Explanation:
Compazine belongs to class of drugs called Antiemetic Agents, Antipsychotics, Phenothiazine.
what is the difference between each distance traveled and displacement travled
Displacement is a vector magnitude that depends on the position of the body which is individualistic for the trajectory.
While, Distance is a scalar magnitude that measures over the trajectory.
Earth’s surface contains a variety of landforms, formed by weathering and erosion. Which of the following describes a change to Earth’s surface due to weathering? Choose the three that apply.
The following describes a change to Earth’s surface due to weathering include the following below:
A. plants creating a crack in a rock formation
B. rocks along the beach being reshaped by wave action.
F. glaciers scraping rocks across the land
What is Weathering?This is referred to as the process which involves the breaking down of rocks and minerals on Earths surface as a result of certain factors such as rain, glacier etc. They form cracks when they come in contact with rocks afterf a given period of time before they are disintegrated.
Weathering occurs when plants creating a crack in a rock formation and also when the rocks along the beach are being reshaped by wave action.It also involves the glaciers scraping rocks across the land which is therefore the reason why option A, B and F was chosen as the correct choice.
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The options are:
A. plants creating a crack in a rock formation
B. rocks along the beach being reshaped by wave action
C. sand being blown to a new location by the wind
D. sediments moved from place to place by a river
E. rain washing soil down a steep hill
F. glaciers scraping rocks across the land
What is the role of the brain in helping an animal interact with its environment?
Answer:
The nature of the environment and the animal's interaction with it determines much of the character of the brain.
Explanation:
In fact, most of what we would use to describe ourselves to others reflects this sort of information storage. Much of this information is unique to the individual and hence may involve different mechanisms from those used for species-typical information storage.
Consider a double-paned window consisting of two panes of glass, each with a thickness of 0.500 cm and an area of 0.760 m2 , separated by a layer of air with a thickness of 1.65 cm . The temperature on one side of the window is 0.00 ∘C; the temperature on the other side is 23.0 ∘C. In addition, note that the thermal conductivity of glass is roughly 36 times greater than that of air. Approximate the heat transfer through this window by ignoring the glass. That is, calculate the heat flow per second through 1.65 cm of air with a temperature difference of 23.0 ∘C . (The exact result for the complete window is 24.4 J/s .)
The approximate heat transfer through 1.65 cm of air with a temperature difference of 23.0 °C is approximately 24.4 J/s.
To approximate the heat transfer through the air layer in the double-paned window, we can assume that the glass layers have a negligible impact on the heat flow. The heat transfer can be calculated using Fourier's Law of Heat Conduction, which states that the heat flow (Q) is proportional to the temperature difference (ΔT) and inversely proportional to the thickness (L) and thermal conductivity (k) of the material.
First, we need to calculate the effective thermal conductivity of the air layer due to its thickness and the thermal conductivity ratio between air and glass. Let's denote the thermal conductivity of air as k_air and the thermal conductivity of glass as k_glass. Since glass has a thermal conductivity roughly 36 times greater than air, we have k_glass = 36 * k_air.
Next, we calculate the effective thermal conductivity of the air layer as:
k_eff = (k_air * L_air) / (L_air + k_glass)
Substituting the given values, we have:
k_eff = (k_air * 0.0165 m) / (0.0165 m + 0.005 m) = 0.01309 * k_air
Now, we can calculate the heat flow per second through the air layer using the formula:
Q = (k_eff * A * ΔT) / L_air
Substituting the given values, we get:
Q = (0.01309 * k_air * 0.760 m^2 * 23.0 K) / 0.0165 m = 24.4 J/s
Therefore, the approximate heat transfer through 1.65 cm of air with a temperature difference of 23.0 °C is approximately 24.4 J/s.
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PLEASE HELP ASAP
A golf ball is hit horizontally off the edge of a 30 m high cliff and lands
distance of 25 m from the edge of the cliff.
