The Krebs cycle produces high-energy electrons that are used by the electron transport chain to change ADP into ATP. Through the electron transport chain, high-energy electrons from NADH and FADH2 are transferred from one carrier protein to the next.
What is an Electron?An electron is a subatomic particle with a negative charge that can be either attached to or detached from an atom (not bound). Along with protons and neutrons, the electron, which is bonded to the atom, is one of the three major types of particles inside an atom.
Electrons, protons, and neutrons comprise the nucleus of an atom. The protons' positive charge counterbalances the electron's negative charge. The number of protons and electrons in an atom must be equal for it to be in a neutral state.
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Which of the following best describes the human population from early times to the present?
Answer:
We have a not significant increase of the population until 1700s or 1800s and then a significant increase growth from these years to the present.
Explanation:
From the figure attached we see the evolution of the human population since early times (1050).
We see that from 1050 until 1750-1850 we have an increase slowly with a low value for the increase per year.
But after these years (1750-1850) we see a considerable increase of the population, like an exponential model.
So then we can conclude in general terms this:
We have a not significant increase of the population until 1700s or 1800s and then a significant increase growth from these years to the present.
The growth of the human population from early times to the present is best described by the Exponential Growth Model, which shows a rapid increase in population over time. It took 123 years to add 1 billion people between 1804 and 1930 and only 24 years to add 2 billion people between 1975 and 1999.
The best mathematical model that describes the growth of the human population from early times to the present is the Exponential Growth Model. Exponential growth occurs when a quantity increases exponentially over time, and this is evident in the rapid increase in the global population over centuries. The provided information shows that it took 123 years to add 1 billion people between 1804 and 1930, but only 24 years to add 2 billion people between 1975 and 1999.
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The probable question may be:
Over the course of history, the human population has experienced significant growth. Starting from an estimated 5 million people in the year 10,000 BCE, it is believed that the population has increased exponentially over the centuries. In 2021, the global population was approximately 7.8 billion.
Based on this data, which of the following mathematical models best describes the growth of the human population from early times to the present?
A) Linear Growth Model
B) Exponential Growth Model
C) Logarithmic Growth Model
D) Polynomial Growth Model
A boat is anchored in Lake Michigan by an anchor that is 30 meters long. The water is only 18 meters deep, but the boat has drifted south of the anchor so that all 30 meters of the anchor is being used. To the nearest degree, what is the angle of depression that the anchor's chain makes with the water level?
Answer:
36.87°
Explanation:
length of anchor (L) = 30 m
depth of water (d) = 18 m
find the angle of depression the anchor chain makes with the water level
from the diagram attached the anchor chain, the water bed and the depth of the water all form a right angle triangle
therefore
cos θ = [tex]\frac{d}{L}[/tex]
cos θ = [tex]\frac{18}{30}[/tex]
θ = [tex]cos^{-1}.\frac{18}{30}[/tex] = 53.13°
the angle of depression (Ф) = 90 - 53.13 = 36.87°
How can researching travel time, routes and weather conditions benefit drivers who are planning a road trip?
Explanation:
They will be alerted of the traffic conditions. They can choose the route according to the weather condition. They will be aware if there is any road construction going on or accident happened. These awareness will save their time and avoid delays. their journey can be more comfortable and less trouble some.
Explanation:
Researching these options time, routes and weather conditions and even more gives the driver ample information about the journey, and places the driver in better position for decision making, with this information and data afore hand he can decides the best route to take should there be any gridlock, he even decides where or not to embark on the journey based on the prevailing weather conditions,
Regarding time of the journey he is well disposed for proper planning and scheduling.
Two gears are connected. Gear A has 10 teeth, while gear b has 40 teeth. If gear B turns at 10 rpms, how fast will gear a turn?
Answer:
w₁ = 40 rpm
Explanation:
Number of teeth of gear A = 10
Number of teeth of gear B = 40
Speed of gear B = w₂ = 10 rpm
Speed of gear A = w₁ = ?
Gear ratio is given by:
N₁/N₂ = w₂ / w₁
w₁ = N₂/N₁ * w₂
⇒ w₁ = 40/10 * 10
⇒ w₁ = 40 rpm
Gear A will turn at 40 rpms.
Explanation:In this scenario, we can use the formula for calculating the speed of rotation of gears. The formula is based on the principle that the number of teeth on a gear is inversely proportional to its speed. In other words, the smaller the gear, the faster it rotates.
