1. (30 pts) Let x(t) = cos(πt/2) be a continuous-time signal,
a. Sketch the signal for -4 b. Find the fundamental period of the signal (if it is periodic).
c. Determine if the signal is odd / even or neither.
d. Compute the energy of the signal for all time.
e. Compute the power of the signal for all time.

In my own words, I would say that physics is an area of science that seeks to explain and understand the fundamental nature of the dynamics of objects, essentially defining how objects can interact, in space and in time.

We need evidence to be able to continually test theories about the composition and origin of our solar system and galaxies in order to verify the theories and to make laws.

A theory is an explanation for observations of the natural world that has been carried by using the scientific method, and which brings together many facts.

So we can conclude that we need evidence to test theories about the composition and origin of our solar system in order to verify the theories and to make laws.

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Hi there!

Begin by using Gauss' Law to find the electric field.

[tex]\oint {E \cdot} \, dA = \frac{Q_{encl}}{\epsilon_0}[/tex]

E = Electric field (N/C)
dA = differential area element

Q = enclosed charge (C)

ε₀ = Permittivity of free space (8.85 * 10⁻¹² C²/Nm²)

We can construct a large cylinder around the wire in order to determine the electric flux. The electric field lines will pass through the LATERAL surface area of the cylinder, so:
[tex]A = 2\pi rL[/tex]

Where 'L' is the length of the cylinder and 'r' is the distance from the capacitor.

The enclosed charge is equivalent to the charge per meter length (λ) multiplied by the length, so:
[tex]\oint {E \cdot} \, dA = \frac{\lambda L}{\epsilon_0}[/tex]

We can rewrite the dot product as EA (where cosθ = 1 since the normal vector points in the direction of the field).

A = the lateral surface area of a cylinder, so:

[tex]E * 2\pi rL = \frac{\lambda L}{\epsilon_0}[/tex]

Rearrange to solve for 'E'.

[tex]E = \frac{\lambda L }{2\pi r L \epsilon _0}\\\\E = \frac{\lambda }{2\pi r \epsilon_0}[/tex]

a)
Plug in the distance into 'r'.

[tex]E = \frac{\lambda }{2\pi r \epsilon_0} \\\\E = \frac{0.0000072}{2\pi * 5.5 * (8.85 * 10^{-12})} = \boxed{23542.18 \frac{N}{C}}[/tex]

b)
Repeat:
[tex]E = \frac{\lambda }{2\pi r \epsilon_0}\\\\E = \frac{0.0000072}{2\pi * 2.5 * (8.85 * 10^{-12})} = \boxed{51792.8 \frac{N}{C}}[/tex]

We can see that the distance from the wire is INVERSELY related to the electric field strength by a power of r⁻¹. The field strength DECREASES as the distance INCREASES.

Explanation:

it is not a arithmetic sequence

3,0,-3,-6 is the correct arithmetic sequence. So, the correct option is C.

An arithmetic sequence is defined as a sequence where the common difference between any two consecutive terms is constant. A sequence is explained as a collection of numbers that follow a pattern such as the sequence 2, 7, 12, 17, ... is an arithmetic sequence as there is a pattern where each number is obtained by adding 5 to its previous term. Is performed.

For above given information,

3,0,-3,-6 is the correct arithmetic sequence.

as, d is called as the common difference of the series

d=0 - 3= - 3 - 0 = -6 - (-3)

d= - 3

An arithmetic sequence is called as the equal common difference in each progressive term.

Thus, 3,0,-3,-6 is the correct arithmetic sequence. So, the correct option is C.

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Your question is incomplete, most probably the complete question is:

Which of the following is an arithmetic sequence?

a.2,4,16,32

b.2,3,7,1,

c.3,0,-3,-6

d.5,-5,5,-5

Answer:

[tex]\displaystyle \sqrt{\frac{(5/2)\, (g - a)\, m\, R^{2}}{M^{2}\, a}}[/tex], assuming that the tension in the rope is the only tangential force on the sphere ([tex]g[/tex] denote the gravitational acceleration.)

Explanation:

The forces on the bucket are:

Since the weight of the bucket and the tension from the rope are in opposite directions, the magnitude of the net force would be:

[tex]\begin{aligned} \|\text{Net Force}\| =\; & \|\text{Weight}\| - \|\text{Tension}\| \end{aligned}[/tex].

The upward tension in the rope prevents the bucket from accelerating at [tex]g[/tex] (free fall.) Rather, the bucket is accelerating at an acceleration of only [tex]a[/tex]. The net force on the bucket would be thus [tex]m\, a[/tex].

Rearrange the equation for the net force on the bucket to find the magnitude of the tension in the rope would be:

[tex]\begin{aligned} & \|\text{Tension}\| \\ =\; & \|\text{Weight}\| - \|\text{Net Force}\| \\ =\; & m\, g - m\, a \\ =\; & (g - a)\, m\end{aligned}[/tex].

