How many quarts are equal to 5 pounds of ethanol? The density of ethanol is 0.789 g/mL.
The required quarts that is equals to 5 pounds of ethanol would be 3 quarts if the density of ethanol is 0.789 g/mL.
What is the density?Density is the ratio of mass and volume.
density = mass/volume
The density of ethanol is 0.789 g/mL.
Convert pounds to grams
∵ 1 pounds = 453.592 grams
∴ 5 pounds = 2267.96 grams
So the mass of ethanol would be 2267.96 grams
Density Equation
density = mass/volume
Solve for volume.
volume = mass / density
volume = 2267.96 g / (0.789 g/mL)
volume = 2267.96 g / (0.789 g/mL)
volume = 2874.47 mL
Convert milliliters to quarts.
∵ 1 mL = 0.00105669 quarts
⇒ 2874.47 mL × 0.00105669 qt /1 mL
⇒ 3 quarts
Hence, the volume of ethanol would be 3 quarts.
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A rope pulls a Tesla out of mud. The guy pulls a force F⊥ of 300N, and theta = 4.2°. The tension force T is ___ Newton.
A rope pulls a Tesla out of mud. The guy pulls a force F⊥ of 300N, and theta = 4.2°. The tension force T is 298.44__ Newton.
The problem describes a Tesla that is stuck in the mud and needs to be pulled out using a rope. the guy pulls a force F⊥ of 300N and that the angle between the rope and the horizontal plane is θ = 4.2°. The goal is to find the tension force T exerted by the rope.To solve for T, we'll need to use trigonometry. We can break the force vector into its horizontal and vertical components as follows:
Fx = F⊥ cosθ and Fy = F⊥ sinθ.
Since the rope is pulling the Tesla horizontally, the horizontal component of the force will be the tension force T. So we have:
T = Fx = F⊥ cosθ = (300 N) cos(4.2°) ≈ 298.44 N
Taking the cosine of the angle is necessary since it's the adjacent side that we're interested in, which is the horizontal component of the force. Therefore, the tension force exerted by the rope is approximately 298.44 N.
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pls help ;-; this is the question btw
The answer is "Infrared"
Hope this helps
Answer:
x-rays
Explanation:
What is the independent variable if a scientist is turning bulb on and off to check behaviour of the earthworm?
The independent variable in this experiment is the act of turning the bulb on and off, while the dependent variable is the behavior of the earthworm in response to changes in light. The scientist can analyze the data collected to determine the impact of light on the earthworm's behavior.
In the experiment where a scientist is turning a bulb on and off to check the behavior of an earthworm, the independent variable is the manipulation performed by the scientist, which is the act of turning the bulb on and off.
The independent variable is the variable that the scientist deliberately changes or controls in order to observe its effect on the dependent variable. In this case, the scientist is interested in investigating how the earthworm responds to changes in light. By turning the bulb on and off, the scientist is manipulating the presence or absence of light in the environment of the earthworm.
The behavior of the earthworm, which is the dependent variable, will be observed and measured in response to the changes in light. The scientist may record various behaviors such as movement, burrowing, or changes in activity level exhibited by the earthworm when the light is turned on and off.
By systematically controlling the independent variable (turning the bulb on and off) and observing the dependent variable (behavior of the earthworm), the scientist can analyze the relationship between light exposure and the earthworm's behavior. This allows for drawing conclusions about how the earthworm responds to light stimuli.
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please help me - i beg u
Answer:
516526.863 m
Explanation:
From the question given above, the following data were obtained:
Acceleration due to gravity (g) = 2.24 m/s²
Mass (M) = 8.96×10²¹ Kg
Gravitational constant (G) = 6.67×10¯¹¹Nm²/Kg²
Radius (r) =?
