration of a pendulum is directly proportional to the displacement of the pendulum from its equilibrium position.

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Complete question is: The period of the pendulum with a length of 68 cm is 1.65 seconds.

N2 + 3H2 + 2NH3
What type of reaction is this

Answers

Answer:It is a combination reaction; nitrogen and hydrogen combine to form ammonia

Explanation:

This is the reaction that is used to make ammonia from hydrogen and nitrogen. In this reaction, only one product is formed. Therefore, this reaction is known as a combination reaction.

The diagram shows squares 1, 2, and 3 constructed on the
sides of a right triangle.
3
2
Which statement about the squares must be true?
A. (Perimeter of 1) + (Perimeter of 2) = (Area of 3)
B. (Area of 1) + (Area of 2) = (Area of 3)
C. (Perimeter of 1) + (Perimeter of 2) = (Perimeter of 3)
D. (Area of 1) + (Area of 2) = (Perimeter of 3)
SUBMIT

Answers

The statement that must be true is:  (Area of 1) + (Area of 2) = (Area of 3). This statement accurately reflects the relationship between the areas of the squares in the given diagram.

The correct answer is option B.

To determine which statement about the squares must be true, let's analyze the given diagram and the properties of squares.

In the diagram, square 1 is constructed on one side of the right triangle, square 2 is constructed on another side of the right triangle, and square 3 is constructed on the hypotenuse of the right triangle.

Statement A: (Perimeter of 1) + (Perimeter of 2) = (Area of 3)

This statement relates to the perimeters of squares 1 and 2 being equal to the area of square 3. However, this is not necessarily true. The perimeters of squares 1 and 2 are related to the lengths of their sides, while the area of square 3 is related to the length of its side. The perimeters and areas are different measures, so this statement is not necessarily true.

Statement B: (Area of 1) + (Area of 2) = (Area of 3)

This statement compares the areas of squares 1 and 2 to the area of square 3. Since squares have all sides equal in length, the areas of squares 1 and 2 are equal to the area of square 3. Therefore, this statement must be true

Statement C: (Perimeter of 1) + (Perimeter of 2) = (Perimeter of 3)

This statement relates to the perimeters of squares 1 and 2 being equal to the perimeter of square 3. However, since the squares have different side lengths, their perimeters are different. Therefore, this statement is not necessarily true.

Statement D: (Area of 1) + (Area of 2) = (Perimeter of 3)

This statement compares the areas of squares 1 and 2 to the perimeter of square 3. As mentioned earlier, the areas of squares 1 and 2 are equal to the area of square 3, which means they are not necessarily equal to the perimeter of square 3. Hence, this statement is not necessarily true.

Therefore, the correct statement is option B.

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When I mix 200g of water at 10°C with 300g of water at 55°C, what is the final temperature of the mixture?​

Answers

Answer:

4th of August is the

Explanation:

5th and then I can help out by getting

which type of electromagnetic wave has more energy than ultraviolet waves?
A Visible light
B Infrared
C Microwaves
D X-rays

Answers

Answer:

D. X-rays have more energy than ultraviolet waves.

In 1994, a pumpkin with a mass of 449 kg was grown in Canada. Suppose you want to push a pumpkin with this mass along a smooth, horizontal ramp. You give the pumpkin a good push, only to find yourself sliding backwards at a speed of 4.0 m/s. How far will the pumpkin slide 3.0 s after the push? Assume your mass to be 60.0 kg.

Answers

After pushing the pumpkin hard, you find yourself reversing direction at a speed of 4.0 m/s. 3.0 seconds after being pushed, the pumpkin will slide 12 m. Assume you weigh 60.0 kg.

We can use the conservation of momentum to solve this problem. After the push, the momentum of the system is given by:

p = (449 kg + 60 kg) * v

where v is the speed of the pumpkin and you after the push. Since you end up sliding backward at 4.0 m/s, we have:

v = -4.0 m/s

Substituting this into the expression for momentum, we find:

p = (449 kg + 60 kg) * (-4.0 m/s) = -2036 kg·m/s

The negative sign indicates that the momentum of the system is in the opposite direction of your motion.

