Solve the differential equation:
dV/dt = k V → 1/V dV/dt = k
→ d/dt [ln(V)] = k
→ ln(V) = k t + C
→ V (t )= exp(k t + C ) = C exp(k t ) = C e ᵏᵗ
At t = 0, the glacier has volume 400 km³ of ice, so
V (0) = 400 → C e⁰ = C = 400
Find when the glacier's volume is 300 km³:
V (t ) = 400 e ᵏᵗ = 300 → e ᵏᵗ = 3/4
→ k t = ln(3/4)
→ t = 1/k ln(3/4)
At this time, the volume is decreasing at a rate of 15 km³/yr, so
V ' (t ) = C k e ᵏᵗ → V ' (1/k ln(3/4)) = 400 k exp(k × 1/k ln(3/4)) = -15
→ 3/4 k = -3/80
→ k = -1/20
Then the volume V (t ) of the glacier at time t is
V (t ) = 400 exp(-1/20 t )
The volume in terms of time will be "V(t) = 400 exp (-[tex]\frac{1}{20}[/tex] t)".
Differential equation and VolumeAccording to the question,
Glacier's volume, V(0) = 400 km³
→ [tex]\frac{dV}{dt}[/tex] = kV
[tex]\frac{1}{V}[/tex] [tex]\frac{dV}{dt}[/tex] = k
ln(V) = kt + C
Now,
V (t) = exp (kt + C)
= C exp (kt)
= C[tex]e^{kt}[/tex]
When volume of glacier be "300 km³",
V(t) = 400 [tex]e^{kt}[/tex] = 300
[tex]e^{kt}[/tex] = [tex]\frac{3}{4}[/tex]
By taking log,
kt = ln([tex]\frac{3}{4}[/tex])
t = [tex]\frac{1}{k}[/tex] ln([tex]\frac{3}{4}[/tex])
When volume decrease at 15 km³/yr, then
→ V'(t) = Ck[tex]e^{kt}[/tex]
= 400 k exp (k × [tex]\frac{1}{k}[/tex] kn ([tex]\frac{3}{4}[/tex]))
= -15
Now,
[tex]\frac{3}{4}[/tex] k = - [tex]\frac{3}{80}[/tex]
By applying cross-multiplication,
k = - [tex]\frac{1}{20}[/tex]
Thus the response above is correct.
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what is 60mph (miles per hour) in meters per second? ( A mile is 5280ft)
please someone help me
Answer:
60mph=26.8224meters per second
Explanation:
A disk of a radius 50 cm rotates at a constant rate of 100 rpm. What distance in meters will a point on the outside rim travel during 30 seconds of rotation?
Answer:
A point on the outside rim will travel 157.2 meters during 30 seconds of rotation.
Explanation:
We can find the distance with the following equation since the acceleration is cero (the disk rotates at a constant rate):
[tex] d = v*t [/tex]
Where:
v: is the tangential speed of the disk
t: is the time = 30 s
The tangential speed can be found as follows:
[tex] v = \omega*r [/tex]
Where:
ω: is the angular speed = 100 rpm
r: is the radius = 50 cm = 0.50 m
[tex] v = \omega*r = 100 \frac{rev}{min}*\frac{2\pi rad}{1 rev}*\frac{1 min}{60 s}*0.50 m = 5.24 m/s [/tex]
Now, the distance traveled by the disk is:
[tex] d = v*t = 5.24 m/s*30 s = 157.2 m [/tex]
Therefore, a point on the outside rim will travel 157.2 meters during 30 seconds of rotation.
I hope it helps you!
explain melting and freezing using the kinetic theory of matter
As a liquid is cooled its molecules lose kinetic energy and their motion slows. When they've slowed to where intermolecular attractive forces exceed the collisional forces from random motion, then a phase transition from liquid to solid state takes place and the material freezes
Hope it helps u
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When carbon bonds with oxygen,
what
gas is formed?
