Answer:
The correct option is d
Explanation:
From the question we are told that
The electric potential is [tex]V = 3000 \ V[/tex]
The power is [tex]P = 60 \ W[/tex]
The charge delivered is [tex]q = 3nC = 3.0 *10^{-9} \ C[/tex]
Generally the power generated is mathematically represented as
[tex]P = I V[/tex]
=> [tex]I = \frac{P}{V }[/tex]
=> [tex]I = \frac{60 }{3000 }[/tex]
=> [tex]I = 0.02 \ A[/tex]
This current flow is mathematically represented as
[tex]I = \frac{q -q_o}{\Delta t }[/tex]
Where [tex]q_o[/tex] is the charge delivered at t=0 s which is 0s
So
[tex]0.02 = \frac{ (3.0 *10^{-9}) -0 }{t - 0 }[/tex]
[tex]t = 1.50 *10^{-7 } \ s[/tex]
[tex]t = 150 *10^{-9 } \ s[/tex]
Some radar systems detect the size and shape of objects such as aircraft and geological terrain. Approximately what is the smallest observable detail (in m) utilizing 495 MHz radar?
Answer:
0.61 m
Explanation:
The smallest observable length by the radar must be at least equal to or greater than the wavelength of the radar.
using the relationship
c = fλ
where
c is the speed of light in vacuum = 3 x 10^8 m/s
f is the frequency of the wave = 495 MHz = 4.95 x 10^8 Hz
λ is the wavelength = ?
λ = c/f = (3 x 10^8)/(4.95 x 10^8) = 0.61 m
answer to your question is 0.6m
What is tensor quantity?
Is Inertia a tensor? give reason
Answer:
A tensor is a quantity, for example a stress or a strain, which has magnitude, direction, and a plane in which it acts. Stress and strain are both tensor quantities. ... A tensor is a quantity, for example a stress or a strain, which has magnitude, direction, and a plane in which it acts.
Inertia Tensor. where I = the inertia tensor. The angular momentum of a rigid body rotating about an axis passing through the origin of the local reference frame is in fact the product of the inertia tensor of the object and the angular velocity. ... As shown in [7], the inertia tensor is symmetric.
Explanation:
Hope dis help
A 12-V battery is connected across a device with variable resisstance. As the resistance of the device increases, determine whether the following quantities increase, decrease, or remain unchanged. Indicate your answers with I, D, or U respectively.
a. The current through the device
b. The voltage across the device
c. The power consumed by the device
Good morning 2 all ,What is mechanical advantage write its formula. Have a good day thank you ✌
The ratio of foort dustance to load distance in a simple machine is called mechanical advantage or MA.
MA= Effort Distance / Load Distance
A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 6.0 cm and released. If the ball makes 30 oscillations in 20 s, what are its (a) mass and (b) maximum speed?
Answer:
a
[tex]m = 0.169 \ kg[/tex]
b
[tex]|v_{max} |= 0.5653 \ m/s[/tex]
Explanation:
From the question we are told that
The spring constant is [tex]k = 14 \ N/m[/tex]
The maximum extension of the spring is [tex]A = 6.0 \ cm = 0.06 \ m[/tex]
The number of oscillation is [tex]n = 30[/tex]
The time taken is [tex]t = 20 \ s[/tex]
Generally the the angular speed of this oscillations is mathematically represented as
[tex]w = \frac{2 \pi}{T}[/tex]
where T is the period which is mathematically represented as
[tex]T = \frac{t}{n}[/tex]
substituting values
[tex]T = \frac{20}{30 }[/tex]
[tex]T = 0.667 \ s[/tex]
Thus
[tex]w = \frac{2 * 3.142 }{ 0.667}[/tex]
[tex]w = 9.421 \ rad/s[/tex]
this angular speed can also be represented mathematically as
[tex]w = \sqrt{\frac{k}{m} }[/tex]
=> [tex]m =\frac{k }{w^2}[/tex]
substituting values
[tex]m =\frac{ 15 }{(9.421)^2}[/tex]
[tex]m = 0.169 \ kg[/tex]
In SHM (simple harmonic motion )the equation for velocity is mathematically represented as
[tex]v = - Awsin (wt)[/tex]
The velocity is maximum when [tex]wt = \(90^o) \ or \ 1.5708\ rad[/tex]
[tex]v_{max} = - A* w[/tex]
=> [tex]|v_{max} |= A* w[/tex]
=> [tex]|v_{max} |= 0.06 * 9.421[/tex]
=> [tex]|v_{max} |= 0.5653 \ m/s[/tex]
How much charge is stored on two parallel-plate capacitors by the 12V battery if one is filled with air and the other is filled with a dielectric (k=3.00)
The question is incomplete, the complete question is;
how much charge is stored on the parallel-plate capacitors by the 12.0 V battery? One is filled with air, and the other is filled with a dielectric for which k = 3.00; both capacitors have a plate area of 5.00×10 −3 m 2 and a plate separation of 2.00 mm.