Using the formula, we can calculate the speed at which gear A turns:
Speed of gear A = (Number of teeth on gear B/Number of teeth on gear A) x Speed of gear B
Plugging in the values, we get:
Speed of gear A = (40/10) x 10 = 40 rpms
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A 296-kg motorcycle is accelerating up along a ramp that is inclined 26.2° above the horizontal. The propulsion force pushing the motorcycle up the ramp is 3106 N, and air resistance produces a force of 286 N that opposes the motion. Find the magnitude of the motorcycle's acceleration.
Answer:
The magnitude of the motorcycle's acceleration is 5.20 m/s².
Explanation:
Given that,
Mass of motorcycle = 296 kg
Angle = 26.2°
Force on motorcycle= 3106 N
Force = 286 N
We need to calculate the magnitude of the motorcycle's acceleration
The net force acting on the motorcycle
Using newton's second law
[tex]ma=F_{p}-F_{air}-F_{g}[/tex]
[tex]ma=F_{p}-F_{air}-mg\sin\theta[/tex]
Put the value into the formula
[tex]296a=3106-286-296\times9.8\times\sin26.2[/tex]
[tex]a=\dfrac{3106-286-296\times9.8\times\sin26.2}{296}[/tex]
[tex]a=5.20\ m/s^2[/tex]
Hence, The magnitude of the motorcycle's acceleration is 5.20 m/s².
A car travels over a dirt road that contains a series of equally spaced bumps (a so-called "washboard" road). While traveling at a given speed the driver experiences a very jarring ride. When the driver drives at a higher speed, however, the ride gets smoother. That is because
Answer:
Explanation:
When a car moves faster then it made suspension to oscillate at a faster rate than the previous frequency. The comfort of the car depends upon the natural frequency of suspension. A low frequency can give discomfort while the high frequency can also be harsh. An optimum frequency matching the level of human comfort is desired in the suspension system to absorb the shock.
The ride is perceived as comfortable when the natural frequency is at the level of 60 to 90 cycles per minute.
The percentage of incident light radiation reflected back to space is termed albedo. True or false?
Answer:True
Explanation:
Albedo is a unit-less, non-dimensional quantity that shows how well a surface reflects solar energy. The value of albedo can vary from 0 to 1, 0 being the black and 1 refers to a white surface. Zero means Surface is a perfect absorber i.e. it absorbs all the incoming rays incidents on it. Albedo 1 means the surface is a perfect reflector.
Albedo usually applies for visible light, even though it may involve some of the infrared regions of the electromagnetic spectrum. The average albedo associated with earth surface is 30%
A) True. The percentage of incident light radiation reflected back to space is termed albedo.
Definition of Albedo: Albedo is a measure of the reflectivity of a surface. It is defined as the fraction or percentage of incoming solar radiation that is reflected back into space by a surface.
Surfaces and Albedo: Different surfaces have varying albedos. Light-colored surfaces, such as snow and clouds, have high albedos and reflect more sunlight, while dark surfaces, such as forests or oceans, have low albedos and absorb more sunlight.
Earth's Albedo: On average, Earth's albedo is approximately 30%, which means that about 30% of the solar radiation that reaches Earth is reflected back into space. This plays a significant role in the Earth's radiation budget and climate.
Why it Matters: The albedo effect is crucial in understanding climate dynamics because it influences how much solar energy is absorbed by the Earth's surface and, consequently, impacts global temperatures.
As motorists drive onto the acceleration lane, they must get up to the speed limit, _______, find a/an ________ and then _______.
Answer:
signal, opening and merge.
Explanation:
As motorists drive onto the acceleration lane, they must get up to the speed limit, signal, find an opening and then merge.
Acceleration lane explanation: an speed variation area or lane of adjustment consisting of additional flooring on the edges of traffic lanes to allow acceleration of vehicles until merging with traffic flow .
The density, rho, of sea-water is 1.2 × 103 kg m−3. Using the expression Wave Power Equation, estimate the gravitational power per metre length available in a wave of height 0.60 m.
Final answer:
The gravitational power per meter length available in a wave of height 0.60 m is calculated using the gravitational potential energy per unit length formula, incorporating the known sea-water density, the wave height, and the acceleration due to gravity.