The radius of the planet can be obtained as follow:
g = GM/r²
2.24 = 6.67×10¯¹¹ × 8.96×10²¹ / r²
2.24 = 5.97632×10¹¹ / r²
Cross multiply
2.24 × r² = 5.97632×10¹¹
Divide both side by 2.24
r² = 5.97632×10¹¹ / 2.24
r² = 2.668×10¹¹
Take the square root of both side
r = √2.668×10¹¹
r = 516526.863 m
Thus, the radius of the planet is 516526.863 m
HI PLEASE HELP ON QUESTION ASAP USING AVERAGE (MEAN) TO ANSWER QUESTION! IF UR ANSWER AND EXPLAINATION IS CORRECT ILL RATE YOU FIVE STARS, A THANKS AND MAYBE EVEN BRAINLIEST. PLEASE MAKE SURE YOU ANSWER MY QUESTION USING AVERAGES.
1) a meal for 6 cost £12 per person. as it is one of the diners birthday , the other 5 decided to pay for his meal. how much do each of the five friends need to pay?
Each of the five friends needs to pay £12 to cover the cost of their own meals and contribute towards the birthday person's meal. Using mean allows us to distribute the cost equally among the friends, ensuring a fair division of expenses for the meal.
To determine how much each of the five friends needs to pay, we can use the concept of averages (mean) and divide the total cost by the number of people paying.
In this scenario, the total cost of the meal for 6 people is £12 per person. Since the other 5 friends have decided to pay for the birthday person's meal, they will collectively cover the cost of their own meals plus the birthday person's meal.
To calculate the total cost covered by the five friends, we can subtract the cost of one person's meal (since the birthday person's meal is being paid by the group) from the total cost. The cost of one person's meal is £12.
Total cost covered by the five friends = Total cost - Cost of one person's meal
= (£12 x 6) - £12
= £72 - £12
= £60
Now, to find out how much each of the five friends needs to pay, we divide the total cost covered by the five friends (£60) by the number of friends (5).
Amount each friend needs to pay = Total cost covered by the five friends / Number of friends
= £60 / 5
= £12
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Which of the following is an advantage of using geothermal energy?
A. It is available only in limited areas.
B. It can cause air and groundwater pollution.
C. It is difficult to transport from place to place.
D. It reduces greenhouse emissions.
Answer:
There are many advantages of geothermal energy but also some challenges ... than the air, it can act as a heat sink/ source with a geothermal heat pump just ... The largest single disadvantage of geothermal energy is that it is location specific. ... energy does not typically release greenhouse gases, there are many of these .
The advantage of using geothermal energy is that It reduces greenhouse emissions. Geothermal energy has a lot of advantage.
What is geothermal energy?Geothermal energy is the thermal energy in the Earth's crust that comes from the planet's creation and radioactive decay of components in nearly equal amount.
The advantage of using the geothermal energy is;
A. It is available only in limited areas.
B. It can cause air and groundwater pollution.
C. It is difficult to transport from place to place.
Following is an advantage of using geothermal energy
D. It reduces greenhouse emissions.
Hence, option D is correct.
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5
What is the electric force between two particles that are 5m apart. One of the
particles has a charge of 100C while the other has a charge of 20C. (k=9x109)
k=
9=
92=
r=
Answer:
\(7.2 \times 10 {}^{11} newton\)
Explanation:
\(the \: magnitude \: of \: the \: forc \: e \: can \: be \: calculated \: using \: coulombs \: formular \\ f = \frac{k \times q1 \times q2}{d {}^{2} } \\ f = \frac{9 \times 10 {}^{9} \times 100 \times 20 }{5 {}^{2} } \\ f = \frac{18000 \times 10 {}^{9} }{25 } \\ f = \frac{18000000000000}{25} \\ f = 7.2 \times 10 {}^{11} newton\)
when light strikes a green opaque object the green wavelength of light is .....
1. reflected
2. absorbed
3. transmitted
while all other wavelengths of visible light are......
