Assuming a two-tailed hypothesis test with a dependent samples t-test, with a sample size large enough to approximate a normal distribution.
The null hypothesis (H0) states that there is no significant difference between the means of the two samples being compared. The alternative hypothesis (Ha) states that there is a significant difference between the means of the two samples.
If tobt = 2.421 and tcrit = 2.447 at the .05 significance level, we can say that:
The calculated t-value (tobt) falls within the acceptance region (between -2.447 and 2.447) of the null hypothesis.
The critical value (tcrit) falls outside the acceptance region, which means that it lies in the rejection region.
Since tobt falls within the acceptance region, we fail to reject the null hypothesis at the 0.05 level of significance.
Therefore, we conclude that there is not enough evidence to support the claim that there is a significant difference between the means of the two samples at the 0.05 level of significance.
In summary, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim of a significant difference between the means of the two samples being compared.
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Which of the following is a variable property for a gas? Select all that apply.
shape
mass
volume
density
Answer:
volume
Explanation:
mass density and shape are not variable to my view.
pressure volume
number of moles and temperature are variable
The image shows positivle and negative charged particles bouncing around. Which state of matter is most likely represented in the image?
Answer:
Gas Solid Liquid Plasma
Explanation:
Answer:
plasma
Explanation:
plasma has charged particles and ions and electrons floating around
(c) Theory suggests that the rate of cooling of the hot water at any time depends on the
difference between the temperature of the water at that time and room temperature.
(i) State and explain whether your answers in (b) support this theory.
Statement
Explanation
The statement is supported by the evidence that we have from theory of the cooling curve.
Is the statement supported?Heat is transferred from an object to the surroundings when it comes into touch with a cooler environment, such as hot water, until thermal equilibrium is reached. The temperature difference between the object and its surrounds affects how quickly this heat transfer takes place.
The faster heat transmission occurs as hot water cools down in a space, the greater the temperature difference between the water and the ambient temperature. The pace of cooling will initially be rather high when the water is much hotter than the ambient temperature. The temperature differential narrows when the water's temperature approaches that of the room, slowing the rate of cooling.
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Plz I need the answer quick!!!
What is the definition of law of conservation of energy
Answer:
The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy to another. This means that a system always has the same amount of energy, unless it's added from the outside. This is particularly confusing in the case of non-conservative forces, where energy is converted from mechanical energy into thermal energy, but the overall energy does remain the same. The only way to use energy is to transform energy from one form to another.
Explanation:
Hope this helps!
Answer:
means that energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another.
Explanation: this is a shorter answer.
Hooke's Law states that the force that the spring exerts on the mass in a mass-spring system is opposite of and proportional to the displacement of the mass from equilibrium. true or false
Hooke's Law states that the force that the spring exerts on the mass in a mass-spring system is opposite of and proportional to the displacement of the mass from equilibrium. The statement is True.
What is force?The force is an action of push or pull on any object to change the state of motion or rest.
The Hookes's law is related to the spring force. The force F is applied on the mass connected to spring to compress or extend it about the equilibrium position at distance x. When force is removed, the mass attached to the spring moves in opposite direction of force.
The larger the force, longer is the distance from equilibrium position. This concludes that the Hooke's law is correct.
Thus, the statement is True.
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According to Newton, the closer gravitationally interacting objects are to each other, the
A) more the gravitational force between them.
B) less the gravitational force between them.
C) constancy of the force between them.
According to Newton's law of universal gravitation, the closer gravitationally interacting objects are to each other, the more the gravitational force between them. So, the correct option is A.
According to Newton's law of universal gravitation, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Therefore, the closer gravitationally interacting objects are to each other, the stronger the gravitational force between them.
This means that option A, ""more the gravitational force between them,"" is the correct answer.
To understand why this is the case, let's look at the mathematical formula for the gravitational force between two objects:
F = G * (m1 * m2) / r^2
where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
As you can see, the force of gravity is directly proportional to the product of the two masses (m1 * m2). This means that if the masses of the objects remain constant, the force of gravity will increase as the distance between them decreases.
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6. Given cost=0 € (2): a) Determine sin28 b) Which quadrant does sin20 lie and what is the angle to the nearest tenth of a degree? Q
Since cost = 0 €, the value of sinθ will be 1. Recall that the Pythagorean identity for sine and cosine states that sin²θ + cos²θ = 1. So, sin²θ = 1 - cos²θ. Given cost=0 €,cosθ=0. Substituting cosθ = 0, we get;sin²θ = 1 - cos²θ. sin²θ = 1 - 0² = 1Therefore,sinθ = √1 = 1
This means that sin28 = 1 Since sin20 lies in the first quadrant (0° to 90°), it will have a positive value. To determine sin20, we can use a calculator or reference a trigonometric table. To the nearest tenth of a degree, sin20 is 0.3 and it lies in the first quadrant.