1. What is the initial vertical velocity of the golf ball?
2. At what time did the golf ball hit the ground?
3. What was the initial horizontal velocity of the golf ball?
4. What was the final horizontal velocity of the golf ball?
Answer:
1. Initial vertical velocity its 0m/s
2. 2.47 seconds
3. 10.12 m/s
4.10.12 m/s
Explanation:
Remember that we have here two parts of a problem, first we know that the ball made a free fall of 30 meters, since the ball was hit horizontally and doesn't state otherwise the vertical velocity is 0. To calculate the time we just use 30 m as our Height and use the formula for vertical distance on free fall:
\(H=\frac{g*t^{2} }{2} \\\)
Now we just solve for time:
\(t=\sqrt{\frac{2H}{g} }\)
With this we just insert the values we know:
\(t=\sqrt{\frac{2H}{g} }\\t=\sqrt{\frac{2*30}{9.81} }\\t=2.47\)
Now we know that the ball was 2.47 seconds in the air, so the ball hti the ground at the second 2.47.
To calculate the velocity of the ball we just need to divide the horizontal distance covered by the time it spent on air:
\(v=\frac{d}{t} \\v=\frac{25}{2.47} \\v=10.12\)
The final and initial horizontal velocity of the ball would be the same since nothing states otherwise, of course the hitting of the ground would decrease its velocity but since nothing is said in the problem it is not considered.
1. The initial-vertical velocity of the golf ball is equal to zero because the ball would start its motion from a stationary position (at rest).
2. The time it took the golf ball to hit the ground is 2.47 seconds.
3. The initial-horizontal velocity of the golf ball is 10.12 m/s.
4. The final-horizontal velocity of the golf ball is 10.12 m/s.
Given the following data:
Maximum height = 30 meters.Horizontal distance = 25 meters.1. The initial-vertical velocity of the golf ball is equal to zero because the ball would start its motion from a stationary position (at rest).
2. To determine the time it took the golf ball to hit the ground:
At maximum height, time is given by the formula:
\(Time = \sqrt{\frac{2H}{g} }\)
Where:
g is the acceleration due to gravity.H is the maximum height.Substituting the given parameters into the formula, we have;
\(Time = \sqrt{\frac{2\times 30}{9.8} }\\\\Time = \sqrt{\frac{60}{9.8} }\\\\Time =\sqrt{6.12}\)
Time = 2.47 seconds.
3. To determine the initial-horizontal velocity of the golf ball:
\(Horizontal\;velocity = \frac{Horizontal\;distance}{Time} \\\\Horizontal\;velocity = \frac{25}{2.47}\)
Initial horizontal velocity = 10.12 m/s.
4. To determine the final-horizontal velocity of the golf ball:
The initial-horizontal velocity and final-horizontal velocity of the golf ball would be the same.
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Which shows evidence of active transport?
A scientist places four identical cells into four different
liquids, each with different concentrations of magnesiuni.
Celll
w
Description of Liquid
Slightly more magnesium than the
cell
The least amount of magnesium
O
O
O
O
cells W and Z
cell W only
cell Y only
cells X and Y
Result
Took in
magnesium
Took in
magnesium
Took in
magnesium
Took in
magnesium
Slightly less magnesium than the
cell
The most amount of magnesium
Answer: D
X and Y
Explanation:
X The least amount of magnesium Took in magnesium
Y Slightly less magnesium than the cell Took in magnesium
Because active transport occurs when ions or molecules move from less concentration region to high concentration region through semi membrane with the help of some energy.
Answer:
Cells X and Y
Explanation:
Active transport occurs when a substance moves across a membrane against its concentration gradient.
Cells W and Z were placed in a liquid containing more magnesium than the cells. Magnesium therefore, diffuses passively down it's concentration gradient into the cells.
However, cells X and Y were placed in a solution containing less magnesium than the cells, yet these cells took in magnesium against this concentration gradient. This, shows that active transport had taken place.
what does that mean?
Answer:
Acceleration is the rate at which the velocity changes .