Explanation:
To estimate the gravitational power per meter length available in a wave of height 0.60 m with the given sea-water density of 1.2 × 103 kg/m3, we use the wave power equation derived from the concept of gravitational potential energy. The gravitational potential energy per unit length of the wave (E) is given by the formula E = ½ × ρgh2L, where ρ represents the density of the seawater, g is the acceleration due to gravity (which is approximately 9.81 m/s2), h is the wave height, and L is the length of the wave under consideration.
Substituting the values, with wave height (h) as 0.60 m and considering a unit length (L = 1 m) for power per meter, we get:
E = ½ × (1.2 × 103 kg/m3) × (9.81 m/s2) × (0.60 m)2 × 1 m
This equation gives us the energy per unit length for a single wave. To get power, we consider energy over time. As waves pass a point with a specific frequency, the power can be calculated by multiplying the energy by the frequency of the waves.
If a motor neuron involved in a reflex arc is damaged, which event in that arc is least likely to occur?
Final answer:
If a motor neuron involved in a reflex arc is damaged, the event that is least likely to occur is the muscle contraction in response to the sensory stimulus.
Explanation:
If a motor neuron involved in a reflex arc is damaged, the event that is least likely to occur is the muscle contraction in response to the sensory stimulus. In a reflex arc, the motor neuron carries the impulse from the interneuron to the muscle, causing it to contract. If the motor neuron is damaged, this communication pathway is disrupted, and the muscle will not receive the signal to contract.
For which of the following situations is the conservation of mechanical energy most likely to be a valid assumption?a. a skateboard rolls across a sewer grate
b. a parachutist falls from a plane
c. you rub your hands together to keep warm
d. a soccer ball flies through the air
Answer: Option c is Correct!
You rub your hands together to keep warm.
Explanation:
First and foremost, mechanical energy is the sum of kinetic energy and potential energy of a system.
M.E = K.E + P.E
Where;
M.E= Mechanical energy
K.E= Kinetic energy
P.E= Potential energy
The kinetic energy is the energy possesed by a moving body, while the Potential energy is possesed by a stationary body.
When you rub your hand together to produce heat that keeps you warm, there is conservation of energy.
According to the first law of thermodynamics also known as the energy conservation law: it states that energy can neither be created nor destroyed, but can be transformed from one form to another.
The rubbing of the hand creates a motion(Kinetic energy) between the palms, this motion is opposed by a force called friction. thus the generation of heat accounts for the transfer of energy from Kinetic to Heat energy, therefore Mechanical energy is conserved according to the law of thermodynamics
A rocket is launched vertically from a point on the ground. An observer who is 1000 m away from the base of the launching pad, notices that the angle of elevation of the rocket is increasing at a rate of π/40 radians per second when the angle of elevation is π/3.
Find the speed of the rocket at that instant.
Answer:
dh/dt=18.75rad/sec
Explanation:
A rocket is launched vertically from a point on the ground. An observer who is 1000 m away from the base of the launching pad, notices that the angle of elevation of the rocket is increasing at a rate of π/40 radians per second when the angle of elevation is π/3.
Find the speed of the rocket at that instant.
you should have a right-angled triangle, where the angle of elevation is Ø, the adjacent is 1000 and the opposite is h, the height of the rocket.
tangent of an angle is opposite over adjacent side
tanØ = h/100 0
h = 1000tanØ
differentiate both sides with respect to dt,change in time
tanØ=sec^2 Ø
dh/dt = 1000sec^2 Ø (dØ/dt)
where Ø = 60° or π/3 rad
dØ/dt = π/40 radians per second
substituting the value into the equation
dh/dt=1000sin^260° *π/40 rad/sec
dh/dt=750*π/40 rad/sec
dh/dt=18.75rad/sec
dh/dt is the same as speed, change in height per time
If water is leaking from a certain tank at a constant rate of 1,200 milliliters per hour, how many seconds does it take for 1 milliliter of water to leak from the tank?
Answer:
It will take 3 seconds for 1 milliliters of water to leak from the tank.
Explanation:
The rate of leak = volume of water/Time
Q = V/t .................................. equation 1
making t the subject of the equation above,
t = V/Q............................. Equation 2.
where Q = rate of leak, V = volume of water, t = time
Given: Q = 1200 milliliters per hour, V = 1 milliliters.
Substituting these values into equation 2
t = 1/1200
t = 0.00083 hours.
If I hours = 3600 seconds,
Then, 0.00083 hours = 0.00083×3600 seconds
= 3 second.
Therefore it will take 3 seconds for 1 milliliters of water to leak from the tank.