At a distance of [tex]R[/tex] from the center of the sphere, the tension in the rope [tex](g - a)\, m[/tex] would exert a torque of [tex](g - a)\, m\, R[/tex] on the sphere. If this tension is the only tangential force on this sphere, the net torque on the sphere would be [tex](g - a)\, m\, R\![/tex].

Let [tex]M[/tex] denote the mass of this sphere. The moment of inertia of this filled sphere would be [tex]I = (2/5)\, M^{2}[/tex].

Therefore, the magnitude of the angular acceleration of this sphere would be:

[tex]\begin{aligned}& \|\text{Angular Acceleration}\| \\ =\; & \frac{\|\text{Net Torque}\|}{(\text{Moment of Inertia})} \\ =\; & \frac{(g - a)\, m\, R}{(2/5)\, M^{2}} \end{aligned}[/tex].

The bucket is accelerating at a magnutide of [tex]a[/tex] downwards. The rope around the sphere need to unroll at an acceleration of the same magnitude, [tex]a\![/tex]. The tangential acceleration of the sphere at the surface would also need to be [tex]\! a[/tex].

Since the surface of the sphere is at a distance of [tex]R[/tex] from the center, the angular acceleration of this sphere would be [tex](a / R)[/tex].

Hence the equation:

[tex]\begin{aligned}& \frac{(g - a)\, m\, R^{2}}{(2/5)\, M^{2}} = \|\text{Angular Acceleration}\| = \frac{a}{R} \end{aligned}[/tex].

Solve this equation for [tex]M[/tex], the mass of this sphere:

[tex]\begin{aligned}& \frac{(g - a)\, m\, R^{2}}{(2/5)\, M^{2}} = \frac{a}{R} \end{aligned}[/tex].

[tex]\begin{aligned}M^{2} &= \frac{(g - a)\, m\, R^{2}}{(2/5)\, a} \\ &= \frac{(5/2)\, (g - a)\, m\, R^{2}}{a}\end{aligned}[/tex].

[tex]\begin{aligned}M&= \sqrt{\frac{(5/2)\, (g - a)\, m\, R^{2}}{a}}\end{aligned}[/tex].

(a) The time of flight be for a tennis ball launched by the ball machine is 0.19 s.

(b) The range of the tennis ball be is 1.01 m.

(c)  The final velocity of the ball with which it reaches the ground is 7.16 m/s.

The time of flight of the tennis ball is calculated as follows;

h = vt + ¹/₂gt²

1.2 = 5.3t + 0.5(9.8)t²

1.2 = 5.3t + 4.9t²

4.9t² + 5.3t - 1.2 = 0

a = 4.9, b = 5.3, c = 1.2

solve using quadratic formula

t = 0.19 s

Thus, the time of flight be for a tennis ball launched by the ball machine is 0.19 s.

The range of the tennis ball is calculated as follows;

R = vt

R = 5.3 x 0.19

R = 1.01 m

The final velocity of the ball with which it reaches the ground is calculated as follows;

vf = vo + gt

vf = 5.3 + 9.8(0.19)

vf = 7.16 m/s

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(a) The force diagram of a coaster sitting under a cup of coffee includes the weight of the coater plus the weight of coffee acting downwards.

(b) The force diagram of a car slowing down as it approaches a stop sign includes force of the car and frictional force opposing the motion.

(c) The force diagram includes the force of the test and action of the fridge which are eqaul and opposite.

(d) The force diagram of baseball before it leaves the bat incudes only the weight of the baseball acting downwards.

The force diagram of a coaster sitting under a cup of coffee includes the weight of the coater plus the weight of coffee acting downwards.

                                        ↑ Fn

                                        Ф                  Fn = W

                                        ↓ W

Where;

The force diagram inlcudes the applied force and frictional force opposing the motion.

                                      Ff ←  Ф  → F

where;

The force diagram includes the force of the test and action of the fridge which are eqaul and opposite.

                               Fb ←  Ф → Fa

where;

The force diagram includes only the weight of the baseball acting downwards.

                                 Ф

                                  ↓

                                 W = mg

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When you rub a dry cloth across glass, it creates charged static electricity, which attracts little non-charged dust particles.

Answer:

Gravitational force is the force that attracts objects towards each other. Two factors that affect the gravitational force between objects are the mass of the two objects and the distance between

Explanation:

Gravity is what pulls us towards the Earth if we were to jump into the air, so it is the force that pulls things towards other things. The bigger the objects are the more gravity they have, so a planet has more gravity than say, an apple. Distance between objects also makes their gravity change, so the Earth's pull on the moon is different than the Earth's pull on the sun.

Hopefully this helps- let me know if you have any questions!

Describe gravitational force in your own words. Which two factors affect the gravitational force between two objects?

[tex]F = \frac{G m{ \tiny1}m{ \tiny2} }{ {r}^{2} } [/tex]

where

The gauge pressure in the balloon as indicated by a difference of 0.0171 m in the heights of the water columns is 167.58 Pa.

The gauge pressure in the balloon is the pressure inside the balloon due to the water columns relative to the atmospheric pressure.