An identity that expresses the Pythagorean theorem in terms of trigonometric functions is known as the Pythagorean trigonometric identity, or simply the Pythagorean identity. It is one of the fundamental relations between the sine and cosine functions, along with the sum-of-angles formulas. The angle can be any real value, and the equation is s i n 2 + c o s 2 = 1. Given both the sine value and the quadrant in which the angle is located, we can use the Pythagorean identity to determine the angle of cosine.
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are hotspots active vocanclos
Answer:
Yes
Explanation:
Thus, as a plate moves over the location of a plume eruption, it carries successively older volcanoes with it. As hotspot volcanoes are transported by plate motion away from the mantle plume, hotspot volcanism ceases. Eventually the hotspot volcanoes become extinct, gradually subside, and are eroded by wave action.
Have the best day! :D
Answer:
yes
Explanation:
Thus, as a plate moves over the location of a plume eruption, it carries successively older volcanoes with it. As hotspot volcanoes are transported by plate motion away from the mantle plume, hotspot volcanism ceases. Eventually the hotspot volcanoes become extinct, gradually subside, and are eroded by wave action.
hope this helps!
a sound wave has a frequency of 540 hz. will this wave diffract while passing through an opening of 80 cm?
Yes, the sound wave with a frequency of 540 Hz will diffract while passing through an opening of 80 cm.
This is because the diffraction of a wave is directly proportional to the wavelength of the wave and inversely proportional to the size of the opening. As the wavelength of a sound wave with a frequency of 540 Hz is approximately 0.63 meters, which is much larger than the size of the opening, it will diffract around the edges of the opening.
Hi! A sound wave with a frequency of 540 Hz will indeed diffract while passing through an opening of 80 cm. The extent of diffraction depends on the wavelength of the sound wave and the size of the opening. In this case, the wavelength is longer compared to the size of the opening, which allows for significant diffraction to occur.
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How much potential energy is stored in a spring with a spring constant of 27 N/m if it is stretched by 16 cm
Answer:
PE = 0.35 J
Explanation:
Elastic potential energy in a spring is defined by PE = (1/2)kx^2, where k is the spring constant and x is the distance compressed/stretched. Converting 16 cm to 0.16 m, we get
PE = (1/2) * 27 * (0.16^2)
PE = 0.35 J
Convert gr 1 (grain) to mg
To convert gr 1 (grain) to mg, you would multiply the number of grains by 64.8. Therefore, 1 grain is equal to 64.8 mg.
To convert a measurement from one unit to another, we need to use a conversion factor that relates the two units. In this case, we want to convert from grains (gr) to milligrams (mg).
The conversion factor between grains and milligrams is 1 gr = 64.8 mg. This means that for every 1 grain, there are 64.8 milligrams. We can use this conversion factor to convert any given number of grains to milligrams.
For example, if we have 5 grains and want to know how many milligrams that is, we would multiply 5 grains by 64.8 mg/gr. This gives us:
5 gr * 64.8 mg/gr = 324 mg
So, 5 grains is equal to 324 milligrams.
Similarly, if we want to convert 1 grain to milligrams, we just need to multiply 1 grain by the conversion factor of 64.8 mg/gr. This gives us:
1 gr * 64.8 mg/gr = 64.8 mg
So, 1 grain is equal to 64.8 milligrams.
Therefore, to convert any number of grains to milligrams, we simply multiply the number of grains by 64.8.
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How would I solve this?
(I just started learning about circuits).
Answer:
1) 3A
2) 4.5A
3) 1.5V
4) 5V
HeLp aSAp!!! If the speed and distance of an object are given, and I need to find the time, I will...
A. add the speed and distance
B.divide the speed and distance
C. multiply the speed and distance
Answer:
B - Divide Speed and Distance
Explanation:
Hope it helps!!
:D
A group of students is investigating whether wheels affect the force of friction. The students push two boxes each with the same force on a table. One box has wheels and the
other does not have wheels. The distance traveled by each box is shown.
Experimental Observations
Student 1 Student 2 Student 3 Student 4
Distance traveled by box with wheels
24 cm
22 cm
20 cm
23 cm
Distance traveled by box without wheels
12 cm
14 cm
15 cm
13 cm
Which step should the students take next?