If the force of gravity suddenly stopped acting on the planets, they would
A. spiral slowly towards the sun.
B. continue to orbit the sun.
C. continue moving straight in the direction they are traveling.
D. spiral slowly away from the sun.
E. fly straight away from the sun.
Answer:c
Explanation:
If the Force of gravity suddenly stops acting on Planets then Planets would continue to move straight in the initial direction.
Gravity constantly acts on Planets to change their trajectory each instant thus in absence of it if a planet is moving in a circular path then it would follow the path of the tangent to the circular path as gravity force is absent to change its trajectory.
Answer:
c
Explanation:
because there would be no force directing the planet in any other direction
Kelli weighs 425 N, and she is sitting on a playground swing that hangs 0.36 m above the ground. Her mom pulls the swing back and releases it when the seat is 1.00 m above the ground. Assume that air resistance is negligible. (a) How fast is Kelli moving when the swing passes through its lowest position?
Answer:
V = 3.54 m/s
Explanation:
Using the conservation of energy:
[tex]E_i = E_f[/tex]
so:
[tex]wh = \frac{1}{2}mV^2[/tex]
where w is te weigh of kelly, h the distance that kelly decends, m is the mass of kelly and V the velocity in the lowest position.
So, the mass of kelly is:
m = 425N/9.8 = 43.36 Kg
and h is:
h = 1m-0.36m =0.64m
then, replacing values, we get:
[tex](425N)(0.64m) = \frac{1}{2}(43.36kg)v^2[/tex]
Solving for v:
V = 3.54 m/s
If cells are placed in a hypertonic solution containing a solute to which the membrane is impermeable what could happena)cells would shrink then later reach equilibriumb)cell swell and ultimately burstc)cell show no changed)loose water and shrink
Answer:
cell swell and burst(b)
Explanation:
This process is called hemolysis. it also occurs in a red blood cell.
"Several light bulbs each of resistance 1.25 Ω are connected in series across a 115 V power supply. If the current through the circuit is 2 A, what is the number of light bulbs in the circuit?
Answer:
The number of bulbs = 46 bulbs
Explanation:
Ohm's Law: Ohm's law states that the current flowing through a conductor is directly proportional to its potential difference across its ends. At constant temperature and pressure. It can be expressed mathematically as
V = IR............. Equation 1
making R the subject of formula in equation 1
R = V/I.............. Equation 2
Where R = combined resistance of the several bulbs, V = potential difference, I = current through the circuit.
Given: V= 115 V. I = 2 A.
Substituting these values into equation 2,
R = 115/2
R = 57.5 Ω
Since the bulbs are connected in series,
Number of bulbs = combined resistance/resistance of each bulb
Number of bulbs = R/Rₙ...................... Equation 3
Where Rₙ = resistance of each bulb, R =combined resistance of the bulb.
Also given: Rₙ = 1.25 Ω, and R = 57.5 Ω
Substituting these values into equation 3
Number of bulbs = 57.5/1.25
Number of bulbs = 46 bulbs.
Therefore the number of bulbs = 46 bulbs
By using Ohm's law to calculate the total resistance of the circuit and dividing it by the resistance of a single bulb, we find that there are 46 light bulbs in the series circuit.
To, calculating the number of light bulbs in a series circuit based on the total resistance of the circuit, which can be found by using Ohm's law. Ohm's law states that the resistance (R) of a circuit can be calculated by dividing the voltage (V) across the circuit by the current (I) through the circuit, which is expressed as R = V/I. Given a 115 V power supply and a current of 2 A, the total resistance of the circuit is R = 115 V / 2 A = 57.5 Ω.
Each light bulb has a resistance of 1.25 Ω, so the number of light bulbs can be calculated by dividing the total resistance by the resistance of a single bulb:
Number of bulbs = Total resistance / Resistance of one bulb
= 57.5 Ω / 1.25 Ω
= 46 bulbs.
A stationary receiver detects a change in frequency of the signal from a jet flying directly away from it at 300 m/s. Which of the following receivers will detect the same change in frequency from a jet moving away at 600 m/s?A) A receiver moving at 900 m/s in the opposite direction as the jetB) A receiver moving at 300 m/s in the opposite direction as the jetC) A stationary receiverD) A receiver moving at 300 m/s in the same direction as the jet
Answer:
d) the receiver should be moving at 300 m/s in the same direction as the jet.