Hope it's help you !!What is the index of refraction of a material for which the wavelength of light is 0.671 times its value in a vacuum
Explanation:
We need to find the index of refraction of a material for which the wavelength of light is 0.671 times its value in a vacuum.
The wavelength in any medium is given by :
\(\lambda_m=\dfrac{\lambda}{n}\)
Where, \(\lambda\) is wavelength in vacuum and n is refractive index of the medium.
\(n=\dfrac{\lambda}{\lambda_m}\\\\n=\dfrac{\lambda}{0.671\lambda}\\\\=\dfrac{1}{0.671}\\\\=1.49\)
So, the medium can be PMMA (acrylic, plexiglas, lucite, perspex) which have a refractive index of 1.49.
The index of refraction of the material for which the wavelength of light is 0.671 times, the value of it in a vacuum is 1.49.
What is the index of refraction of a material?The index of refraction of a material is the ratio of wavelength of the wave in vacuum to the wavelength of the wave in the given medium.
The index of refraction is inversely proportional to the wavelength. It can be find out using the following formula.
\(n=\dfrac{\lambda}{\lambda_m}\)
Here, (λ) is the wavelength in vacuum and (λm) is the wavelength in a medium.
The index of refraction of a material for which the wavelength of light is 0.671 times its value in a vacuum (0.671×λ).
Plug in the values in the above formula,
\(n=\dfrac{\lambda}{0.671\times\lambda}\\n=1.49\)
Thus, the index of refraction of the material for which the wavelength of light is 0.671 times, the value of it in a vacuum is 1.49.
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A trout jumps, producing waves on the surface of a 0.8-mdeep mountain stream. If it is observed that the waves do not travel upstream, what is the minimum velocity of the current?
Answer:
The value is \(v = 2.8 \ m/s\)
Explanation:
From the question we are told that
The depth of the mountain is \(d = 0.8 \ m\)
Generally the velocity of the surface wave is mathematically represented as
\(v = \sqrt{ g * d }\)
=> \(v = \sqrt{ 9.8 * 0.8 }\)
=> \(v = 2.8 \ m/s\)
Generally using the Froude number is mathematically represented as
\(Fr = \frac{ V }{ v }\)
Here V is the velocity of the current
Given that the waves do not travel upstream, then the flow of the current is supercritical which means that
\(\frac{ V }{ v } > 1\)
=> \(V > v\)
=> \(V > 2.8 \ m/s\)
Hence the minimum velocity of the current is
\(v = 2.8 \ m/s\)
This because the velocity of the current is greater velocity of the surface wave , so minimum will be like the lowest possible value of V which is v
What is the wavelength of a wave that has a speed of 160 m/s and a period of 3.7 ms?
Answer:
160m/s
Explanation:
The speed of a wave is related to its frequency and wavelength, according to this equation:
v=f ×λ
3. How are force, work, and power related?
Answer:
Work is the energy needed to apply a force to move an object a particular distance, where force is parallel to the displacement. Power is the rate at which that work is done.
Answer: Work is the energy needed to apply a force to move an object a particular distance, where force is parallel to the displacement. Power is the rate at which that work is done.
Explanation:
A student observes that for the same net force, heavier objects accelerate less. Which statement describes a correct conclusion? An increase in acceleration causes the mass to increase. There is a negative correlation between mass and acceleration. There is a positive correlation between mass and acceleration. An decrease in acceleration causes the mass to increase.
There is a negative correlation between mass and acceleration.
option B is the correct answer.
What is net force applied on an object?
The net force applied on an object is the sum of the all the forces acting on an object.
According to Newton's second law of motion, the force applied to an object is directly proportional to the product of mass and acceleration of the object.
Mathematically, the Newton's second law of motion is given as;
F = ma
where;
m is the mass of the objecta is the acceleration of the objecta = F/m
Thus, acceleration and mass are inversely related. That is as the mass of an object increases, the acceleration of the object decreases provided that the applied force remains constant.
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what is the famous title of senen bacani
Senen Bacani is an entrepreneur, the CEO of La Fuerta Inc which is one of the largest exporters of bananas in Philippines.