The capacitance of the capacitor is the quantity of charge stored by the capacitor.
Given that;
C1= εo k * A/d
εo = permittivity of free space
C1 = 8.85 x 10-12 farad per meter *1 * 5.00×10 −3 m 2/2 * 10^-3
= 2.21 * 10^-11 F
C2 = 8.85 x 10-12 * 3 * 5.00×10 −3 m 2/2 * 10^-3
= 6.63 * 10^-11 F
q1 = C1V1 = 2.21 * 10^-11 C * 12 V
= 2.65 * 10^-10 C
q2 = C2V2 = 6.63 * 10^-11 F * 12 V
= 7.96 * 10^-10 C
qtotal = 2.65 * 10^-10 C + 7.96 * 10^-10 C
qtotal = 1.061 * 10^-9C
https://brainly.com/question/17176550
Read the following sentence from the article. Life can evolve into complex and specialized forms that exploit every possible niche in their surroundings. What is the definition of "exploit" as it is used in this sentence? A to turn to advantage B to invent a new application C to draw on an earlier experience D to narrow down options
Answer:
C. To draw on an earlier experience.
00
Use base units to check whether the following equations are balance
(a) pressure = depth x density gravitational field strength,
(b) energy = mass x (speed of light).
dod to molt solid
Answer:
In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the column than at the top. This difference in pressure results in a net force that tends to accelerate an object upwards.
The pressure at a depth in a fluid of constant density is equal to the pressure of the atmosphere plus the pressure due to the weight of the fluid, or p = p 0 + ρ h g , p = p 0 + ρ h g , 14.4
Granite: 2.70 × 10 32.70 × 10 3
Lead: 1.13 × 10 41.13 × 10 4
Iron: 7.86 × 10 37.86 × 10 3
Oak: 7.10 × 10 27.10 × 10 2
The base unit prefix used for 1,000× is _____. kilo milli centi deka
Answer:
[tex]\Large \boxed{\sf kilo}[/tex]
Explanation:
kilo is a prefix that means [tex]1000[/tex] of the base unit.
Answer:
kilo is the correct answer
Explanation:
because my exam says sooo....
When the magnet falls toward the copper block, the changing flux in the copper creates eddy currents that oppose the change in flux. The resulting braking force between the magnet and the copper block always opposes the motion of the magnet, slowing it as it falls. The braking force on the magnet is nearly equal to its weight, so it falls very slowly. The rate of the fall produces a rate of flux change sufficient to produce a current that provides the braking force. If the magnet is pushed, forcefully, toward the block, the rate of change of flux is much higher than this. When the magnet is moving much more quickly than it will fall unaided, what is the direction of the net force on the magnet?
Answer:
The net force is directed downwards.
Explanation:
Since the magnet is falling much more faster than it would unaided, then there is a net force that is accelerating the magnet downwards. We know that acceleration is due to a force acting on a mass, and in this case, the magnet is the mass. Also, the acceleration is always in the direction of the force producing it, which means that the net force on the magnet is vertically downwards.