When carbon bonds with oxygen, what gas is formed?
Answer:
Carbon dioxide
Explination:
I remember it from biology.
I hope this helps ^-^
In a chemical reaction, carbon combines with oxygen to form carbon dioxide gas.
What is a chemical reaction?A chemical reaction can be defined as a process that causes the chemical transformation of one chemical substance to another. The chemical reactions accompany chemical changes that involve the rearrangement of electrons in the forming and breaking of bonds between atoms, with no change to the nuclei.
The substances which are primarily involved in a reaction are known as reactants or reagents. Chemical reactions are commonly characterized by a chemical change, and yield products, which exhibit properties different from the reactants.
Chemical reactions take place at a characteristic rate of reaction at a given temperature, pressure, and chemical concentration. The rates increase with the increasing temperature of the reaction when more thermal energy is available to achieve the activation energy for breaking bonds between atoms.
The combustion reaction takes place when carbon combines with oxygen to produce carbon dioxide gas.
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*PLEASE HELP***
Which of the following technologies uses electromagnetic radiation with the
shortest wavelength?
O A. Wireless communications transmitter
O B. Infrared sensor on a DVD player
C. Microwave industrial drying equipment
O D. Compact fluorescent lightbulb
Answer:
A) wireless communications transmitter
Explanation:
Answer:
Compact fluorescent lightbulb
Explanation:
This is because it has the shortest wavelength
Which statement is true for two pieces of iron at the same temperature ? A. The total kinetic energy of their particles is equal
The complete options are;
A. The average kinetic energy of their particles is the same.
B. The total kinetic energy of their particles is equal.
C. Heat flows from the larger object to the smaller object.
D. Heat flows from the object with higher potential energy to the object with lower potential energy.
Answer:
Explanation:
From the relationship between average kinetic energy and temperature, we have the formula;
E_k = (3/2)kT
Where;
k is a constant known as boltzmann constant.
T is known as temperature
We can see that at the same temperature (T), kinetic energy will remain the same because from the formula, E_k depends km only the temperature.
Thus, average kinetic energy of their particles saying that.
A 1,571 kilogram car travelling at 129 kilometers per hour is driving down a highway. The driver suddenly realizes a large animal is standing stationary on the highway in the way of the car. The driver manages to release their foot off the accelerator peddle, but does not have time to hit the brake peddle. The car strikes the animal which gets stuck to the car hood. Immediately after the collision the car slows to 59 kilometers per hour. Given this information, accident investigators are able to determine the mass of the animal as what
Answer:
[tex]1863.9\ \text{kg}[/tex]
Explanation:
[tex]m_1[/tex] = Mass of car = 1571 kg
[tex]u_1[/tex] = Initial velocity of car = 129 km/h
[tex]u_2[/tex] = Initial velocity of the animal = 0
[tex]v[/tex] = Velocity of combined mass = 59 km/h
[tex]m_2[/tex] = Mass of the animal
As the momentum of the system is conserved we have
[tex]m_1u_1+m_2u_2=(m_1+m_2)v\\\Rightarrow \dfrac{m_1u_1+m_2u_2}{v}-m_1=m_2\\\Rightarrow m_2=\dfrac{1571\times 129+0}{59}-1571\\\Rightarrow m_2=1863.9\ \text{kg}[/tex]
The mass of the animal is [tex]1863.9\ \text{kg}[/tex].
As you rise upwards in the atmosphere air pressure___
Answer:
Gases - Water vapor, Nitrogen, Oxygen etc. Describe what happens to air pressure as you rise upwards in the atmosphere. What causes this change in air pressure? As altitude increases, air pressure will decrease As altitude increases the gas molecules that make up the air spread further apart
Answer: As you rise upwards in the atmosphere, air pressure decreases
Explanation: Because there are fewer molecules in the air, the air has a lower density, which results in a drop in air pressure. At different altitudes, the air is not the same. The area close to the earth is denser. As we rise, it continues to thin out. As a result of more air nearby, there is also increased air pressure. The weight and pressure of the air also continue to reduce as the volume of air does.
what is energy and types of energy
An Atwood's machine consists of blocks of masses
m1 = 11.0 kg
and
m2 = 19.0 kg
attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass
M = 7.90 kg
and radius
r = 0.200 m.