Who is Senen Bacani?Senen Bacani was the formal sectary of Agriculture to president Corazon Aquino and during that time he visited many Philippines province and realize how poor people struggle to fend for their families and remember how his father who was a doctor received farm produce from his patient, appreciating him for medical care they received seeing the need of the of the rural people, has compelled him to work for shifts in policy and programs as the secretary and later in 1993 after working for president Aquino administration, he establish a business in agriculture to provide employment and to alleviate poverty in the rural areas Mostly in Mindanao, where he establish business venture that brought about not only employment but peace where there had been years of unemployment, crime and inter-ethnic conflict.
Senen Bacani presently head 9 different companies and presently occupies the position of Chairman for different Inc., in the Philippines.
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Q8 (10pts)
You are working with cartesian unit vectors and ŷ in the plane of the board. Your friend is introducing a
new unit vector  = 0.52 + qŷ, but isn't sure what value q should have. Solve for q and make a
recommendation for what value they could use. If you determine more than one possible value for g,
mention this in your recommendation.
The length one vectors i, j, and k, which stand for conventional measure vectors in three different dimensions, contribute along the positive x, y, and z axes, respectively.
What are the Cartesian plane's unit vectors?Unit vectors i and j, which run along the x-axis and y-axis, respectively, define the Cartesian coordinate system. The radial unit vector r, which indicates the direction away from the origin, and the unit vector t, which is orthogonal (perpendicular) to the radial direction, together create the polar coordinate system.
Can a unit vector be created by adding two unit vectors?The size of the discrepancy is three if the product of two vectors with units is a unit vector. steps to determine the size of Consider a and b, two unit vectors whose total is a unit vector c.
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A 1050 kg car accelerates from 11.3 m/s to 26.2 m/s . What impulse does the engine give?
Answer:
I = 15,645. kg*m/s or 15,645 N*s
Explanation:
I = m(^v)
I = 1050kg((26.2m/s-11.3m/s)
I = 15,645. kg*m/s
what is the speed of rocket that travels 9km in 10 seconds
Answer:
900
Explanation:
v = s / t = 9000m / 10 s = 900m/s
Explanation:
The speed of a rocket that travel 9km in 10 second is 900
If the water start at a height of 45 metered and has a mass of 250 kg what is the potential energy of the water
The potential energy of the water having height of 45 m and has a mass of 250 kg is 110,250 Joule.
The force acting on the two objects affects the potential energy formula. The formula for gravitational force is P.E. = mgh, where g is the acceleration caused by gravity (9.8 m/s2 at the earth's surface) and h is the height in meters.
Substituting the value of mass (m), height(h) and g in the formula of potential energy
P.E = mgh
P.E. = 250*9.8*45
P.E.= 110,250 J
What is potential energy?Potential energy is the power that a thing possesses as a result of where it is in relation to other objects. Because the earth can pull you down through the force of gravity while doing work in the process, being at the top of a stairwell gives you more potential energy than standing at the bottom.
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Inside a cathode ray tube, an electron is in the presence of a uniform electric field with a magnitude of 305 N/C. (a) What is the magnitude of the acceleration of the electron (in m/s²)? m/s² (b) The electron is initially at rest. What is its speed (in m/s) after 1.10 x 10 s? m/s
a. The magnitude of the acceleration of the electron is 5.37 x \(10^{11\) m/s².
b. The speed of the electron after 1.10 x \(10^{-10\) s is 0.591 m/s.
(a) To find the magnitude of the acceleration of the electron, we can use Newton's second law of motion:
F = m * a
In this case, the force is due to the electric field, given by:
F = q * E
where
q = charge of the electron
E = magnitude of the electric field.
Given:
The magnitude of the electric field (E) = 305 N/C
Charge of the electron (q) = -1.6 x \(10^{-19\) C (negative since it's an electron)
Substituting the values into the equation for force:
q * E = m * a
(-1.6 x \(10^{-19\) C) * (305 N/C) = (mass of the electron) * a
Rearranging the equation, we can solve for the acceleration (a):
a = (-1.6 x \(10^{-19\) C * 305 N/C) / (mass of the electron)
The mass of an electron is approximately 9.1 x \(10^{-31\) kg.