Explanation:
The change in the frequency of a moving sound (or wave) source is called Doppler Effect. The change in frequency is:
[tex]\Delta f=\frac{\Delta v}{v}f_{o}[/tex] (1)
with [tex]\Delta v=\mid v_{r}-v_{s}\mid[/tex] the velocity of the receptor respect the source, [tex] f_{o} [/tex] the real frequency and [tex] v [/tex] the velocity of the waves in the medium, we should be verty careful because the direction of the velocities are important so we have to select a reference frame and take on account the sign of the velocities. We're going to select positive direction as airplane direction. If we assume the frequency of the airplane sound and the velocity of waves on air remain constant, we should find the option that give us [tex] \Delta v=\mid v_{r}-v_{s}\mid = 300 [/tex] as the stationary case; let's see for:
a) [tex] \Delta v=\mid v_{r}-v_{s}\mid =\mid -900-600 \mid= 1500[/tex]
b) [tex]\Delta v=\mid v_{r}-v_{s}\mid = \mid-300-600 \mid= 900 [/tex]
c) [tex]\Delta v=\mid v_{r}-v_{s}\mid = \mid0-600\mid = 600 [/tex]
d) [tex]\Delta v=\mid v_{r}-v_{s}\mid= \mid300-600\mid = 300 [/tex]
So, the correct answer is d)
How is work related to potential energy and kinetic energy?
Work is defined as the force acting on an object because it changes a distance. While work is done on an object, the potential energy can be stored in that object. Thus, the relationship between work and energy is direct because the difference in kinetic energy of an object is the work done by the object.
What is Work done?Work done by a force is defined as the product of displacement and the component of force exerted by the object in the direction of displacement, thus when we push a block with some force the body starts moving with some acceleration moves, that's why the work is done.
Some transfer of energy may occur in the method of force where the amount of energy transferred by a force to move an object is called the work done.
Potential energy and work done are the same as kinetic energy and work done because potential energy is a state of the system, a way of storing energy as a property of its configuration or motion, while work is done in most cases there is a way to convert this energy from one body to another which is known as kinetic energy
Thus, Work is defined as the force acting on an object because it changes a distance.
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An oxygen sensor is being tested with a digital multimeter using the MIN/MAX function. The readings are: minimum = 78 mV; maximum = 932 mV; average = 442 mV. Technician A says that the engine is operating normally. Technician B says that the oxygen sensor is skewed too rich. Which technician is correct?
Answer:
Technician A
Explanation:
An oxygen sensor is being tested with a digital multimeter using the MIN/MAX function. The readings are: minimum = 78 mV; maximum = 932 mV; average = 442 mV. Technician A says that the engine is operating normally. Technician B says that the oxygen sensor is skewed too rich. Which technician is correct?
an oxygen sensor detects te amount of oyen in an engine at the exhaust pipe.
if the oxygen sensor detects oxygen at the above boundary condition, ten the engine is in good working condition
Which region of the early universe was most likely to become a galaxy?
Answer:
This is likely possible for a region whose matter density is higher than the normal average.
Explanation:
A galaxy is a collection of lumps in space which are clumped together and interact with each other. There are a lot of speculations on how galaxies were birthed. some believe its formed by a collection of massive gas, dust which eventually collapsed under their own gravitational pull. others says its formed by the combination of large lumps of matter which accumulated forming thee galaxies. The possibility of a galaxy forming is dependent on how massive the matter in the region of the universe is.
High density regions in the early universe, referred to as colder spots, eventually evolved into galaxies. The process began with the creation of small galaxies and star clusters followed by massive star formation due to galaxy-galaxy collisions. Over time, the universe developed into the structure we see today.
Regions in the early universe that had higher-than-average density were most likely to become galaxies.
These regions attracted additional matter due to their higher density, and were sometimes referred to as the darkest or 'colder' spots of the early universe.
These colder spots of high density matter were where small galaxies and large star clusters first formed.
In these high density regions: the creation of small galaxies and large star clusters began when the universe was about two percent of its current age.
Galaxy-galaxy collisions in these regions erupted into massive bursts of star formation, some of which led to the formation of black holes.
Over time, clusters and superclusters of galaxies emerged and the universe began to resemble what we see today.
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A ball is thrown up into the air with an initial velocity of 64 ft/sec. The ball is 4 ft above the ground when it is released. Its height, in feet, at time t seconds is given by: h(t) = −16t^2 + 64t + 4. What is the time when it reaches its maximum height?