The block of mass m2 is allowed to drop, and the cord turns the pulley without slipping.
Answer:
Explanation:
Given that:
[tex]mass \ m_ 1 = 11.0 \ kg[/tex]
[tex]mass \ m_2 = 19.0 \ kg[/tex]
[tex]mass \ of \ the \ pulley\ M = 7.90 \ kg[/tex]
[tex]Radius \ of \ the \ pulley = 0.200\ m[/tex]
1) Provided that the mass in [tex]m_2[/tex] is greater than the mass we have in [tex]m_1[/tex], then likewise the tension we have in [tex]T_2[/tex] will be greater than the tension in [tex]T_1[/tex]
Using Newton's second law to mass [tex]m_1[/tex], we have:
[tex]m_2g - T_2 = m_2 a \\ \\ T_1 = m_1 g +m_1 a \\ \\ T_1= m_1 (g+a) --- (1)[/tex]
By using the second law, we have:
[tex]m_2g - T_2 = m_2a \\ \\ T_2 = m_2 (g-a)---(2)[/tex]
For the pulley, let's use the torque equation, so we have:
[tex]T_2 r -T_1 r = I \alpha \\ \\ T_2r -T_1r = \Big ( \dfrac{Mr^2}{2}\Big) \dfrac{a}{r} \\ \\ T_2 -T_1 = \dfrac{Ma}{2} ---- (3)[/tex]
Altogether, from equation (1)(2) and (3), we have:
[tex]m_2(g-a) -m_1 (g+a) = \dfrac{Ma}{2} \\ \\ m_2g -m_2a -m_1g-m_1a = \dfrac{Ma}{2} \\ \\ a = \dfrac{(m_2 -m_1) g}{(m_1 + m_2 + \dfrac{M}{2})} \\ \\ a = \dfrac{(19.0 \ kg - 11.0 \ kg ) ( 9.8 \ m/s^2)}{(19.0 \ kg + 11.0 \ kg + \dfrac{7.90 \ kg }{2} )}[/tex]
[tex]a = 2.31 \ m/s^2[/tex]
Also; from equation (1), the tension in the string is:
[tex]T_1[/tex] = (11.0 kg ) ( 9.8 + 2.31) m/s²
[tex]T_1[/tex] = 133.21 N
[tex]T_1[/tex] ≅ 133 N
From equation (2):
[tex]T_1[/tex] = m_2(g-a)
[tex]T_1[/tex] = (19.0 kg) ( 9.8 - 2.31) m/s²
[tex]T_1[/tex] = 142.31 N
[tex]T_1[/tex] = 142 N
Which structure is represented by letter C?
Choose 1 answers
A. Cell wall
B. Cell membrane
C. Ribosome
D. Cytosol
Answer: C. Ribosome
Explanation: Ribosome is responsible for protein synthesis. I got it right on khan academy :) hope this helps have a blessed day.
The structure which is represented by the letter C is known as free ribosomes. Thus, the correct option for this question is C.
What are Ribosomes?Ribosomes may be defined as a type of cell organelle which is spherical and glandular in shape. They occur freely in the matrix or remain bound with ER.
The major components of ribosomes may include RNA and protein. Ribosomes were first discovered by Palade in 1953. There are two types of ribosomes, ie. the 70s and 80s.
Ribosomes play an important function in the process of protein synthesis. The structure which is represented by the letter A is known as the cell membrane. The structure which is represented by the letter B is known as Cytosol.
Therefore, the structure which is represented by the letter C is known as free ribosomes. Thus, the correct option for this question is C.
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45 J of work were done on the object that moved 5 meters. How much force was applied to the object?