A simple pendulum is 3.00 m long. (a) What is the period of small oscillations for this pendulum if it is located in an elevator accelerating upward at 3.00 m/s2? s (b) What is the period of small oscillations for this pendulum if it is located in an elevator accelerating downward at 3.00 m/s2? s (c) What is the period of this pendulum if it is placed in a truck that is accelerating horizontally at 3.00 m/s2? s
Answer:
a,)3.042s
b)4.173s
c)3.281s
Explanation:
For a some pendulum the period in seconds T can be calculated using below formula
T=2π√(L/G)
Where L = length of pendulum in meters
G = gravitational acceleration = 9.8 m/s²
Then we are told to calculate
(a) What is the period of small oscillations for this pendulum if it is located in an elevator accelerating upward at 3.00 m/s2?
Since oscillations for this pendulum is located in the elevator that is accelerating upward at 3.00 then
use G = 9.8 + 3.0 = 12.8 m/s²
Period T=2π√(L/G)
T= 2π√(3/12.8)
T=3.042s
b) (b) What is the period of small oscillations for this pendulum if it is located in an elevator accelerating downward at 3.00 m/s2?
G = 9.8 – 3.0 = 6.8 m/s²
T= 2π√(3/6.8)
T=4.173s
C)(c) What is the period of this pendulum if it is placed in a truck that is accelerating horizontally at 3.00 m/s2?
Net acceleration is
g'= √(g² + a²)
=√(9² + 3²)
Then period is
T=2π√(3/11)
T=3.281s
Three crates with various contents are pulled by a force Fpull=3615 N across a horizontal, frictionless roller‑conveyor system. The group of boxes accelerates at 1.516 m/s2 to the right. Between each adjacent pair of boxes is a force meter that measures the magnitude of the tension in the connecting rope. Between the box of mass m1 and the box of mass m2, the force meter reads F12=1387 N. Between the box of mass m2 and the box of mass m3, the force meter reads F23=2304 N. Assume that the ropes and force meters are massless.
The question is incomplete. Here is the complete question.
Three crtaes with various contents are pulled by a force Fpull=3615N across a horizontal, frictionless roller-conveyor system.The group pf boxes accelerates at 1.516m/s2 to the right. Between each adjacent pair of boxes is a force meter that measures the magnitude of the tension in the connecting rope. Between the box of mass m1 and the box of mass m2, the force meter reads F12=1387N. Between the box of mass m2 and box of mass m3, the force meter reads F23=2304N. Assume that the ropes and force meters are massless.
(a) What is the total mass of the three boxes?
(b) What is the mass of each box?
Answer: (a) Total mass = 2384.5kg;
(b) m1 = 915kg;
m2 = 605kg;
m3 = 864.5kg;
Explanation: The image of the boxes is described in the picture below.
(a) The system is moving at a constant acceleration and with a force Fpull. Using Newton's 2nd Law:
[tex]F_{pull}=m_{T}.a[/tex]
[tex]m_{T}=\frac{F_{pull}}{a}[/tex]
[tex]m_{T}=\frac{3615}{1.516}[/tex]
[tex]m_{T}=2384.5[/tex]
Total mass of the system of boxes is 2384.5kg.
(b) For each mass, analyse each box and make them each a free-body diagram.
For [tex]m_{1}[/tex]:
The only force acting On the [tex]m_{1}[/tex] box is force of tension between 1 and 2 and as all the system is moving at a same acceleration.
[tex]m_{1} = \frac{F_{12}}{a}[/tex]
[tex]m_{1} = \frac{1387}{1.516}[/tex]
[tex]m_{1}[/tex] = 915kg
For [tex]m_{2}[/tex]:
There are two forces acting on [tex]m_{2}[/tex]: tension caused by box 1 and tension caused by box 3. Positive referential is to the right (because it's the movement's direction), so force caused by 1 is opposing force caused by 3:
[tex]m_{2} = \frac{F_{23}-F_{12}}{a}[/tex]
[tex]m_{2} = \frac{2304-1387}{1.516}[/tex]
[tex]m_{2}[/tex] = 605kg
For [tex]m_{3}[/tex]:
[tex]m_{3} = m_{T} - (m_{1}+m_{2})[/tex]
[tex]m_{3} = 2384.5-1520.0[/tex]
[tex]m_{3}[/tex] = 864.5kg
Hi Friends!
please help me with these questions!