Answer:
2 seconds and maximum height reached is 68 ft
Explanation:
h (t) = -16t^2 +64t +4
differentiate with respect to t
h'(t) = -32t +64
for maximum height velocity which is h'(t) must be zero
-32t +64 = 0
-32t = -64
t = 2 s
hence height is
h(2) = -16(2)^2 +64(2) +4
h(2) = -64+128+4
h(2) = 68 feet
On a spending spree in Malaysia, you buy an ox with a weight of 28.9 piculs in the local unit of weights: 1 picul = 100 gins, 1 gin = 16 tahils, 1 tahil = 10 chees, and 1 chee = 10 hoons. The weight of 1 hoon corresponds to a mass of 0.3779 g. When you arrange to ship the ox home to your astonished family, how much mass in kilograms must you declare on the shipping manifest? (Hint: Set up multiple chain-link conversions.)
Answer:
1747.41 kg
Explanation:
If 1 piculs = 100 gins,
Then 28.9 piculs = (28.9 × 100) gins = 2890 gins.
Also,
If 1 gin = 16 tahils
then 2890 gins =( 16 × 2890 ) = 46240 tahils
Also,
If 1 tahil = 10 chees,
Then 46240 tahils = 46240 × 10 chees = 462400 chees.
Also,
If 1 chee = 10 hoons
Then 462400 chees =( 10 × 462400) hoons = 4624000 hoons.
Also,
If 1 hoon = 0.3779 g,
Then 4624000 hoons = 0.3779 × 4624000 = 1747409.6 g.
The mass in kg that i will declare in the shipping manifest = (1747409.6/100 )kg = 1747.41 kg
The magnitude of the gravitational force between a particle of mass m1 and one of mass m2 is given by F(x) = G m1m2 / x2, where G is a constant and x is the distance between the particles. (Use any variable or symbol stated above as necessary.) (a) What is the corresponding potential energy function U(x)? Assume that U(x) → 0 as x → [infinity]. U(x) =
The corresponding potential energy function U(x) = -Gm1m2/x, where G is the gravitational constant.
The potential energy function corresponding to the given gravitational force function is represented by the equation U(x) = -Gm1m2/x, where G is the gravitational constant.
To find the potential energy function, we need to integrate the force function with respect to the distance x.
This integration results in the negative sign and the inverse relation in the potential energy function.
The property that U(x) approaches 0 as x approaches infinity means that the potential energy becomes negligible at large distances, which is consistent with the behavior of gravitational potential energy.
In a conversation with a friend, he expresses skepticism about global warning. When you inquire about his reasons, he responds by saying that the weather in that area has been the coolest he can remember. Using the information you have learned, what information could you offer to encourage your friend to reevaluate his position?
Answer:
Explanation:
A friend observes only the weather which is different than climate. Weather refers to short term change in the atmosphere while climate refers to what weather is like over a while in a specific area.
The weather may change when we move from one area to another. Cooler weather does not mean that the climate is cooler.
Global warming is the increase in average temperature globally due to which heat is increasing but it does not imply that temperature is hotter everywhere.
For trapezoid JKLM, A and B are midpoints of the legs. Find AB.
Question 3 options:
29
20
59
58
Answer:
AB = 29
Explanation:
For a better understanding, we must work this problem in a graphic way. In the attached image we can see the solution.
First, we draw a vertical dotted lines from the point J & K to the line ML, then we can see two new portions with the same length. Then with this simple analysis:
2x = 39 - 19
x = 10
Then we know that x = 10, another important data to find the answer is that the AB line is located in the midpoints of the legs. We also can see the right triangle MJ and the dotted line.
Now for every single right triangle, no matter its size and relationship between the vertical and the horizontal lengths, if some point is located in the hypotenuse (leg) at the middle of its length. This will be proportional to the vertical and the horizontal cathetus, therefore we will have the middle point on those two lines.
So, the AB line will be the sum of JK plus two times 5
AB = 19 + 5 + 5 = 29
A particle of mass 4.00 kg is attached to a spring with a force constant of 100 N/m. It is oscillating on a frictionless, horizontal surface with an amplitude of 2.00 m. A 6.00-kg object is dropped vertically on top of the 4.00-kg object as it passes through its equilibrium point. The two objects stick together.
a. Does the amplitude of the vibrating system increase or decrease as a result of the collision? By how much does the amplitude of the vibrating system change as a result of the collision?
b. How does the period change? By how much does the period change?
c. How does the mechanical energy of the system change? By how much does the energy change?
d. Account for the change in energy.