1. reflected
2. absorbed
3. transmitted
When light strikes a green opaque object, the green wavelength of light is absorbed, while all other wavelengths of visible light are reflected.
Why does a green object appear green to our eyes?A green object appears green to our eyes because it selectively absorbs all wavelengths of visible light except for the green wavelength of light, which is reflected back to our eyes.
When light strikes a green opaque object, the green wavelength of light is absorbed by the object. This means that the green light is not reflected or transmitted, but rather it is absorbed by the object.
What happens to the energy of the absorbed light when it is absorbed by an opaque object?When light is absorbed by an opaque object, the energy of the absorbed light is converted into other forms of energy, such as thermal energy. This is because the absorbed light energy causes the atoms in the object to vibrate, which in turn generates heat energy.
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if the mass of the object is doubled and the speed is halved then kinetic energy will change by a factor of:
2
4
1/2
1/4
Answer:
kinetic energy will change by a factor of 1/2
Option C) 1/2 is the correct answer
Explanation:
Given the data in the question;
we know that;
Kinetic energy = 1/2.mv²
given that mass of the object is doubled; m1 = 2m
speed is halved; v1 = V/2
Now, New kinetic energy will be; 1/2.m1v1²
we substitute
Kinetic Energy = 1/2 × 2m × (v/2)²
Kinetic Energy = 1/2 × 2m × (v²/4)
Kinetic Energy = 1/2 × m × (v²/2)
Kinetic Energy = 1/2 [ 1/2mv² ]
Kinetic Energy = 1/2 [ KE ]
Therefore; kinetic energy will change by a factor of 1/2
Option C) 1/2 is the correct answer
C. propan-1-one D. pentan-1-ol Question 2 ceiling -↑ 1,8 m 3,5 m mais (2) [12] A girl stands on a table in a classroom. She throws a ball of 0.2 kg vertically downwards to the floor hoping that the ball, after it bounced on the floor, will hit the the classroom. of She throws the ball with a velocity of 8 m.s-1 from a height of 1,8 m above the floor. Ignore the effects of friction. Write down the magnitude and direction of the acceleration of the ball immediately after ball left her hand. ( Is the ball in free fall while it moves downwards? Answer YES or NO and give an explana for the answer. Calculate the magnitude of the velocity with which the ball hits the floor.
2.1. The acceleration of the ball immediately after it leaves the girl's hand is -9.8 m/s², directed downwards.
2.2. Yes, the ball is in free fall while it moves downwards. This is because the only force acting on the ball is gravity, which is a constant downward force.
How to calculate the magnitude of velocity?The magnitude of the velocity with which the ball hits the floor can be calculated using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, v is the final velocity, and so is the distance traveled. In this case, u = 8 m/s, a = -9.8 m/s², and s = 1.8 m. Plugging these values into the equation, we get v = √ (8² - 2 × (-9.8) × 1.8) = √ (64 + 35.28) = √ (99.28) = 9.96 m/s.The time it takes for the ball to hit the floor can be calculated using the equation t = (v-u)/a, where t is the time, v is the final velocity, a is the acceleration and u is the initial velocity. In this case, v = 9.96 m/s, u = 8 m/s, and a = -9.8 m/s². Plugging these values into the equation, we get t = (9.96 - 8)/-9.8 = 1.97 s.
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A string on a violin is 25.4 cm long produces a fundamental frequency of 440 Hz. What must its length be shortened to in order to produce a tone with a frequency of 523.3 Hz?
Given,
The length of the string, L₁=25.4 cm
The fundamental frequency, f₁=440 Hz
The new frequency, f₂=523.3 Hz
The frequency of a standing wave is related to the length of the string as,
\(f=\frac{v}{2L}\)On rearranging the above equation,
\(\begin{gathered} fL=\frac{v}{2} \\ \Rightarrow fL=\text{ constant} \\ \Rightarrow f_1L_1=f_2L_2 \end{gathered}\)Where L₂ is the shortened length of the string.