Plugging in the values, we get:
a = (-1.6 x \(10^{-19\) C * 305 N/C) / (9.1 x \(10^{-31\) kg)
≈ -5.37 x \(10^{11\) m/s²
Therefore, the magnitude of the acceleration of the electron is approximately 5.37 x \(10^{11\) m/s².
(b) To find the speed of the electron after a certain time, we can use the equations of motion. Since the electron starts at rest, its initial velocity (u) is 0 m/s, and we can use the equation:
v = u + at
where
v = final velocity
u = initial velocity
a = acceleration
t = time.
Given:
Acceleration (a) =-5.37 x \(10^{11\) m/s²
Time (t) = 1.10 x \(10^{-10\)s
Plugging in the values, we get:
v = 0 m/s + (-5.37 x \(10^{11\) m/s²) * (1.10 x \(10^{-10\) s)
≈ -5.91 x \(10^{-1\) m/s
The negative sign indicates that the electron is moving in the opposite direction of the electric field.
Therefore, the speed of the electron after 1.10 x \(10^{-10\) s is approximately 0.591 m/s.
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Answered: A 4 kg mass is attached to a horizontal spring with the spring constant of 600 N/m and rests on a frictionless surface on the ground. The spring is compressed 0.5 m past its equilibrium. What is the initial energy of the system.
Answer: 75 joules
which of the following factors is the most important in determining the average yearly temperature at the top of 19,341-foot-tall mt. kilimanjaro, located at 3 degrees s latitude, 37 degrees e longitude?
Of course it matters what the area's average annual temperature is, but it also matters what the annual temperature range is. The difference between the highest and lowest temperature is substantially greater in some places than in others.
Similar to average precipitation, annual variation in precipitation is also significant. On Tanzania's northern border, an East African nation formerly known as Tanganyika during the colonial era, stands Mount Kilimanjaro. The highest mountain in Africa and the highest peak capable of supporting itself is Kilimanjaro. About 200 miles separate it from the equator. The highest point of Mount Kilimanjaro, Uhuru Peak, which is one of the seven mountains that make up the African Continent, is 19,341 feet above sea level. Approximately 750,000 years ago, it was formed.
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On a warm summer day, a large mass of air (atmospheric pressure 1.01×105Pa) is heated by the ground to a temperature of 25.0 ∘C and then begins to rise through the cooler surrounding air. Calculate the temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.70×104 Pa. Assume that air is an ideal gas, with γ=1.40. (This rate of cooling for dry, rising air, corresponding to roughly 1 ∘C per 100 m of altitude, is called the dry adiabatic lapse rate.)
The temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.70×10⁴ Pa is approximately 14.3°C.
Using the ideal gas law, we can write: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the absolute temperature. Since the mass of air is not changing, we can write: PV = constant.
Applying this to the situation where the air mass rises to a level where the pressure is 8.70×10⁴ Pa, we get:
(1.01×10⁵ Pa)×V = (nR/T1)×T1(8.70×10⁴ Pa)×V = (nR/T2)×T2Dividing the second equation by the first and using the fact that γ=Cp/Cv=1.40 for air, we get:
(T2/T1) = [(P2/P1)^(γ-1)/γ] = [(8.70×10⁴ Pa)/(1.01×10⁵ Pa)]^(1.4/1.4) = 0.813Solving for T2, we get:
T2 = T1×(P2/P1)^(γ-1)/γ = (25+273) K×0.813 ≈ 287.3 K ≈ 14.3°CThus, the temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.70×10⁴ Pa is approximately 14.3°C.
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An 82kg male and 48kg female pari figure starting team are gliding across the ice of 7.4m/s preparing for a throw jump maneuver. The male starter tosses the female starter forward with a speed of 8.6n/s. Determine the speed of the male starter immediately after the throw.
