Answer:
the focal length of the mirror is : [tex]f=-2.5\,\,cm[/tex]
Explanation:
Use the formula for the formation of image using a divergent mirror and recalling that the image (s') that this mirror formed is virtual, so it is entered as a negative number in the formula. Use the object position (s) as 10, the image position (s') as -2, and derive the value of the focal length:
[tex]\frac{1}{s} +\frac{1}{s'}=\frac{1}{f}\\\frac{1}{10} +\frac{1}{-2}=\frac{1}{f}\\\frac{1}{10} -\frac{1}{2}=\frac{1}{f}\\\frac{10\,f}{10} -\frac{10\,f}{2}=\frac{10\,f}{f}\\f-5\,f=10\\-4\,f=10\\f=-2.5\,\,cm[/tex]
Explain.
4. State the limitations of our senses to obtain accurate in
formation concerning
our environment.
Answer:
The limits of our senses are
Limits of Sight
Our vision field of view is 120° sideways and 135° vertically
Angular visual resolution is about an 1/60 of one degree
The presence of blind spots in the eyes
Limits of sound
The hearing range is within 20 - 20,000 Hz and our threshold hearing above 0 to 5 decibel of sound
Limits of taste
We have very limited sense of taste which is partly dependent on our sense of smell with little objectivity in distinguishing tastes
Sense of smell
The establishing of the effectiveness of human sense of smell is gauged on numerous parameters with certain tests being inconsistent, as such, it is difficult to clearly establish the effectiveness of the human sense of smell
In comparison with the sense of smell of other living things such as dogs, the human sense organ is comparatively low
Explanation:
Students are going to conduct an experiment to study the effect of a net force applied to an object on the object’s motion. In each trial of the experiment, the students will apply a net force on the object. They also need to take two other measurements. What are the other quantities they should measure in each trial of the experiment?(1 point) velocity and time mass and acceleration mass and velocity acceleration and time
Answer:
A. velocity and time
Explanation:
A force can be define as an agent which has the capacity to change the state of an object. It can either increase the velocity of a body, change its direction of motion or cause a moving object to come to rest.
From Newton's second law of motion;
F = ma
where F is the force on the object, m is the mass of the object and a is the acceleration of the object. The unit of force is kgm/[tex]s^{2}[/tex] or Newtons.
a = [tex]\frac{change in velocity}{change in time}[/tex]
In the given question, apart from the mass of the object which is constant, the students should take the measurements of the velocity and time in each trial so as to calculate the required acceleration.
Answer:
mass and acceleration!
Explanation:
Because i am in class just like you and got it wrong because i didn't choose my first answer:(
A square is cut out of a copper sheet. Two straight scratches on the surface of the square intersect forming an angle theta. The square is heated uniformly. As a result, the angle between the scratches?a) increasesb) decreasesc) stays the samed) depends on whether theta is obtuse or acute
Answer:
a) increases
Explanation:
Almost all substance or material undergoes expansion due to heating. Heat gives thermal energy to the molecules of a substance increasing their body temperature. The temperature of a substance is the measure of the average kinetic energy of the molecules of that substance. When the temperature of a substance increases, the molecules begin to agitate and try to move far from each other, leading to either a linear, area, or cubic expansion, or all three of them. Metals like copper expand very well on heating, and their expansion is relatively minute, but very observable. When the face of such a copper is scratched to give and angle, heating the copper uniformly will cause the copper to expand, leading to an increase in the angle formed.
Please Help
A skydiver jumps out of a hovering helicopter, so there is no forward velocity. Use this information to answer questions. Ignore wind resistance for this exercise.
What is the skydiver's velocity after one second? Show your work and include direction.
Answer:
I suppose that by forward velocity the question refers to horizontal velocity
Since the acceleration due to gravity is 10 m/s2.The object gains an increase of 10 m/s in speed per second.In after one second its speed will be 10M/S
The direction will be downward i.e vertical
Monochromatic light of wavelength 649 nm is incident on a narrow slit. On a screen 2.25 m away, the distance between the second diffraction minimum and the central maximum is 1.99 cm. (a) Calculate the angle of diffraction θ of the second minimum. (b) Find the width of the slit.