During the sliding motion, the net force on the system is given by:

Fnet = (449 kg + 60 kg) * g * sin(θ)

where g is the acceleration due to gravity (9.81 m/s^2) and θ is the angle of the ramp. Since the ramp is smooth and horizontal, θ = 0 and Fnet = 0. Therefore, there is no net force to change the momentum of the system.

Using the equation for motion with constant acceleration, we can find the distance the pumpkin slides in 3.0 seconds:

x = x0 + v0t + (1/2)at²

Since the initial speed of the pumpkin is -4.0 m/s and there is no net force acting on it, its speed remains constant during the slide. Therefore, v0 = -4.0 m/s and a = 0. Substituting these values, we find:

x = x0 + v0t = (-4.0 m/s) * (3.0 s) = -12 m

The negative sign indicates that the pumpkin slides in the opposite direction to your motion. Therefore, the pumpkin slides 12 meters backward (i.e., towards you) in 3.0 seconds after the push.

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a wheel has angular velocity 4.00 rad/s. which of the following is closest to the number of revolutions that the wheel makes in 15.0 s?
a.10 revolutions
b.20 revolutions
c.15revolutions
d.25 revolutions
e. 5 revolutions
f. i dont know yet

Answers

Answer:

10 revolutions

Explanation:

By using the equation Δ=Δ, we get that Δ=(4.00rad/s)(15.0s)=60.0rad. Since there are 2 radians per revolution, this angular displacement corresponds to (60.0rad)/(2rad/rev)=9.55rev.

The angular velocity of the wheel is 4 rad/s and the time interval is 15 s. Then the number of rotations in radians is 60 radians. This is equal to 9.5 revolutions.

What is angular velocity ?

Angular velocity is a physical quantity that describes the speed of an object in an angular path. It is the rotational o revolutional analogue of of the linear velocity.

The angular velocity of an object is the product of the linear velocity and the radius of the angular path.

Given that, the angular velocity of the wheel = 4 rad/s

time  = 15 s

then, number of radians = 4 rad/s × 15 s = 60 radians.

1 revolution  = 2π radians.

then 60 radians = 60/2π = 9.5 revolutions.

Therefore, the number of revolutions for the wheel in 15 s is 9.5 revolutions.

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Two stars of masses M and 6M are separated by a distance D. Determine the distance (measured from M) to a point at which the net gravitational force on a third mass would be zero.

Answers

Answer:

0.29D

Explanation:

Given that

F = G M m / r2

F = GM(6m) / (D-r)2

G Mm/r2 = GM(6m) / (D-r)2

1/r2 = 6 / (D-r)2

r = D / (Ö6 + 1)

r = 0.29 D

See diagram in attached file

Two stars of masses M and 6M are separated by a distance D. Determine the distance (measured from M)

The highness or lowness of a sound is perceived as
a.
compression.
c.
ultrasound.
b.
wavelength.
d.
pitch.

Answers

Answer:

i think its D

Explanation:

Answer:

The highness or lowness of a sound is perceived as pitch. Pitch is a perceptual property of sound that allows us to distinguish between sounds that have the same loudness and duration, but differ in their frequency content. The pitch of a sound is determined by the frequency of the sound wave, with higher frequencies producing higher pitches and lower frequencies producing lower pitches. The pitch is what makes a sound distinguishable and is important in music, language, and communication.

Kinetic and Potential energy

Answers

The main difference between potential and kinetic energy is that one is the energy of what can be and one is the energy of what is. In other words, potential energy is stationary, with stored energy to be released; kinetic energy is energy in motion, actively using energy for movement.

there’s a tornado warning where i live rn

Answers

Answer:

same

Explanation:

aww good luck, i hope u n ur family turn out okkk

what is energy and the characteristics​

Answers

Energy is a fundamental concept in physics that represents the ability or capacity of a system to do work.

It is a scalar quantity, meaning it has magnitude but no specific direction. Energy exists in various forms and can be converted from one form to another. The characteristics of energy include:

1. Forms of Energy: Energy can exist in different forms such as kinetic energy (energy of motion), potential energy (stored energy), thermal energy (heat), chemical energy, electrical energy, and many more.

2. Conservation of Energy: The law of conservation of energy states that energy cannot be created or destroyed; it can only be transformed from one form to another. The total amount of energy in a closed system remains constant.

3. Transfer and Conversion: Energy can be transferred from one object to another or converted from one form to another. For example, electrical energy can be converted into light energy in a light bulb.