[tex]\\ \sf\longmapsto Work\:done=Force(Displacement)[/tex]
[tex]\\ \sf\longmapsto Force=\dfrac{Work\:done}{Displacement}[/tex]
[tex]\\ \sf\longmapsto Force=\dfrac{45}{5}[/tex]
[tex]\\ \sf\longmapsto Force=9N[/tex]
Given values:
Work done,
W = 45 JDisplacement,
d = 5 mWe know that,
→ [tex]Work \ done = Force\times Displacement[/tex]
or,
→ [tex]Force = \frac{Work \ done}{Displacement}[/tex]
By putting the values, we get
[tex]= \frac{45}{5}[/tex]
[tex]= 9 \ N[/tex]
Thus the response above is right.
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help plz fast :(((( need helpl
Answer:
True
Explanation:
I’m not 100% sure
What is a cyclic behavior
Answer:
Uzi
Explanation:
When somebody comes to me I don’t have any
A disk of known radius and rotational inertia can rotate without friction in a horizontal plane around its fixed central axis. The disk has a cord of negligible mass wrapped around its edge. The disk is initially at rest, and the cord can be pulled to make the disk rotate. Which of the following procedures would best determine the relationship between applied torque and the resulting change in angular momentum of the disk?
a. Pulling on the cord, exerting a force of 15 N for 2 s and then 25 N for 3 s, and measuring the final angular velocity of the disk
b. For five forces of different time intervals, pulling on the cord for 5 s, exerting a force of 15 N, and then measuring the angle through which the disk rotates in each case
c. For five forces of different time intervals, pulling on the cord for 5 s, exerting a force of 15 N, and then measuring the final angular velocity of the disk
d. For five forces of different magnitude, pulling on the cord for 5 s, and then measuring the final angular velocity of the disk
Pulling on the cord, exerting a force of 15 N for 2 s and then 25 N for 3 s, and measuring the final angular velocity of the disk.
What is torque?Torque is defined as the rate of change of angular momentum.[tex]\tau = \frac{dL}{dt} \\\\[/tex]
[tex]Fr = \frac{\Delta L}{\Delta t} \\\\Fr = \frac{\Delta m\omega ^2r}{\Delta t} \\\\F = \frac{\Delta m\omega ^2}{\Delta t}[/tex]
[tex]F = \frac{m\Delta \omega ^2}{\Delta t} \\\\F = \frac{m(\omega _f^2 - \omega _i^2)}{t_2 - t_1}[/tex]
where;
[tex]\omega _i[/tex] is the initial angular velocity
[tex]\omega _f[/tex] is the final angular velocity
Since the disk is initial at rest, applying a force such as 15 N gives the disk its first angular velocity and applying 25 N force for 3 seconds gives the disk its final angular velocity.
Thus, the best procedure to determine the relationship between applied torque and the resulting change in angular momentum of the disk is
Pulling on the cord, exerting a force of 15 N for 2 s and then 25 N for 3 s, and measuring the final angular velocity of the disk.Learn more about torque on a disk here: https://brainly.com/question/25482609
what is Muscular system
What is the force holding you down?
Answer:
The force holding you down is gravity.
Explanation:
Gravity is a force between two objects with mass. It pulls things together. You have mass, and the Earth has mass, so gravity tries to pull you and the Earth together. The gravitational force is much bigger for more massive objects.
Answer:
Gravitational Force
Explanation:
Gravitational Force holding everything down
-TheUnknownScientist
how is the medium of a wave and transmit of a wave similar and different?
plssss I really need helpppp
Answer:
Sound and light are similar in that both are forms of energy that travel in waves. They both have properties of wavelength, freqency and amplitude. Here are some differences: Sound can only travel through a medium (substance) while light can travel through empty space.
It is measured that 3/4 of a body's volume is submerged in oil of density 800kg/m³
Complete question:
It is measured that 3/4 of a body's volume is submerged in oil of density 800kg/m³. What is the specific gravity of oil?