SUBJECT: Chemistry, Physics,Biology
Answer:
q.1 : Air near candle gets heated up and after this it rises by convection so the thermometer B will receive more heat than the thermometer A So, according to the given condition thermometer B will show a greater rise in temperature.
q.2 : x is the pure sample of compound . y is the pure sample of element . z is the mixture of different elements
q.3 : the saliva contains an enzyme salivary amylase (ptyalin) which converts starch in roti into maltose, isomaltose and small dextrins called a-dextrin.
A resistor, an inductor, and a capacitor are connected in series to an AC source. The AC source is operating at the resonance frequency. Which of the following statements are true?
a. The peak voltage across the resistor is equal to the peak voltage across the inductor.
b. The total voltage across the inductor and the capacitor at any instant is equal to zero.
c. The peak voltage across the resistor is equal to the peak voltage across the capacitor.
d. The peak voltage across the inductor is greater than the peak voltage across the capacitor.
e. The peak voltage across the capacitor is greater than the peak voltage across the inductor.
f. The current is in phase with the driving voltage.
I believe the correct answer is a
The true statement is that, at resonance, current is in phase with the driving voltage.
Resonance occurs in an RLC circuit at the point when the inductive reactance is equal to the capacitive reactance. At the point of resonance, the voltage across the inductor and capacitor are equal.
It should noted that, at resonance, the current is in phase with the driving voltage. This is the true statement in the list.
Learn more: https://brainly.com/question/10038290
an electron starts from rest from a fixed point charge with q. what total potential difference accelerates the electron to being very far away from Q
Answer:
V = (k*Q)/R
Explanation:
Total potential difference accelerates the electron to being very far away from Q is;
V = (k*Q)/R
Where,
V is the Potential Difference in Joules per Coulomb
k is the constant
Q is the charge in Coulomb
R is Electron distance in cm or m
Example
An electron starts from rest 66.1 cm from a fixed point charge with Q = -0.120 μC. What total potential difference accelerates the electron from being very far away from Q
For k = 9.0*10^9 N*m^2/C^2
V = (k*Q)/R
V = (9.0*10^9 * -0.120*10^-6)/0.661
V = -1633.9 Volt.
The answer will change to positive because V = (k*Q)/R is negative at the outset and Zero far away.
The electron (with a negative charge) has a positive energy in the beginning and that gets converted into a positive kinetic energy "far away".
A charge of 15 is moving with velocity of 6.2 x17 which makes an angle of 48 degrees with respect to the magnetic field. If the force on the particle is 4838 N, find the magnitude of the magnetic field.
a. 06.0T.
b. 08.0T.
c. 07.0T.
d. 05.0 T.
Complete question:
A charge of 15C is moving with velocity of 6.2 x 10³ m/s which makes an angle of 48 degrees with respect to the magnetic field. If the force on the particle is 4838 N, find the magnitude of the magnetic field.
a. 0.06 T
b. 0.08 T
c. 0.07 T
d. 0.05 T
Answer:
The magnitude of the magnetic field is 0.07 T.
Explanation:
Given;
magnitude of the charge, q = 15C
velocity of the charge, v = 6.2 x 10³ m/s
angle between the charge and the magnetic field, θ = 48°
the force on the particle, F = 4838 N
The magnitude of the magnetic field can be calculated by applying Lorentz force formula;
F = qvBsinθ
where;
B is the magnitude of the magnetic field
B = F / vqsinθ
B = (4838) / (6.2 x 10³ x 15 x sin48)
B = 0.07 T
Therefore, the magnitude of the magnetic field is 0.07 T.