Answer:
a)0.51°
b)1.47×10^-4m
Explanation:
a)for a single slit experiment, the minima that has an angle of θ towards the centre needs to satisfy the expression below.
bsin(θ)= mλ.........................(*)
Where b= width of the slit
The distance on the screen from Central angle can be expressed as
Sin(θ)= y/d............. (**)
d and y is the horizontal distance between slit and screen
If we input eqn(**) into equation (*) we have
y= mλd/b................(z)
In order to find angle (θ) we have
(θ)= sin-(1.99×10^-2)/2.25
= 0.51°
Therefore, angle of diffraction θ of the second minimum is 0.51°
b)to find the width of the sloth using eqn(z) by substitute the values, we have
b= (2)(649×10^-9)(2.25)/1.99×10^-2
b= 1.47×10^-4m
Therefore, the width of the slit is 1.47×10^-4m
when do you use cos and sin in situations like these? is horizontal always cos and vertical always sin?
Answer:
yes
Explanation:
this is simple
the horizontal line is adjacent
the vertical line is opposite
recall that cos x=adj/hyp
adj=hyp(cos x)
while opp=hyp(sin x)
A negative charge feels a force when stationary in an electric field. moving parallel to an electric field. moving parallel to a magnetic field. moving perpendicular to a magnetic field. stationary in a magnetic field. moving perpendicular to an electric field.
Answer:
stationary in an electric field.
moving perpendicular to a magnetic field.
moving perpendicular to an electric field.
Explanation:
Negative charge: In physics, the term "negative charge" is defined as a phenomenon that consists of a surplus or different electrons in any field i.e magnetic or electric field.
However, the correct answer in the question above, would be:
"stationary in an electric field".
"moving perpendicular to a magnetic field".
"moving perpendicular to an electric field".
A ball is thrown vertically upwards at an initial speed of
23
m s
−
1
. What is the displacement of the ball 3 seconds after it was thrown?
Answer:
114m
Explanation:
s=ut + 1/2 at^2
s=23 m/s ×3s + 1/2×3×3s^2×10m/s^2
= (69+45)m
= 114m
calculate the power of an engine which can supply 60kg of energy per minute
Answer:
1 Watt
Explanation:
Power (P) = w / Δt
w = work done
Δt = change in time
Power (P) = 60kg / 60 seconds
Power (P) = 1 Watt
HELP ME PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE A student uses a spring scale attached to a textbook to compare the static and kinetic friction between the textbook and the top of a lab table. If the scale measures 1,580 g while the student is pulling the sliding book along the table, which reading on the scale could have been possible at the moment the student overcame the static friction? 1,140 g 1,580 g 820 g 1,860 g
Answer:
1,860
Explanation:
is work the same as power justify the statement
Answer: No
Explanation: Simply Power’s Si base unit is kgm^2s^-3 but work done‘s Si base unit is kgm^2s^-2.
So this itself proves that they arent the same!
Matter must have two physical properties 1. Have mass, and 2
∆ Must move
∆ Use energy
∆ Take up space
∆ Be measure
able
Answer:
Take up space
Explanation:
Actually we know this by the definition of matter which states that "matter is any substance that has mass and takes up space by having volume."
hope it helped you:)
An object of mass 25kg is at rest. What is its momentum ?
Answer:
[tex]\boxed{0}[/tex]
Explanation:
Momentum is the measure of mass in motion.
[tex]\sf momentum = mass \times velocity[/tex]
An object at rest has a velocity of 0.
[tex]p=mv[/tex]
[tex]p = 25 \times 0[/tex]
[tex]p=0[/tex]
The momentum of an object at rest is always 0.
Why does it take a longer time for a kilogram of water than a kilogram of copper to reach the same temperature?
Answer:
Since water has a higher specific heat than copper.
Explanation:
Dimensionally speaking, the specific heat of a material ([tex]c[/tex]) is represented by:
[tex][c] = \frac{[Energy]}{[Mass]\cdot [Temperature]}[/tex]
The specific heats of water and copper are [tex]4186\,\frac{J}{kg\cdot ^{\circ}C}[/tex] and [tex]390\,\frac{J}{kg\cdot ^{\circ}C}[/tex], respectively. Let suppose that temperature change and masses of water and copper are the same. Then, a kilogram of water takes a longer time than a kilogram of copper since the first has a higher specific heat.