The amplitude and mechanical energy of the vibrating system decrease as a result of the collision, while the period increases. The decrease in mechanical energy is due to some kinetic energy being converted into heat and sound during the collision.
Explanation:a. The amplitude of the vibrating system decreases. Since kinetic energy is conserved, and the total mass is now larger (6.00 kg + 4.00 kg = 10.00 kg), the amplitude decreases. The new amplitude is equal to the original amplitude multiplied by the ratio of the original mass to total mass (4.00 kg / 10.00 kg) after the collision. Hence, the new amplitude is 2.00 m * 4.00 kg / 10.00 kg = 0.80 m.
b. The period of the oscillation increases as a result of the collision. The period (T) of oscillation is given by T = 2*π*(m/K)^(1/2), where K is the spring constant and m is the total mass. The mass is now larger (10.00 kg) leading to an increase in the period. As period depends on the root of the mass, the new period isn't directly proportional to the change in mass.
c. The mechanical energy of the system decreases as a result of the collision. This is because during the collision, some kinetic energy is lost and converted into heat and sound. Exact change in energy depends on how much energy is converted in these forms.
d. The change in energy can be accounted for by considering conservation of energy. Energy is never lost or gained, merely transformed from one form to another. In this case, the mechanical energy of the system decreased because some of it got converted into heat and sound during collision.
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car gets 12 miles per gallon uphill and 24 miles per gallon downhill. If the car goes to the top of Pikes Peak and back (48 miles uphill followed by 48 miles downhill), what is the car's gas mileage, in miles per gallon, for the entire trip?
Explanation:
Car gets 12 miles per gallon uphill and 24 miles per gallon downhill.
Uphill mileage = 12 miles per gallon
Downhill mileage = 24 miles per gallon
Distance to peak = 48 miles.
Distance to peak = Uphill mileage x Gas used uphill
48 = 12 x Gas used uphill
Gas used uphill = 4 gallon
Distance to peak = Downhill mileage x Gas used downhill
48 = 24 x Gas used downhill
Gas used downhill = 2 gallon
Total distance traveled by car = 48 + 48 = 96 miles
Total gas used = 4 + 2 = 6 gallons
Total distance = Mileage x Gas used
96 = Mileage x 6
Mileage = 16 miles per gallon
The car's gas mileage, in miles per gallon, for the entire trip is 16.
Answer:
16
Explanation:
An athlete notices that, after lifting a 100 kilogram weight, he has to increase the weight to 105 kilograms before he feels that the weight is actually heavier. If the athlete later lifts a 200 kilogram weight, which of the following coincides with the just noticeable difference for this weight?
a. A 190 kg weight
b. A 205 kg weight
c. A 215 kg weight
d. A 220 kg weight
Answer:
option A
Explanation:
given,
lifting weight = 100 Kg
increase in the weight = 105 Kg
later athlete lift = 200 Kg
Weber's law states that Just noticeable difference of weight is equal to ratio of change to the original.
Just noticeable difference for weight will be
=[tex]\dfrac{105-100}{100}[/tex]
= 5 %
since second weight is 200 Kg
so, Just noticeable difference of 200 Kg will be equal to ± 5 % of 200 Kg which is equal to ± 10 Kg.
now,
Just noticeable difference for 200 Kg
= 200 + 10 or 200 -10
= 210 Kg or 190 Kg
Hence, the correct answer is option is option A
Two bicyclists , starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1080 m due east and then turns due north and travels another 1430 m before reaching the campground. The second cyclist starts out by heading due north for 1950 m and then.turns and heads directly toward the campground.
(a) At the turning point, how far is the second cyclist from the campground?
(b) What direction (measured relative to due east) must the second cyclist head during the last part of the trip?
Answer:
[tex]DC=1198.6659\ m[/tex]
Explanation:
Refer the schematic for explanation.
According to the given condition the first cyclist covers 1080 meters eastwards and then travels 1430 meters northwards to reach the camp.
But the second cyclist travels 1950 meters northwards therefore he travelled 520 meters more in the north than the first cyclist.
So, according to the schematic we find the distance DC in the triangle DCE using Pythagoras theorem:
[tex]DC=\sqrt{1080^2+520^2}[/tex]
[tex]DC=1198.6659\ m[/tex]