Fish is cold blooded animal
A dentist uses a concave mirror (focal length 2 cm) to examine some teeth. If the distance from the object to the mirror is 1 cm, what is the magnification of the tooth
Answer: 2
Explanation:
1/2=1/1 +1/x
x=-2
magnification= 2/1
magnification=2
A metal cube with sides of length a=1cm is moving at velocity v0→=1m/sj^ across a uniform magnetic field B0→=5Tk^. The cube is oriented so that four of its edges are parallel to its direction of motion (i.e., the normal vectors of two faces are parallel to the direction of motion).Find E, the magnitude of the induced electric field inside the cube. Express your answer numerically, in newtons per coulomb.
Answer:
the magnitude of the electric field is 1.25 N/C
Explanation:
The induced emf in the cube ε = LB.v where B = magnitude of electric field = 5 T , L = length of side of cube = 1 cm = 0.01 m and v = velocity of cube = 1 m/s
ε = LB.v = 0.01 m × 5 T × 1 m/s = 0.05 V
Also, induced emf in the cube ε = ∫E.ds around the loop of the cube where E = electric field in metal cube
ε = ∫E.ds
ε = Eds since E is always parallel to the side of the cube
= E∫ds ∫ds = 4L since we have 4 sides
= E(4L)
= 4EL
So,4EL = 0.05 V
E = 0.05 V/4L
= 0.05 V/(4 × 0.01 m)
= 0.05 V/0.04 m
= 1.25 V/m
= 1.25 N/C
So, the magnitude of the electric field is 1.25 N/C
The magnitude of the electric field is 1.25 N/C
Calculation of the magnitude of the electric field:But before that the following calculations need to be done.
ε = LB.v = 0.01 m × 5 T × 1 m/s
= 0.05 V
Now
ε = ∫E.ds
here ε = Eds because E is always parallel to the side of the cube
So,
= E∫ds ∫ds
= 4L so we have 4 sides
Now
= E(4L)
= 4EL
So,4EL = 0.05 V
Now
E = 0.05 V/4L
= 0.05 V/(4 × 0.01 m)
= 0.05 V/0.04 m
= 1.25 V/m
= 1.25 N/C
hence, The magnitude of the electric field is 1.25 N/C
learn more about electric field here: https://brainly.com/question/1834208
At the B end of the recessed horizontal bar, forces F1 and F2 of magnitudes 3 KN and 2KN respectively are applied and oriented as shown in the figure. Determine the magnitude of the resulting force and its orientation with respect to the horizontal.
Answer:
2.98 kN, 69.1° below the horizontal
Explanation:
Sum of forces in the x direction:
Fₓ = 3 kN cos 30° − 2 kN cos 40°
Fₓ ≈ 1.07 kN
Sum of forces in the y direction:
Fᵧ = -3 kN sin 30° − 2 kN sin 40°
Fᵧ = -2.79 kN
Magnitude of the resultant force is:
F² = Fₓ² + Fᵧ²
F = 2.98 kN
The direction of the resultant force is:
tan θ = Fᵧ / Fₓ
θ = -69.1°
explain how does a convex lens produce real image from virtual object
Answer:
Real images are formed where rays of light actually converge, whereas virtual images occur with they are perceived to converge. Real images can be produced by passing light through converging lenses or with a concave mirror of some sort.
Explanation:
hope that helped a little :)
Real images are formed when the object is located beyond the focal length from the lens. A virtual image is formed if the object is place between focal length and pole of the converging lens.
What is convex lens?The converging lens which forms the real images by the intersection of light rays.
Real images are produced by light passing through converging lens or a concave mirror.
The real meeting of the rays coming from the focal point of the rays after reflection. Real images are formed where rays of light actually converge, whereas virtual images occur with they are appear to converge. Real images are formed when the object is located beyond the focal length from the lens. A virtual image is formed if the object is place between focal length and pole of the converging lens.
Thus, a convex lens produce real image from virtual object.
Learn more about convex lens.
https://brainly.com/question/1604692
#SPJ2
Improved balance is a primary benefit of regular cardiovascular exercise .
Answer:
Cardiovascular exercise is the activity use that aerobic metabolism and cellular reaction.