Shortly after receiving a traffic ticket for speeding, Fred made numerous comments about the road signs being inadequate and is GPS telling him a different speed limit. This would be an example of:
Answer:
External locus of control
Explanation:
External locus of control is an attitude people possess that makes them attribute their failures or successes to factors other than themselves. The opposite of this type of attitude is the Internal locus of control where the individuals take responsibility for the outcomes of their actions whether good or bad. One good thing about the external locus of control is that when the individuals with this characteristic record successes, they attribute it to others and this presents them as people with team spirit. However, when they record failures, they do not want to take the blame, but rather attribute it to others.
Fred exhibits an external locus of control because he attributed his speeding to other factors like the road signs and GPS instead of fully admitting that it was his fault.
The energy consumed by a home during a month is 90 kWh, how many Joules are we talking about? a good explanation please is for today
Answer:
3.24×10⁸ J, or 324 MJ
Explanation:
"kWh" is a kilowatt-hour. It's the energy used by 1 kilowatt of power after one hour.
A kilowatt is a kilojoule per second.
90 kWh
= 90 kW × 1 hr
= 90 kJ/s × 1 hr
= 90 kJ/s × 3600 s
= 324,000 kJ
= 324,000,000 J
The energy is 3.24×10⁸ J, or 324 megajoules.
Will mark as BRAINLIEST....... The Displacement x of particle moving in one dimension under the action of constant force is related to the time by equation 4x³+3x²-5x+2 , where x is in meters and t is in sec. a)Find velocity of particle at i) t=2 sec ii) t=4 sec. b) Find the acceleration of the particle at t=3 sec.
Explanation:
It is given that,
The Displacement x of particle moving in one dimension under the action of constant force is related to the time by equation as:
[tex]x=4t^3+3t^2-5t+2[/tex]
Where,
x is in meters and t is in sec
We know that,
Velocity,
[tex]v=\dfrac{dx}{dt}\\\\v=\dfrac{d(4t^3+3t^2-5t+2)}{dt}\\\\v=12t^2+6t-5[/tex]
(a) i. t = 2 s
[tex]v=12(2)^2+6(2)-5=55\ m/s[/tex]
At t = 4 s
[tex]v=12(4)^2+6(4)-5=211\ m/s[/tex]
(b) Acceleration,
[tex]a=\dfrac{dv}{dt}\\\\a=\dfrac{d(12t^2+6t-5)}{dt}\\\\a=24t+6[/tex]
Pu t = 3 s in the above equation
So,
[tex]a=24(3)+6\\\\a=78\ m/s^2[/tex]
Hence, this is the required solution.
(b) A cylinder of cross-sectional area 0.65m2 and
height 0.32m has a mass of 2. Ikg. If there is a
cavity inside, find the volume of the cavity.
(Density of cylinder = 11.053 kg/m^3)
Answer:
The volume of the cavity is 0.013m^3
Explanation:
To find the volume of the cavity, the major parameter missing is the diameter of the cavity itself. we can obtain this using the following steps:
Step one:
Obtain the volume of the cylinder by dividing the mass of the cylinder by the density.
Volume of the cylinder = 2.1 / 11.053 =0.19[tex]m^{3}[/tex]
Step two:
From the volume of the cylinder, we can get the radius of the cylinder.
[tex]radius = \sqrt{\frac{V}{\pi \times h}} = \sqrt{\frac{0.19}{\pi \times 0.32}} =0.44m[/tex]
Step three:
From the cross-sectional area, we can obtain the radius of the cavity.
Let the radius of the cavity be = r, while the radius of the cylinder be = R
CSA of cavity =
[tex]\pi({R^2}-r^2) = CSA\\0.65 = \pi (0.32^2-r^2)\\r= 0.115m[/tex]
Step Four:
calculate the volume of the cavity using volume =[tex]\pi r^2 \times h[/tex]
Recall that the cavity has the same height as the original cylinder
[tex]volume = \pi \times 0.115^2\times 0.32= 0.013m^3[/tex]
in the derivation of the time period of a pendulum in electric field when considering the fbd of bob to find the g effective why do we neglect tension
Answer:
we learned that an object that is vibrating is acted upon by a restoring force. The restoring force causes the vibrating object to slow down as it moves away from the equilibrium position and to speed up as it approaches the equilibrium position. It is this restoring force that is responsible for the vibration. So what forces act upon a pendulum bob? And what is the restoring force for a pendulum? There are two dominant forces acting upon a pendulum bob at all times during the course of its motion. There is the force of gravity that acts downward upon the bob. It results from the Earth's mass attracting the mass of the bob. And there is a tension force acting upward and towards the pivot point of the pendulum. The tension force results from the string pulling upon the bob of the pendulum. In our discussion, we will ignore the influence of air resistance - a third force that always opposes the motion of the bob as it swings to and fro. The air resistance force is relatively weak compared to the two dominant forces.