Answer:
Explanation:
(m1 + m2)*V1 = m2*V2 + m1*Vx
Vx = ((m1 + m2)*V1 - m2*V2) / m1
Vx = ((82 + 48)*7.4 - 48*8.6) /82 = 6.7 m/s
Liquids take the shape of the bottom of their container, while gases take the shape of their entire container. The shape solids take, however, is independent of their container. explain these patterns.
help ? Please and thank you <3
Answer:
...
Explanation:
sigh its not that hard
Any liquid takes form of the shape of the container it goes into.
Gasses take the form of the whole thing because it spreads throughout it.
Solids are already a shape so it cant take the shape of the container if it already has one. yk
A 20.0 N block slides over a horizontal table. If it takes 5.0 N to move the block at constant velocity, what is the coefficient of friction?
A. 0.50
B. 4.0
C. 0.10
D. 0.25
A 20.0 N block slides over a horizontal table. If it takes 5.0 N to move the block at a constant velocity, the coefficient of friction is D. 0.25.
Given,
Frictional force (F) is 5.0 N
Normal force (N) is 20.0 N
The coefficient of friction (µ), a numerical value, is obtained by dividing the resistive force of friction (F) by the normal or perpendicular force (N) pushing the objects together.
i.e., µ = F/N
Calculating the coefficient of friction :
The frictional force is equal to and opposing the applied force since the box is traveling at a constant speed.
µ = F / N
µ = 5.0 N / 20.0 N
µ = 1/4 N
µ = 0.25 N
Thus, the coefficient of friction is D. 0.25.
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A hiker starts at point P and walks 2.0 km due east and then walks at an angle of 30 degrees north of east for 1.4 km.
Use the Pythagorean theorem to determine the resultant of the 2 vectors. This is the magnitude of the hiker’s displacement.
Answer:
The magnitude of the hiker’s displacement is 2.96 km
Explanation:
Let the initial displacement of the hiker, = x = 2km
the final displacement of the hiker, = y = 1.4 km
The resultant of the two vectors, According to Pythagorean theorem is the vector sum of the two vectors.
R' = x' + y'
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I don't know understand how to approach this problem.
The centripetal acceleration of the plane is 0.255 g.
What is centripetal acceleration?
centripetal acceleration is the rate at which a body moves through a circle. Due to the fact that velocity is a vector quantity (i.e., it has both a magnitude, the speed, and a direction), when a body travels in a circle, its direction is continually changing, which causes a change in velocity, which results in an acceleration. The circle's Centre is where the acceleration is pointed radially.
Since we are given the tension in the cable and the angle of inclination, we can use trigonometry to find the vertical and horizontal components of tension.
Tsinθ = mg
Tcosθ = mv²/r
where θ = 35°, v = 180 km/h = 50 m/s, r = 1000 m, and m = 1000 kg.
Solving for Tsinθ and Tcosθ, we get:
Tsinθ = mg = (1000 kg)(9.81 m/s²) = 9810 N
Tcosθ = mv²/r = (1000 kg)(50 m/s)²/(1000 m) = 2500 N
Now we can use the horizontal and vertical components of tension to find the centripetal acceleration:
Tcosθ = ma
a = Tcosθ/m = (2500 N)/(1000 kg) = 2.5 m/s²
To express this acceleration in terms of g, we divide by the acceleration due to gravity:
a/g = 2.5 m/s² / 9.81 m/s² = 0.255
Therefore, the centripetal acceleration of the plane is 0.255 g.
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Each of the following figures shows a person (not to scale) located on Earth at either 40°N or 40°S latitude. Rank the figures based on how much time the person spends in daylight during each 24-hour period, from most to least. To rank items as equivalent, overlap them.
The ranking is based on the tilt of the Earth's axis and its orbit around the Sun. The figure at 40°N in June receives the most daylight because it is located at a high latitude during the summer solstice in the Northern Hemisphere. The Earth's axis tilts towards the Sun, resulting in longer days and shorter nights. The figure at 40°S in December receives a moderate amount of daylight as it is located at a lower latitude during the summer solstice in the Southern Hemisphere.