Explanation:
Cardiovascular exercise is activity increase heart rate and raises oxygen large muscle group of the body.Cardiovascular exercise is that contain cardio improve to the health mental health, heart health.Cardiovascular exercise such as walking, swimming, running is that exercise is benefit to the health.Cardiovascular exercise to the internal body organs that the healthy heart for the function and performance of the heart.Cardiovascular exercise that having involve feet of the ground this type of activity is called high impact of cardio.Cardio is a good and maintaining exercise for the lungs and heart or healthy bones.Cardio exercise is performed that to a water in reduce to the gravity of that pull on the body weight.Cardiovascular daily to build the stronger muscle and that control the blood pressure.Which nucleus complete the following equation
(C) [tex]^{208}_{84}\text{Po}[/tex]
Explanation:
[tex]^{212}_{86}\text{Rn} \rightarrow \:^4_2\text{He} + \:^{208}_{84}\text{Po}[/tex]
Which of the following regions of the electromagnetic spectrum have longer wavelengths than visible light? 1. infrared radiation 2. ultraviolet radiation 3. microwave radiation
Answer:infrared radiation
Explanation:
Infrared radiation and microwave radiation of the electromagnetic spectrum have longer wavelengths than visible light.
What is electromagnetic wave?EM waves are another name for electromagnetic waves. When an electric field interacts with a magnetic field, electromagnetic waves are created. These electromagnetic waves make up electromagnetic radiations. It is also possible to say that electromagnetic waves are made up of magnetic and electric fields that are oscillating. The basic equations of electrodynamics, Maxwell's equations, have an answer in electromagnetic waves.
If we arrange electromagnetic wave with decrease in wavelength, we get:
Radio waves > microwave > Infrared > Visible light > Ultraviolet > X-rays > Gamma radiation.
Hence, Infrared radiation and microwave radiation of the electromagnetic spectrum have longer wavelengths than visible light.
Learn more about electromagnetic wave here:
https://brainly.com/question/29774932
#SPJ5
Given the solution [tex]y_{1}(x)[/tex] from EDO below, develop a second solution.
[tex]x\frac{d^{2}y }{dx^{2} } +3\frac{dy}{dx} -y=0,\\y_{1} (x)=1+\frac{x}{3} +\frac{x^{2} }{24} +\frac{x^{3} }{360} + ...[/tex]
We're given
[tex]\displaystyle y_1(x) = 1 + \frac x3 + \frac{x^2}{24} + \frac{x^3}{360} + \cdots = \sum_{n=0}^\infty a_nx^n[/tex]
so let's see if we can find a closed form for the n-th term's coefficient.
Notice that
[tex]\displaystyle a_0 = 1 \\\\ a_1 = \frac13 = \frac1{1\times3} \\\\ a_2 = \frac1{24} = \frac1{(1\times3) \times (2\times4)} \\\\ a_3 = \frac1{360} = \frac1{(1\times3) \times (2\times4) \times (3\times5)}[/tex]
If the pattern continues, the next few terms are likely
[tex]\displaystyle a_4 = \frac1{8640} = \frac1{(1\times3) \times (2\times4) \times (3\times5) \times (4\times6)} \\\\ a_5 = \frac1{302400} = \frac1{(1\times3) \times (2\times4) \times (3\times5) \times (4\times6) \times (5\times7)} \\\\ a_6 = \frac1{14515200} = \frac1{(1\times3) \times (2\times4) \times (3\times5) \times (4\times6) \times (5\times7) \times (6\times8)}[/tex]
which leads up to the n-th term,
[tex]\displaystyle a_n = \frac1{(1\times3) \times (2\times4) \times \cdots \times (n\times(n+2))} = \frac2{n!(n+2)!}[/tex]
where the numerator is multiplied by 2 in order to "complete" the factorial pattern in (n + 2)!.