On substituting the known values,
\(\begin{gathered} 440\times25.4=523.3\times L_2 \\ L_2=\frac{440\times25.4}{523.3} \\ =21.36\text{ cm} \end{gathered}\)Therefore the shortened length of the string in order to produce the required frequency is 21.36 cm.
A charge of -3.00 x 10 C is at the origin of a coordinate system, and a charge of 8.00 x 10 C is pn the x-axis at 2.00 m. At what two locations on the x-axis is the electric potential zero?
The two locations on the x-axis where the electric potential is zero are
x₁ = 1.00 m and x₂ = 1.00 m.
To find the two locations on the x-axis where the electric potential is zero, we can use the formula for the electric potential due to a point charge:
V = kq/r
where V is the electric potential, k is Coulomb's constant (9 x 10⁹ N m²/C²), q is the charge, and r is the distance between the point charge and the location where we want to find the electric potential.
Let's call the unknown distances on the x-axis from the charge at the origin as x₁ and x₂.
The electric potential:
V₁ = k(-3.00 x 10-6 C)/x₁ and V₂ = k(8.00 x 10-6 C)/(2.00 - x2).
The total electric potential at any position on the x-axis is the algebraic sum of the electric potentials owing to the two charges since the electric potential due to each charge is a scalar quantity so,
V = V₁ + V₂
We want to find the two values of x₁ and x₂ that make V = 0. Setting V to zero and rearranging the terms, we get:
k(-3.00 x 10⁻⁶ C)/x₁ + k(8.00 x 10⁻⁶ C)/(2.00 - x₂) = 0
Multiplying both sides by x₁(2.00 - x₂),
-3.00 x 10⁻⁶ (2.00 - x₂) + 8.00 x 10⁻⁶ x₁ = 0
Expanding and rearranging, we get:
8.00 x 10⁻⁶ x₁ = 6.00 x 10⁻⁶ x₂ - 4.00 x 10⁻⁶
x₁ = 1.00 m and x₂ = 1.00 m are the two points where electric potential is zero on x axis
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Sample Question: 4
A 5 kg mass is lifted from the ground to
a height of 10m.
The gravitational potential energy of
the mass is increased approximately
by
The gravitational potential energy of the mass in increased approximately by 490 J
Gravitational Potential energy formula is
P=mgh
where mass is given my m= 5 Kg
g is the gravitational force i.e. 9.8 \(m/s^{2}\)
h is the height above the ground that is given by 10 m
P = 5*9.8*10
P = 490 J
What is gravitational potential energy?
The potential energy that a huge item has in relation to another massive object due to gravity is known as gravitational energy or gravitational potential energy. When two objects descend toward one another, the potential energy associated with the gravitational field is released (transformed into kinetic energy).
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In an element's square on the periodic table, the number with the greatest numerical value represents the
number of neutrons.
O number of electrons.
88
atomic nunner.
O atomic mass.
Answer:
0 atomic mass because it widens as the numerical value represents
Answer: ATOMIC MASS
Explanation:
I got it right
HELPPPP LATE HOMEWORK DUE TODAY
If F₁ has a greater magnitude than F₂, the box will accelerate backward because the net force is in the backward direction (1st option)
How do i know which direction the box will move to?To obtain the direction in which the box will move, we shall determine the net force acting on the box. This is illustrated below:
Assumption:
Magnitude of force 1 (F₁) = 40 NMagnitude of force 2 (F₂) = 25 NNet force (F) =?Net force = Magnitude of force 1 (F₁) - Magnitude of force 2 (F₂)
Net force = F₁ - F₂
Net force = 40 - 25
Net force = 15 N backward
From the above illustration, we can see that the net force is 15 N backward.