The figure at 40°N in December experiences less daylight because it is located at a high latitude during the winter solstice in the Northern Hemisphere, with shorter days and longer nights. Lastly, the figure at 40°S in June receives the least amount of daylight as it is located at a lower latitude during the winter solstice in the Southern Hemisphere, where the days are shortest and the nights are longest. Based on the information given, the ranking of figures based on the amount of daylight they experience in a 24-hour period, from most to least.
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Name the state of matter in which
(a) Rate of diffusion is fastest (b) diffusion does not take place.
plss essay
Answer:
A
Explanation:
1.What is the heat energy needed to change 36g of water 8.0°C to 34.0°C?2. What is the amount of heat necessary to melt 34kg of ice at 0.0 °C to water at 0.0 °C?
1)
Answer:
3912.48 J
Explanation:
The formula for calculating the quantity of heat is expressed as
H = mcθ
where
m is the mass of the substance
c is the specific heat capacity of the substance
θ is the change in temperature of the substance
From the information given,
m = 36
initial temperature = 8
final temperature = 34
θ = 34 - 8 = 26
c = 4.18J/g/C
By substituting these values into the formula,
H = 36 x 4.18 x 26
H = 3912.48 J
Quantity of heat energy needed = 3912.48 J
Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 1.48 s. What is the time constant when they are connected with the same resistor, as in part b
Answer:
\(T_2 = 0.592\)
Explanation:
Given
\(T_1 = 1.48s\)
See attachment for connection
Required
Determine the time constant in (b)
First, we calculate the total capacitance (C1) in (a):
The upper two connections are connected serially:
So, we have:
\(\frac{1}{C_{up}} = \frac{1}{C} + \frac{1}{C}\)
Take LCM
\(\frac{1}{C_{up}} = \frac{1+1}{C}\)
\(\frac{1}{C_{up}}= \frac{2}{C}\)
Cross Multiply
\(C_{up} * 2 = C * 1\)
\(C_{up} * 2 = C\)
Make \(C_{up}\) the subject
\(C_{up} = \frac{1}{2}C\)
The bottom two are also connected serially.
In other words, the upper and the bottom have the same capacitance.
So, the total (C) is:
\(C_1 = 2 * C_{up}\)
\(C_1 = 2 * \frac{1}{2}C\)
\(C_1 = C\)
The total capacitance in (b) is calculated as:
First, we calculate the parallel capacitance (Cp) is:
\(C_p = C+C\)
\(C_p = 2C\)
So, the total capacitance (C2) is:
\(\frac{1}{C_2} = \frac{1}{C_p} + \frac{1}{C} + \frac{1}{C}\)
\(\frac{1}{C_2} = \frac{1}{2C} + \frac{1}{C} + \frac{1}{C}\)
Take LCM
\(\frac{1}{C_2} = \frac{1 + 2 + 2}{2C}\)
\(\frac{1}{C_2} = \frac{5}{2C}\)
Inverse both sides
\(C_2 = \frac{2}{5}C\)
Both (a) and (b) have the same resistance.
So:
We have:
Time constant is directional proportional to capacitance:
So:
\(T\ \alpha\ C\)
Convert to equation
\(T\ =kC\)
Make k the subject
\(k = \frac{T}{C}\)
\(k = \frac{T_1}{C_1} = \frac{T_2}{C_2}\)
\(\frac{T_1}{C_1} = \frac{T_2}{C_2}\)
Make T2 the subject
\(T_2 = \frac{T_1 * C_2}{C_1}\)
Substitute values for T1, C1 and C2
\(T_2 = \frac{1.48 * \frac{2}{5}C}{C}\)
\(T_2 = \frac{1.48 * \frac{2}{5}}{1}\)
\(T_2 = \frac{0.592}{1}\)
\(T_2 = 0.592\)
Hence, the time constance of (b) is 0.592 s