So we have
[tex]\displaystyle y_1(x) = \sum_{n=0}^\infty \frac2{n!(n+2)!} x^n[/tex]
Now we use reduction of order to find a linearly independent solution of the form [tex]y_2(x) = v(x)y_1(x)[/tex], with derivatives
[tex]\displaystyle \frac{\mathrm dy_2}{\mathrm dx} = v(x) \frac{\mathrm dy_1}{\mathrm dx} + y_1(x) \frac{\mathrm dv}{\mathrm dx} \\\\ \frac{\mathrm d^2y_2}{\mathrm dx^2} = v(x) \frac{\mathrm d^2y_1}{\mathrm dx} + 2 \frac{\mathrm dv}{\mathrm dx} \frac{\mathrm dy_1}{\mathrm dx} + y_1(x) \frac{\mathrm d^2v}{\mathrm dx^2}[/tex]
Substitute [tex]y_2[/tex] and its derivatives into the DE, and simplify the resulting expression to get a DE in terms of v(x) :
[tex]\displaystyle x y_1 \frac{\mathrm d^2v}{\mathrm dx^2} + \left(2x\frac{\mathrm dy_1}{\mathrm dx}+3y_1\right)\frac{\mathrm dv}{\mathrm dx} + \left(x\frac{\mathrm d^2y_1}{\mathrm dx^2}+3\frac{\mathrm dy_1}{\mathrm dx}-y_1\right)v = 0[/tex]
but since we know [tex]y_1(x)[/tex] satisfies the original DE, the last term vanishes and we're left with
[tex]\displaystyle x y_1 \frac{\mathrm d^2v}{\mathrm dx^2} + \left(2x\frac{\mathrm dy_1}{\mathrm dx}+3y_1\right)\frac{\mathrm dv}{\mathrm dx} = 0[/tex]
Reduce the order by substituting [tex]w(x)=\dfrac{\mathrm dv}{\mathrm dx}[/tex] to get yet another DE in w(x) :
[tex]\displaystyle x y_1 \frac{\mathrm dw}{\mathrm dx} + \left(2x\frac{\mathrm dy_1}{\mathrm dx}+3y_1\right)w = 0[/tex]
This equation is separable:
[tex]\displaystyle \frac{\mathrm dw}w = - \frac{2x\frac{\mathrm dy_1}{\mathrm dx}+3y_1}{xy_1}\,\mathrm dx \\\\ \frac{\mathrm dw}w = -\left(\frac2{y_1}\frac{\mathrm dy_1}{\mathrm dx} + \frac3x\right)\,\mathrm dx[/tex]
From here you would integrate to solve for w(x), then integrate again to solve for v(x), and finally for [tex]y_2(x)[/tex] by multiplying [tex]y_1(x)[/tex] by v(x). Using the fundamental theorem of calculus, you would find
[tex]\displaystyle \ln|w| = -2 \int_1^x \frac{{y_1}'(\xi)}{y_1(\xi)}\,\mathrm d\xi - 3\ln|x| + C_1 \\\\ w = \frac{C_1}{x^3} \exp\left(-2 \int_1^x \frac{{y_1}'(\xi)}{y_1(\xi)} \,\mathrm d\xi\right)\right) \\\\ v = C_1 \int_1^x \frac1{\omega^3} \exp\left(-2 \int_1^\omega \frac{{y_1}'(\xi)}{y_1(\xi)}\,\mathrm d\xi\right) \,\mathrm d\omega + C_2[/tex]
so that you end up with
[tex]\displaystyle y_2(x) = C_1 y_1(x) \int_1^x \frac1{\omega^3} \exp\left(-2 \int_1^\omega \frac{{y_1}'(\xi)}{y_1(\xi)}\,\mathrm d\xi\right) \,\mathrm d\omega + C_2y_1(x)[/tex]
But the second term is already accounted for by [tex]y_1(x)[/tex] itself, so the second solution is
[tex]\displaystyle y_2(x) = \boxed{y_1(x) \int_1^x \frac1{\omega^3} \exp\left(-2 \int_1^\omega \frac{{y_1}'(\xi)}{y_1(\xi)}\,\mathrm d\xi\right) \,\mathrm d\omega}[/tex]
You could go the extra mile and try to find a power series expression for this solution, but that's a lot of work for little payoff IMO.