Thus, we can conclude from the box will accelerate backward (1st option)
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A 514 turn solenoid , 21 cm long has a diameter of 2.6 cm. A 14 turn coil is tightly wound around the center of the solenoid. If the current in the solenoid increases uniformly from 0.3 A to 2.79 A in 0.8 s, what will be the induced emf in the short coil during this time
Answer:
Explanation:
no of turns per unit length n = 514 / .21 = 2447.62 per meter .
magnetic field in solenoid = μ₀ nI
= 4π x 10⁻⁷ x 2447.62 x I = 3.07 x 10⁻³ I T
magnetic flux through the small coil = 14 x 3.07 x 10⁻³ x π x 1.3² x10⁻⁴ I
φ= 72.63 x 10⁻⁷ I Web
emf induced in it
= dφ / dt = 72.63 x 10⁻⁷ dI / dt
= 72.63 x 10⁻⁷ x ( 2.79 - .3) / .8
= 226 x 10⁻⁷ V
= 22.6 x10⁻⁶ V
= 22.6 μ V .
1. A book resting on a shelf was found
to have a gravitational potential energy
of 12 J relative to the ground. If the
book falls to the ground, neglecting air
resistance, what is the kinetic energy of
the book just as it was about to hit the
ground?
Answer:
12J
Explanation:
Right before it hits the ground, the initial potential energy and the final kinetic energy will equal each other due to conservation of energy.
A fisherman has caught a fish on his pole, and to keep the pole steady he has to apply an upward force of F2 = 240 N at an angle of 83.5° with respect to the pole (see figure). The length of his pole is 4.1 m, and he is holding it a distance 0.35 m from the end, where he is applying a downward force F1.
With how much force, F1, in newtons, does he have to push straight downward on the end of his pole to keep the pole from moving? You may assume the pole is massless. F1 = What is the mass of the fish on the end of the pole, in kilograms? m =
The mass of the fish on the end of the pole, in kilograms m =2.090Kg.
What is Force?
Force is an influence that can cause an object to change its motion, direction, shape, or other physical attributes. Forces can be applied to objects, creating a change in their acceleration, velocity, or momentum. Forces can be either contact forces, such as pushing or pulling on an object, or non-contact forces, such as gravity, magnetism, and electricity. Forces can be described in terms of magnitude, direction, and point of application. Magnitude is the strength of the force, direction is the path the force is applied, and point of application is the point on the object where the force is applied. Forces can also be classified as balanced or unbalanced. Balanced forces occur when two forces of equal magnitude and opposite direction act on an object, resulting in no net force. Unbalanced forces occur when two forces of unequal magnitude act on an object, resulting in a net force.
Given that,
F2 = 240N
Angle = 83.5 degree
Length = 4.1m
Distance = 0.35m
How much force, F1 in newtons ?
What kind of fish is that hanging off the end of the pole?
Thus,
Calculating Torque about ‘A’
For equillibrium ∑τa= 0
F1 * L + F2 * (L – d) = 0
F1 * L= - F2* (L – d)
F1L SinΘ= F2(L – d) SinΘ
F1 = F2 (L – d)/L
F1 = 240 (4.1 – 0.35)/4.1
F1 = 219.51N
For equillibrium ∑ Fnet = 0
F2 + F1 + mg = 0
mg = F2- F1
m = F2 - F1/ g
m = 2.090Kg
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Which electromagnet is the strongest?
An illustration of a metal bar with a coil of wire around it.
An illustration of a metal bar with a coil of wire around it it has more coils.
An illustration of a metal bar with a coil of wire around it it has less coils.
* The Answer is the 2nd picture - An illustration of a metal bar with a coil of wire around it it has more coils.
Therefore, of the three options given, the electromagnet with more coils around the metal rod is the most powerful if all other factors such as current and core material are kept constant.
What is the very short response to an electromagnet?
An electromagnet is a temporary magnet made by winding a wire around an iron core. When current flows through the coil, iron becomes a magnet, and when the current is cut off, it loses its magnetic properties.
What is Electromagnetism?