Answer:
The specific gravity of the oil is 0.8.
Explanation:
Given;
density of the oil, [tex]\rho_o[/tex] = 800 kg/m³
density of water, [tex]\rho_w[/tex] = 1000 kg/m³
The specific gravity of any substance is the ratio of the substance density to the density of water.
Specific gravity of the oil = density of the oil / density of water
Specific gravity of the oil = 800/1000
Specific gravity of the oil = 0.8
Therefore, the specific gravity of the oil is 0.8.
You set a tuning fork into vibration at a frequency of 683 Hz and then drop it off the roof of the Physics building where the acceleration due to gravity is 9.80 m/s2. Determine how far the tuning fork has fallen when waves of frequency 657 Hz reach the release point
Answer:
The distance traveled by the tuning fork is 9.37 m
Explanation:
Given;
source frequency, [tex]f_s[/tex] = 683 Hz
observed frequency, [tex]f_o[/tex] = 657 Hz
The speed at which the tuning fork fell is calculated by applying Doppler effect formula;
[tex]f_o = f_s [\frac{v}{v + v_s} ][/tex]
where;
[tex]v[/tex] is speed of sound in air = 343 m/s
[tex]v_s[/tex] is the speed of the falling tuning fork
[tex]657 = 683[\frac{343}{343 + v_s} ]\\\\\frac{657}{683} = \frac{343}{343 + v_s}\\\\0.962 = \frac{343}{343 + v_s}\\\\0.962(343 + v_s) = 343\\\\343 + v_s = \frac{343}{0.962} \\\\343 + v_s = 356.55\\\\v_s = 356.55 - 343\\\\v_s = 13.55 \ m/s[/tex]
The distance traveled by the tuning fork is calculated by applying kinematic equation as follows;
[tex]v_s^2 = v_o^2 + 2gh[/tex]
where;
[tex]v_o[/tex] is the initial speed of the tuning fork = 0
g is acceleration due to gravity = 9.80 m/s²
[tex]v_s^2 = 0 + 2gh\\\\h = \frac{v_s^2}{2g} \\\\h = \frac{13.55^2 }{2\times 9.8} \\\\h = 9.37 \ m[/tex]
Therefore, the distance traveled by the tuning fork is 9.37 m
Waldo needs to know how much force to apply in order to move a 4000-kg object at 2 m/S2. Which law should he refer to
A.
first law
B.
second law
C.
third law
D.
law of gravity
Answer:
B . Second law
Explanation:
According to second law:
Net Force acting on the body produce acceleration. The magnitude acceleration of the body is directly proportional to net force and inversly proportional to the mass.
Mathematically:
a = [tex]\frac{F}{m}[/tex]
and
F = ma
So according to the given condition Waldo should use Second law.
PLEASE HELPPPPPP <333
Answer:
B. As gravity increases weight increases and as gravity decreases weight decreases
Explanation:
Option B is the correct answer.
From the information given, we can deduce that as the gravity increases, the weight also increases and as the gravity decreases, the weight decreases as well.
This is true from the given table. On earth, the gravity of the man was 9.8m/s² and his weight 588N. But get to space, moon precisely, the gravity reduced to 1.62m/s². Then we discover that such decrease in his gravity also led to the sharp decrease in the weight. The weight decreased from 588N on earth to 96N on the moon.
This actually reveals that weight and gravity are related in a way. Weight of an object is known to be the force of gravity on the object. The weight actually vary as a result of varying gravity.
Answer: b
since the pull of gravity on the moon is less we weigh less.
PLEASE HELP, PLEASE A CORRECT ANSWER!
Answer: I like your profile picture
Explanation:
examples of transfer of energy
Answer:
by radiation
by heating
electrically
mechanically
PLEASE HELP ME PLEASE!
Answer:
40N
Explanation:
The weight is "how much force of gravity drags this down".