A 2-slit arrangement with 60.3 μm separation between the slits is illuminated with 482.0 nm light. Assuming that a viewing screen is located 2.14 m from the slits, find the distance from the first dark fringe on one side of the central maximum to the second dark fringe on the other side. A. 24.1 mm B. 34.2 mm C. 68.4 mm D. 51.3 mm
Answer:
The distance is [tex]y = 0.03425 \ m[/tex]
Explanation:
From the question we are told that
The distance of separation is [tex]d = 60.3 \mu m= 60.3 *10^{-6}\ m[/tex]
The wavelength is [tex]\lambda = 482.0 \ nm = 482.0 *10^{-9} \ m[/tex]
The distance of the screen is [tex]D = 2.14 \ m[/tex]
Generally the distance of a fringe from the central maxima is mathematically represented as
[tex]y = [m + \frac{1}{2} ] * \frac{\lambda * D}{d}[/tex]
For the first dark fringe m = 0
[tex]y_1 = [0 + \frac{1}{2} ] * \frac{482*10^{-9} * 2.14}{ 60.3*10^{-6}}[/tex]
[tex]y_1 = 0.00855 \ m[/tex]
For the second dark fringe m = 1
[tex]y_2 = [1 + \frac{1}{2} ] * \frac{482*10^{-9} * 2.14}{ 60.3*10^{-6}}[/tex]
[tex]y_2 = 0.0257 \ m[/tex]
So the distance from the first dark fringe on one side of the central maximum to the second dark fringe on the other side is
[tex]y = y_1 + y_2[/tex]
[tex]y = 0.00855 + 0.0257[/tex]
[tex]y = 0.03425 \ m[/tex]
A straight wire that is 0.56 m long is carrying a current of 2.6 A. It is placed in a uniform magnetic field, where it experiences a force of 0.24 N. The wire makes an angle of 900 with the magnetic field. What is the magnitude of the magnetic field
Answer:
0.165TeslaExplanation:
The Force experienced by the wire in the uniform magnetic field is expressed as F = BILsin∝ where;
B is the magnetic field (in Tesla)
I is the current (in amperes)
L is the length of the wire (in meters)
∝ is the angle that the conductor makes with the magnetic field.
Given parameters
L = 0.56 m
I = 2.6A
F = 0.24N
∝ = 90°
Required
magnitude of the magnetic field (B)
Substituting the given values into the formula given above we will have;
F = BILsin∝
0.24 = B * 2.6 * 0.56 sin90°
0.24 = B * 2.6 * 0.56 (1)
0.24 = 1.456B
1.456B = 0.24
Dividing both sides by 1.456 will give;
1.456B/1.456 = 0.24/1.456
B ≈ 0.165Tesla
Hence the magnitude of the magnetic field is approximately 0.165Tesla
A 23 cm tall object is placed in front of a concave mirror with a radius of 37 cm. The distance of the object to the mirror is 86 cm. Calculate the focal length of the mirror.
Answer:
18.5 cm
Explanation:
From;
1/u + 1/v = 1/f
Where;
u= object distance = 86cm
image height = 23 cm
Radius of curvature = 37 cm
The radius of curvature (r) is the radius of the sphere of which the mirror forms a part.
Focal length (f) = radius of curvature (r)/2 = 37cm/2 = 18.5 cm
Therefore, the focal length of the mirror is 18.5 cm
Take an electric field sensor and move it in a straight line, crossing the equipotential lines. Describe the relationship between the distance between the equipotential lines and the strength of the electric field.
Answer:
E = - dV / dx
Explanation:
The equipotential lines are lines or surfaces that have the same power, therefore we can move in them without carrying out work between equipotential lines, work must be carried out, therefore the electric field changes.
The electric field and the potential are related by
E = - dV / dx
therefore when the change is faster, that is, the equipotential lines are closer, the greater the electric field must be.
what is the average flow rate in of gasoline to the engine of a plane flying at 700 km/h if it averages 100.0 km/l
Answer:
1.94cm³/s
Explanation:
1L = 1000cm³
Ihr = 3600s
So
Using
Average flow rate
Fr= 1L/100Km x 700Km/1hr x 1hr/3600s x 1000cm³/ 1L
= 1.94cm³/s