Electromagnetism is the branch of physics that deals with the electromagnetic forces that occur between charged particles. Electromagnetic force is one of the four basic forces and describes the electromagnetic field.
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Answer: The answer is B
Explanation:
A car of mass 1800000 g, going 150 km/h rear ends a truck, 5500 kg going 100000 m/h. What are their velocities after an elastic collision in one dimension?
Answer:
v = 2099.5 km/h, v' = -618.8 km/h
or
v =-1996.6 km/h, v' = 721.7 km/h
Explanation:
From the law of conservation of momentum,
Total momentum before collision = Total momentum after collision
For elastic,
mu+m'u' = mv+m'v'..................... Equation 1
Total kinetic energy before collision is equal to total kinetic energy after collision
mu²+m'u'² = mv²+m'v'²............. Equation 2
Where m and m' are the mass of the car and truck respectively, and u and u' are the initial velocity of the car and the truck respectively, v and v' are the final velocity of the car and the truck respectively.
Given: m = 1800000 g = 1800 kg, m' = 5500 kg, u = 150 km/h, u' = 100000 km/h
Substitute these values into equation 1 and 2
1800(150)+5500(100000) = 1800v+5500v'
1800v+5500v' = 375500................... Equation 3
1800(150²) +5500(100000²) = 1800v²+5500v'²...................... Equation 4
Solving equation 3 and 4 simultaneously,
v = 2099.5 km/h, v' = -618.8 km/h
or
v =-1996.6 km/h, v' = 721.7 km/h
An OP AMP has CMRR = 100 dB and open-loop gain =250000.
Determine the common mode gain ACM
Answer:
ACM = 2.5
Explanation:
The common mode rejection ratio, is a parameter that is used to measure the ability of an Operational-Amplifier, to reject or eliminate the noises of same polarity. The common mode rejection ratio is given by the following formula:
CMMR = AV/ACM
for the value of CMMR in deciBels (dB), the formula becomes:
CMMR = 20 log(AV/ACM)
where,
CMMR = Common Mode Rejection Ratio = 100 dB
AV = Open Loop Gain = 250000
ACM = Common Mode Gain = ?
Therefore,
100 = 20 log (250000/ACM)
100/20 = log (250000/ACM)
10⁵ = 250000/ACM
ACM = 250000/10⁵
ACM = 2.5
PLZZZ HELP
Question 2 Multiple Choice Worth 2 points)
(04.05 LC)
Which of the following scenarios describe an object being acted on by a non-conservative force?
O Apuck hovers and glides across an air track at constant velocity.
A dishwasher was pulled up to a window by a rope using a pulley system.
O A feather falls from one end of a tube to the other inside a vacuum.
O A charged particle was pushed away by another charged particle.
Answer:
C
Explanation:
A feather falls from one end of a tube to the other inside a vacuum.
The radioactive hydrogen isotope 3H is called tritium. It decays by beta-minus decay with a half-life of 12.3 years.
A. What is the daughter nucleus of tritium?
B. A watch uses the decay of tritium to energize its glowing dial. What fraction of the tritium remains 20 years after the watch was created?
Answer:
a) A Helium nucleus with two protons and one neutron
b) 0.324 of the original amount
Explanation:
a) When Tritium decays, the nucleus emits an electron and an antineutrino, which then changes it from a Triton with one proton and two neutrons, to a Helium nucleus with two protons and one neutron.