4. Units of Measurement: Energy is typically measured in joules (J) in the International System of Units (SI). Other common units include kilowatt-hours (kWh) for larger quantities of energy and calories (cal) for thermal energy.

5. Energy and Work: Energy is closely related to the concept of work. When work is done on an object, energy is transferred to it or from it, resulting in a change in its energy state.

Understanding the nature and characteristics of energy is crucial in various fields, including physics, engineering, and environmental science, as it plays a central role in explaining and analyzing various phenomena and processes.

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For 1983 through 1989, the per capita con-
sumption of chicken in the U.S. increased at a
rate that was approximately linear. In 1983,
the
per capita consumption was 30.9 pounds,
and in 1989 it was 48 pounds.
Write a linear model for
per capita con-
sumption of chicken in the U.S. Let t repre-
sent time in years,
where t = 3
represents
1983. Let y represent chicken consumption in
pounds.

Answers

Part 1: Finding slope

Solving the slope requires two points: \($\left(\left(t_{1}, y_{1}\right)\right.$\) and \($\left.\left(t_{2}, y_{2}\right)\right)$\). The year 1983 corresponds to \($t=3$\) so the first point is (3,33.7). The year 1989 is 6 years after 1983, so the corresponding t value for 1989 should be 6 years after \($t=3$\); that is, the second point should be (9,47)

Using the slope formula, we determine the slope m:

\(m=\frac{\Delta y}{\Delta t}=\frac{y_{2}-y_{1}}{t_{2}-t_{1}}=\frac{47 \mathrm{lb}-33.7 \mathrm{lb}}{9 \mathrm{yr}-3 \mathrm{yr}}=\frac{13.3}{6} \approx 2.22 \mathrm{lb} / \mathrm{yr}\)

Part 2: Finding y-intercept

By plugging the initial point (3,33.7) into the equation, we can compute the y-intercept b of our linear model \($y=2.22 t+b$\) :

\($33.7 \mathrm{lb}=(2.22 \mathrm{lb} / \mathrm{yr})(3 \mathrm{yr})+b$\)

\($$b=33.7 \mathrm{lb}-(2.22 \mathrm{lb} / \mathrm{yr})(3 \mathrm{yr})=27.04 \mathrm{lb}$$\)

Part 3: Conclusion

The whole linear model explaining per capita consumption in the United States is as follows:

\($$y=(2.22 \mathrm{lb} / \mathrm{yr}) t+27.04 \mathrm{lb}$$\)

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A speed skater moving across frictionless ice at 8.8 m/s hits a 6.0 m -wide patch of rough ice. She slows steadily, then continues on at 5.8 m/s . What is her acceleration on the rough ice?

Answers

Recall that

v² - u² = 2 ax

where u and v are initial and final velocities, respectively; a is acceleration; and ∆x is the distance traveled (because the skater moves in only one direction).

So we have

(5.8 m/s)² - (8.8 m/s)² = 2 a (6.0 m)

a = ((5.8 m/s)² - (8.8 m/s)²) / (12 m)

a = -3.65 m/s²

1. Odysseus traveled from Troy to Ithaca. What
was the acceleration of Odysseus' ship if its mass
was 900,000 kg and it moves across the water with
a force of 300,000 N?

Answers

Answer: 0.33 m/s^2

Explanation:

The acceleration of Odysseus' ship as it moves across the water from Troy to Ithaca is 0.33m/s²

Given the data in the question;

Mass of Odysseus' ship; \(m= 900000kg\)Force with which Odysseus' ship moves across the water; \(F = 300000N\)Acceleration; \(a = ?\)

To determine the acceleration of the ship, We the equation from Newton's Second Law of Motion:

\(F = m\ *\ a\)

Where F is the force, m is the mass and a is the acceleration

Lets make acceleration ''a'', the subject of the formula

\(a = \frac{F}{m}\)

Now, we substitute our given values into the equation

\(a = \frac{300000N}{900000kg}\)

We know that, A newton is defined as \(1 kg.m/s^2\)

\(a = \frac{300000 kg.m/s^2}{900000kg} \\\\a = 0.33m/s^2\)

Therefore, the acceleration of Odysseus' ship as it moves across the water from Troy to Ithaca is 0.33m/s²

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