The gravity force is highly predictable; it is always in the same direction (down) and always of the same magnitude - mass*9.8 N/kg. The tension force is considerably less predictable. Both its direction and its magnitude change as the bob swings to and fro. The direction of the tension force is always towards the pivot point. So as the bob swings to the left of its equilibrium position, the tension force is at an angle - directed upwards and to the right. And as the bob swings to the right of its equilibrium position, the tension is directed upwards and to the left. The diagram below depicts the direction of these two forces at five different positions over the course of the pendulum's path.
that's what I know so far
How many centimeters (cm) are in 1 mile? _
Knowns:
1.61 kilometer (km) = 1 mile
1000 meter (m) = 1 kilometer (km)
100 centimeter (cm) - 1 m
Answer:
161,000 cm
Explanation:
1 mi × (1.61 km/mi) × (1000 m/km) × (100 cm/m) = 161,000 cm
Bus starts from rest if the acceleration of the bus is 0.5 MS square what will be the velocity at the end of two minutes and what distance will it cover during that time
Answer:
1. 60 m/s.
2. 3600 m.
Explanation:
The following data were obtained from the question:
Initial velocity (u) = 0
Acceleration (a) = 0.5 m/s²
Time (t) = 2 mins
Final Velocity (v) =?
Distance travelled (s) =?
1. Determination of the velocity at the end of 2 minutes.
Initial velocity (u) = 0
Acceleration (a) = 0.5 m/s²
Time (t) = 2 mins = 2 x 60 = 120 secs
Final Velocity (v) =?
v = u + at
v = 0 + (0.5 x 120)
v = 60 m/s
Therefore, the velocity at the end of 2 minutes is 60 m/s.
2. Determination of the distance travelled.
Initial velocity (u) = 0
Acceleration (a) = 0.5 m/s²
Final velocity (v) = 60 m/s
Distance travelled (s) =..?
v² = u² + 2as
60² = 0 + 2 x 0.5 x s
3600 = 1 x s
s = 3600 m
Therefore, the distance travelled is 3600 m.
A block is attached to the end of a spring. The block is then displaced from its equilibrium position and released. Subsequently, the block moves back and forth on a frictionless surface without any losses due to friction. Which one of the following statements concerning the total mechanical energy of the block-spring system this situation is true?
1. The total mechanical energy is dependent on the maximum displacement during the motion.
2. The total mechanical energy is at its maximum when the block is at its equilibrium position
3. The total mechanical energy is constant as the block moves back and forth.
4. The total mechanical energy is only dependent on the spring constant and the mass of the block.
Answer:
The correct option is;
3. The total mechanical energy is constant as the block moves back and forth
Explanation:
The total mechanical energy is the sum of the potential and kinetic energies of the system
For a system that is isolated from the effects of external forces, but being acted upon by the internal conservative forces within the system, the total mechanical energy is constant
For a black and spring system, we have total mechanical energy, E = 1/2×K×A².
Where;
K = Constant
A = The amplitude of motion
Therefore, where there is no loss to friction, with A, remaining constant, the total mechanical energy will be constant.
High voltage power is often carried in wire bundles made up of individual strands. In your initial post to the discussion, discuss the forces on the strands of wire due to the current flowing through them. What would happen if the force acted opposite of the known behavior? Provide a detailed description.
Answer:
There will be a huge problem of holding the wire strands together, and the power losses will also be amplified.
Explanation:
The force per unit length on two current carrying conductors, lying parallel to each other is proportional to the product of the current through the conductors, and inversely proportional to their distance apart. This force is attractive if the current flows through these conductors in the same direction, and is repulsive if it flows in the opposite direction.