The decay constant for the decay of Tritium is gotten from
\(t_{1/2}\) = 0.693/k
where
\(t_{1/2}\) is the half life = 12.3 yrs
k is the decay constant = ?
substituting, we have
12.3 = 0.693/k
k = 0.693/12.3 = 0.0563
The fraction that will remain after 20 years can be calculated from
\(N\) = \(N_{0} e^{-kt}\)
where
\(N\) is the final remaining amount of Tritium after 20 years
\(N_{0}\) is the original amount of Tritium
k is the decay constant = 0.0563
t is the time = 20 years
Equation can be re-written as
\(N/N_{0}\) = \(e^{-kt}\)
where
\(N/N_{0}\) is the fraction of the tritium that will be remaining after 20 years.
substituting values, we have
\(N/N_{0}\) = \(e^{-0.0563 * 20}\)
\(N/N_{0}\) = \(e^{-1.126}\)
\(N/N_{0}\) = 0.324 of the original amount
3. Batteries create electricity and generators create electricity. *
True
False
Which of these parameters is directly related to sound frequency?
Answer:Velocity
Explanation:
Velocity is directly proportional to the frequency of a wave.
Velocity=frequency x wavelength
Which is the right one?
(Show work)
a ballon is filled with air. what forces are acting on the ballon and the air?
Answer: Three forces act significantly on a freely floating helium-
filled balloon: gravity, air resistance (or drag force), and a
buoyant force.
Explanation:
The air pressure on the bottom of the balloon is slightly higher than the air pressure on the top of the balloon (because of the altitude difference). This difference gives rise to the bouyant force. This force competes with gravity as the two main forces acting on the balloon. Every time your feet hit the ground when you are running, the ground hits your feet with an equal and opposite force. Newton’s third law explains how balloons and rocket engines work. When the neck of an inflated balloon is released, the stretched rubber material pushes against the air in the balloon. The air rushes out of the neck of the balloon.
Which statement correctly compares nuclear fission with nuclear fusion?A. Nuclear fission uses uranium, and nuclear fusion uses hydrogen.B. Nuclear fission joins nuclei, and nuclear fusion splits them.C. Nuclear fission produces energy from matter, and nuclear fusionproduces matter from energy.D. Nuclear fission produces radioactive waste, and nuclear fusiondoes not.
Option (A) is correct. As nuclear fission uses heavy nuclei to break into smaller fragments whereas nuclear fusion uses lighter nuclei to make heavier nuclei.
An ant climbs vertically on a fence. Its motion is shown on the following graph of vertical position � yy vs. time � tt. Graph of y (in meters) vs. t (in seconds) that starts at 6 m at 0sec, decreases linearly to 2m at 4 sec, stays constant at 2m from 4 sec to 7 sec, increases linearly to 5 m from 7 sec to 9 sec, then stays constant until 10 sec. Graph of y (in meters) vs. t (in seconds) that starts at 6 m at 0sec, decreases linearly to 2m at 4 sec, stays constant at 2m from 4 sec to 7 sec, increases linearly to 5 m from 7 sec to 9 sec, then stays constant until 10 sec. What is the instantaneous speed of the ant at time � = 8 s t=8 st, equals, 8, start text, space, s, end text?
The instantaneous speed of the ant at t=8s is equal to the slope of the segment between t=7s and t=9s, which is 1.5m/s.
To find the instantaneous speed of the ant at time t=8s, we need to calculate the derivative of the displacement function with respect to time. Since the displacement of the ant is given by a piecewise function, we need to differentiate each segment of the function separately and then piece them together. From 0s to 4s, the displacement of the ant decreases linearly from 6m to 2m. The slope of this segment is -1m/s. From 4s to 7s, the displacement of the ant is constant at 2m. The slope of this segment is zero. From 7s to 9s, the displacement of the ant increases linearly from 2m to 5m. The slope of this segment is 1.5m/s. Finally, from 9s to 10s, the displacement of the ant is constant at 5m. The slope of this segment is zero.
Therefore, the instantaneous speed of the ant at t=8s is equal to the slope of the segment between t=7s and t=9s, which is 1.5m/s. This means that the ant is moving upwards at a constant speed of 1.5m/s at time t=8s. It's important to note that the instantaneous speed of the ant tells us how fast it's moving at a specific moment in time. It's not the same as the average speed over a given time interval, which would be calculated by dividing the total displacement by the total time elapsed.
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