The gauge pressure in the balloon as indicated by a difference of 0.0171 m in the heights of the water columns is calculated as follows;

P = ρgΔh

P = (1,000)(9.8)(0.0171)

P = 167.58 Pa

Thus, the gauge pressure in the balloon as indicated by a difference of 0.0171 m in the heights of the water columns is 167.58 Pa.

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Increasing the temperature causes an increase in the average kinetic energy of the particles of a material.

The average kinetic energy of particles is the energy possessed by particles due to their constant motion.

The constant motion of particles occurs due to the energy acquired by the particles, when the temperature of the particles increases, the average kinetic energy increases which in turn increases the speed of the particles.

Thus, we can conclude that, increasing the temperature causes an increase in the average kinetic energy of the particles of a material.

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Answer:

0

Explanation:

because no distance covered by body

Now

[tex]\\ \sf\rightarrowtail Power=\dfrac{Work\:done}{Time\:taken}[/tex]

[tex]\\ \sf\rightarrowtail Power=\dfrac{250}{1}[/tex]

[tex]\\ \sf\rightarrowtail Power=250W[/tex]

Answer:

wait in comments.................

Answer:

1716.75 J

Explanation:

Step 1: First check what we are provided with. As per given question we have:

mass (m) = 70 kg, height (h) = 2.5 m and acceleration due to gravity (g) = 9.81 m/s².

Step 2: Check what we are asked to find out.

Work done = Change in Potential energy

The stuff required to solve this question is potential energy. Using the formula: P = mgh. Where P is Potential energy, m is mass, g is acceleration due to gravity and h is height.

Step 3: Substitute the known values in the above formula.

→ P = 70 × 2.5 × 9.81

→ P = 1716.75 J

Hence, the work done against the force of gravity is 1716.75 J.

Answer:

16 reflection,incidence

Answer:

what is heat and transfer

1. The car should move with velocity of 46.28 m/s

2. The force exerted on the receiver is 375 N

3.  The player delivered an impulse of !.6 N s to the ball

In Physics, Impulse is the product of mass and change in velocity. from Newtons law change in momentum is equal to impulse

m ( v - u ) = f * t = impulse = momentum

m = mass

v = final velocity

u = initial velocity

f = force

t = time

1.

Given:

mass = 1210 kg

momentum = 5.6 x 10^4 kg m/s

change in velocity = v - u = ?

u = 0 so change in velocity = v

momentum = mass * velocity

velocity = momentum / mass

velocity = 5.6 x 10^4 / 1210

velocity =  46.28 m/s

2.

Given:

m = 0.50 kg

u = 15 m/s

v = 0

t = 0.020 s

m ( v - u ) = f * t

f = 0.50 * ( 0 - 15 ) / 0.02

f = -375 N (the negative sign indicates the direction of the stoppage force as against the force that produces the motion )

force = 375 N

3.

Given:

m = 0.40 kg

u = 18 m/s to the North

v = 22 m/s

m ( v - u ) = impulse

impulse = 0.4 (22 - 18 )

impulse = 1.6 N s

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Answer:

Newton

Explanation:

The SI unit for weight is newton.

For A block of mass m = 8.40 kg, moving on a horizontal frictionless surface with a speed of 4.20 m/s  is mathematically given as

F = 193.2N

Generally, the equation for the  magnitude of the average force mathematically given as

F = m(v1+v2)/t

F = 8.40(4.2+O.4)/t

F = 193.2N

In conclusion magnitude of the average force is

F = 193.2N

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Answer:

300 m/s

Explanation:

2d = vt

v = 2d/t

v = 2×90/.3

v=300 m/s

d = distance

t = time

v = velocity/speed of sound

If a person generates about 412005 joules of heat from the body,  the water temperature is mathematically given as

t=21.6296C

Question Parameter(s):

The person is submerged neck-deep into a tub containing 2124 kg of water at 20.9 °C

Generally, the equation for the Heat   is mathematically given as

Heat gained =Heat loess

Thereofore

mw*cw*(t-2160)=1.5*10^5

[tex]t=21.60+\frac{1.5*10^5}{mw*Cw}\\\\t=21.60+\frac{1.5*10^5}{1.2*10^3*4186}[/tex]

t=21.6296C

In conclusion, the tempreature

t=21.6296C

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Give the mathematical expression for coulomb's force if q1, q2 are the magnitude of charges and r is the distance between them.

F=K q1q2/r2

Answer:

R1 + R2 = R = 12 for resistors in series - so R1 = R2 if they are identical

2 R1 = 12         and R1 = R2 = 6 ohms

1 / R = 1 / R1 + 1 / R2     for resistors in parallel

R = R1 * R2 / (R1 + R2) = 6 * 6 / (6 + 6) = 3

The equivalent resistance would be 3 ohms if connected in parallel

Answer:

p = rho× g × h

Explanation:

p: pressure

rho : density

g : gravity acceleration

h : height

[tex]\text{Given that, mass m = 70 kg and velocity v = 3 m/s}\\\\\text{Momentum,}~ p = mv = 70 \times 3 = 210~ kg ~ms^{-1}[/tex]