For the strand of wire that make up a high voltage wire bundle, there will be a force of attraction pulling the wires closer to each other, and they will experience the maximum pulling force possible, since they lie next to each other. This force helps to hold these wires in a high tension wire strand together, limiting the area, and reducing "skin effect."
In the case that this wires in the wire strand acts in opposite of the known behavior, the wires will repel and push each other apart. This pushing apart will increase power loss due "skin effect" which is increased by an increase in exposed surface area of the wire strands. This will pose a big problem for high tension transmission.
5. A combination of waves is producing oscillations on a rope that is fixed at both ends and has a tension of 100 ????. The wavelength of the resulting net wave is equal to the length of the rope. If the equation for the displacement of a point on the rope is given by y(x, t) = (0.1 m) sin π x sin 12πt, where the rope begins at x = 0, x is in meters, and t is in seconds, what are the a) length of the rope, b) the speed of the waves on the rope, and c) the mass of the rope?
Answer:
a) 4 m
b) 24 m/s
c) 0.174 kg
Explanation:
a) Tension in string equation
The information given are;
The wavelength is equal to the rope length , λ = L
The tension = 100 N
The displacement of a point on the rope is y(x, t) = (0.1 m) sinπ x sin 12πt
Given that the wavelength = the length of the rope, the rope is on second harmonic
L = 2·n and the length of the wire = 2 × 2 = 4 m given the dimensions are in meters
b) Where k = 2·π/λ
v = ω/k = 12π/(2·π/λ)= (12π/2π)×λ = 24 m/s
c) f = v/λ = 24/4 = 6 Hz
[tex]f = \dfrac{\sqrt{\dfrac{T}{m/L} } }{2L} = \dfrac{\sqrt{\dfrac{100}{m/4} } }{2 \times 4}[/tex]
[tex]6 \times 8= {\sqrt{\dfrac{100}{m/4} } }[/tex]
m/4 = 100/2304
m = 0.174 kg.
state three effects of malnutrition in farm animals
Answer:
Cows,Pigs,Chicken. They are always in farm
You have a hot reservoir held at 30°C and a cold reservoir held at 0°C. If you move 400 J of heat from the hot reservoir to the cold reservoir, what is the total change in entropy?
Answer:
Explanation:
Given the following :
Temperature (Th) of hot reservoir = 30°C (30 +273) = 303K
Temperature (Tc) of cold reservoir = 0°C (273K)
Quantity (Q) of heat transferred from hot reservoir = 400 J
Total change in entropy (ΔStotal) :
ΔStotal = ΔShot + ΔScold
ΔS = Q/T
Hot reservoir is losing 400J of heat ;
Q = - 400 J
ΔShot = Q/Th
ΔShot = - 400/303
ΔShot = - 1.32 J/K
ΔScold = Q/T
ΔScold = 400 / 273
ΔScold = 1.47 J/K
ΔStotal = ΔShot + ΔScold
ΔStotal = - 1.32 + 1.47
ΔS total = 0.15 J/K
Answer:
-400/303 = -1.32
400/273 = 1.47
-1.32 + 1.47 =
.15 J/K
Explanation:
a p e x
A 2-kg cart, traveling on a horizontal air track with a speed of 3m/s, collides with a stationary 4-kg cart. The carts stick together. The impulse exerted by one cart on the other has a magnitude of
Answer:
The impulse exerted by one cart on the other has a magnitude of 4 N.s.
Explanation:
Given;
mass of the first cart, m₁ = 2 kg
initial speed of the first car, u₁ = 3 m/s
mass of the second cart, m₂ = 4 kg
initial speed of the second cart, u₂ = 0
Let the final speed of both carts = v, since they stick together after collision.
Apply the principle of conservation of momentum to determine v
m₁u₁ + m₂u₂ = v(m₁ + m₂)
2 x 3 + 0 = v(2 + 4)
6 = 6v
v = 1 m/s
Impulse is given by;
I = ft = mΔv = m(
The impulse exerted by the first cart on the second cart is given;
I = 2 (3 -1 )
I = 4 N.s
The impulse exerted by the second cart on the first cart is given;
I = 4(0-1)
I = - 4 N.s (equal in magnitude but opposite in direction to the impulse exerted by the first).
Therefore, the impulse exerted by one cart on the other has a magnitude of 4 N.s.
Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. If there is no air resistance, when they hit the ground A) both will have the same kinetic energy. B) the heavier one will have twice the kinetic energy of the lighter one. C) the heavier one will have four times the kinetic energy of the lighter one. D) the heavier one will have half the kinetic energy of the lighter one. E) the heavier one will have one-fourth the kinetic energy of the lighter one.
Answer:
option b
Explanation:
the heavier one will have twice the kinetic energy of the lighter one
The heavier one will have twice the kinetic energy of the lighter one. Hence, option (B) is correct.
Given data:
The mass of object 1 is, m.
The mass of object 2 is, 2m.
Here, the concept of kinetic energy is used. The kinetic energy of an object is the energy possessed by the object by virtue of its motion. Motion means something related with the speed.
And the mathematical expression for the kinetic energy is given as,
[tex]KE =\dfrac{1}{2}mv^{2}[/tex]
Here,
m is the mass of body.
v is the speed of body.
Now considering the kinetic energy for the two given objects as,
[tex]KE=\dfrac{1}{2}mv^{2}\\\\KE'=\dfrac{1}{2}(2m)v^{2}[/tex]
Comparing both the values of kinetic energies, we find that,
KE' = 2KE
Thus, we can conclude that the heavier one will have twice the kinetic energy of the lighter one. Hence, option (B) is correct.
Learn more about the kinetic energy here:
https://brainly.com/question/12669551
When is the net force on an object equal to zero? A. When the object is in motion B. When the object is changing direction C. When the forces acting on the object are balanced D. When inertia is not present pls i need the answers quick
Answer: C. when the forces acting on the object are balanced.
Answer:
c
Explanation:
The law of conservation of momentum states that the total momentum of interacting objects does not change . This means the total momentum a collision or explosion is equal to the total momentum a collision or explosion.what is momentum
Answer:
The momentum of an object is equal to the product of its mass and its velocity.
Explanation:
Consider an object of mass [tex]m[/tex] travelling at a velocity [tex]\vec{v}[/tex]. The momentum [tex]\vec{p}[/tex] of this object would be:
[tex]\vec{p} = m \cdot \vec{v}[/tex].
For the law of conservation of momentum, consider two objects: object [tex]\rm a[/tex] and object [tex]\rm b[/tex]. Assume that these two objects collided with each other.
Let [tex]m_{\rm a}[/tex] and [tex]m_{\rm b}[/tex] denote the mass of the two objects. Let [tex]\vec{v}_{\rm a}(\text{initial})[/tex] and [tex]\vec{v}_{\rm b}(\text{initial})[/tex] denote the velocity of the two object right before the interaction. Let [tex]\vec{v}_{\rm a}(\text{final})[/tex] and [tex]\vec{v}_{\rm b}(\text{final})[/tex] denote the velocity of the two objects right after the interaction. The momentum of the two objects right before the collision would be [tex]m_{\rm a}\cdot \vec{v}_{\rm a}(\text{initial})[/tex] and [tex]m_{\rm b}\cdot \vec{v}_{\rm b}(\text{initial})[/tex], respectively. The momentum of the two objects right after the collision would be [tex]m_{\rm a}\cdot \vec{v}_{\rm a}(\text{final})[/tex] and [tex]m_{\rm b}\cdot \vec{v}_{\rm b}(\text{final})[/tex], respectively.The sum of the momentum of the two objects would be:
[tex]m_{\rm a}\cdot \vec{v}_{\rm a}(\text{initial}) + m_{\rm b}\cdot \vec{v}_{\rm b}(\text{initial})[/tex] right before the collision, and[tex]m_{\rm a}\cdot \vec{v}_{\rm a}(\text{final}) + m_{\rm b}\cdot \vec{v}_{\rm b}(\text{final})[/tex] right after the collision.Assume that the system of these two objects is isolated. By the law of conservation of momentum, the sum of the momentum of these two objects should be the same before and after the collision. That is:
[tex]m_{\rm a}\cdot \vec{v}_{\rm a}(\text{initial}) + m_{\rm b}\cdot \vec{v}_{\rm b}(\text{initial}) = m_{\rm a}\cdot \vec{v}_{\rm a}(\text{final}) + m_{\rm b}\cdot \vec{v}_{\rm b}(\text{final})[/tex].