Because we're told that gravity on the Moon exerts 1.6N of force per kg, a 25kg object will weigh:
[tex]F_g = 25kg \cdot 1.6\frac{N}{kg} = 40N[/tex]
What major region does this profile
most likely represent?
Given the information on the graph, we can confirm that this profile represents the Ocean floor profile.
What causes the spike in the graph?The spike in the graph demonstrates a sharp change in depth. This is caused by the irregularities we expect to find on the ocean floor. Many parts of the ocean floor are deeper than others, caused by the movement of tectonic plates over time.Therefore, we can confirm that the profile belongs to the ocean floor profile, firstly because of the information provided, as well as it being consistent with the irregularities in the depth of the ocean floor.
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180 N
40 kg
140 N
Net Force =
Also how do you find the net force?
Answer:
720N
Explanation:
180+(40×10)+140=720 remember we can only add with same units ;1kg=10N therefore 40 kg=(40×10)N=400N
The net force would be the summation of all the forces in addition to the weight force of the 40 kg weight, thus the net force of all the forces would come out to be 712.4 Newtons.
What is Newton's second law?Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.
F = ma
As given in the problem we have to find the net force,
Let us assume the acceleration due to gravity would be 9.81 m/s².
The force generated by the 40-kilogram weight =40 ×9.81 Newtons.
The force generated by the 40-kilogram weight = 392.4 Newtons
Net force = 180 + 140 +392.4
=712.4 Newtons
Thus, the net force of all the forces would come out to be 712.4 Newtons.
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An electromagnetic wave of frequency 7.55 x 10^14 Hz propagates in carbon tetrachloride with a speed of 2.05 x 10^8 m/s. What is the wavelength of the wave in carbon tetrachloride?
A. 3.38 x 10^-7 m
B. 3.61 x 10^-7 m
C. 3.97 x 10^-7 m
D. 3.01 x 10^-7 m
E. 2.72 x 10^-7 m
Answer:
2.72*10^-7m
Explanation:
Using the formula
v = fλ
v is the speed
f is the frequency
λ is the wavelength
Substitute for λ
λ = v/f
λ = 2.05 x 10^8/7.55 x 10^14
λ = 2.05/7.55 * 10^{8-14}
λ = 0.272 * 10^-6
λ = 2.72*10^-7m
Hence the wavelength of the wave in carbon tetrachloride is 2.72*10^-7m
A seismic wave is detected 100m, 5s after and explosion. Calculate the wave speed
we know that,
Frequency = 1/ time period
hence, Feq = 1/5 ===> 0.2 Hz
hence, wave velocity = freq * wavelength
hence,
V = 0.2 * 100
==> Wave velocity = 20 m/s
What is the approximate size of the Earth's magnetic field? (dont ask me to specify thats what the question is and im as confused as heck too)
Answer:
The Earth's magnetic field intensity is roughly between 25,000 - 65,000 nT (.25 -.65 gauss).
Explanation:
To measure the Earth's magnetism in any place, we must measure the direction and intensity of the field. The Earth's magnetic field is described by seven parameters. These are declination (D), inclination (I), horizontal intensity (H), the north (X), and east (Y) components of the horizontal intensity, vertical intensity (Z), and total intensity (F). The parameters describing the direction of the magnetic field are declination (D) and inclination (I). D and I are measured in units of degrees, positive east for D and positive down for me. The intensity of the total field (F) is described by the horizontal component (H), vertical component (Z), and the north (X) and east (Y) components of the horizontal intensity. These components may be measured in units of gauss but are generally reported in nanoTesla (1nT * 100,000 = 1 gauss). The Earth's magnetic field intensity is roughly between 25,000 - 65,000 nT (.25 - .65 gauss). Magnetic declination is the angle between magnetic north and true north. D is considered positive when the angle measured is east of true north and negative when west. The magnetic inclination is the angle between the horizontal plane and the total field vector, measured positive into Earth. In older literature, the term “magnetic elements” is often referred to as D, I, and H.