Make a hypothesis
Test another variable
Analyze the results
Share their conclusion
C. analyze the results....
If the wavelength of a 4. 40 ✕ 102 Hz sound in fresh water is 3. 30 m, what is the speed of sound in water?
When, the wavelength of a 4. 40 × 102 Hz sound in fresh water will be 3. 30 m. Then, the speed of sound in fresh water is approximately 1452 m/s.
To determine the speed of sound in water, we can use the relationship between frequency, wavelength, and the speed of sound. The formula is;
speed of sound = frequency × wavelength
Given;
Frequency (f) = 4.40 × 10² Hz
Wavelength (λ) = 3.30 m
By substituting the given values into the formula, we can calculate the speed of sound in water;
Speed of sound = 4.40 × 10² Hz × 3.30 m
When we multiply the frequency by the wavelength, we obtain the speed of sound.
Calculating the product, we get;
Speed of sound = 1452 m/s
Therefore, the speed of sound in fresh water will be approximately 1452. m/s.
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If an airplane is flying 100 mph South but there is a crosswind pushing the airplane 30 mph to the West, then what would the resulting velocity be?
O 104.4 mph, NE
O 104.4 mph, SW
O 10900 mph, NE
O 11.4 mph, SW
The resultant velocity of the plane has a magnitude 104.4 mph and direction south of west .
What do you mean by velocity?The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.The speed at which something moves in a specific direction is known as its velocity. as the speed of a car driving north on a highway or the pace at which a rocket takes off. Because the velocity vector is scalar, its absolute value magnitude will always equal the motion's speed.The plane is flying south at a speed of 100 mph and is blown by a 30mps strong wind due west.
⇒ The angle between the direction of flight of plane and the direction of the wind is 90° .
⇒ By Pythagoras theorem, the resultant speed is
\(\sqrt{100^{2} +30^{2} } =\sqrt{10900}\) =104.4 mph
⇒ The resultant velocity of the plane has a magnitude 104.4 mph and direction south of west
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Una persona cierra una puerta de 1 metro de ancho aplicando una fuerza de 40 [N], perpendicular a ella, a 90 [cm] de su eje de rotación. El módulo del torque aplicado es
Answer:
El módulo del torque aplicado es 36 Nm
Explanation:
En los movimientos rotatorios, la cantidad de fuerza aplicada no depende de la acción gravitacional sino del momento inercial, que es el equivalente angular de la inercia (masa) y representa la resistencia que un objeto ofrece al rotar alrededor de su eje. Cuando un cuerpo rígido rota alrededor de su eje debe considerarse , además de la masa, el radio de giro ya que estos dos factores determinan la resistencia del cuerpo a los cambios de movimiento rotatorio a través de un eje determinado.
De esta manera, se llama torque o momento de una fuerza a la capacidad de dicha fuerza para producir un giro o rotación alrededor de un punto.
En muchas ocasiones el punto de aplicación de la fuerza no coincide con el punto de aplicación en el cuerpo. En este caso la fuerza actúa sobre el objeto y su estructura a cierta distancia, mediante un elemento que traslada esa acción de esta fuerza hasta el objeto. Entonces, el momento de una fuerza es, matemáticamente, igual al producto de la intensidad de la fuerza (módulo) por la distancia desde el punto de aplicación de la fuerza hasta el eje de giro:
M=F*d*sen θ
donde F es la fuerza en Newton (N), d la distancia en metros (m), θ el ángulo que forma la fuerza con el objeto al cual se le aplica la fuerza y M el momento, que se mide en Newton por metro (Nm).
En este caso:
F= 40 Nd= 90 cm= 0.9 m (siendo 100 cm= 1 m)θ= 90° ya que la fuerza se aplica de forma perpendicular. Entonces sen θ= sen 90= 1Reemplazando:
M=40 N*0.9 m* 1
Resolviendo:
M= 36 Nm
El módulo del torque aplicado es 36 Nm
What is the percentage of error that would result from assuming the speed of sound is infinite?
Assuming the speed of sound is infinite would result in a percentage error of 100% because the actual speed of sound is finite and measurable.
The speed of sound refers to the rate at which sound waves propagate through a medium, such as air, water, or solids. It is a fundamental property of the medium and is determined by various factors like temperature, pressure, and density.
When we assume the speed of sound is infinite, we are disregarding its actual finite value and assuming that sound travels instantaneously. This assumption contradicts the well-established understanding of sound as a wave that requires time to propagate through a medium.
Sound waves travel at different speeds in different mediums, and even in the same medium, the speed can vary based on environmental conditions.
The percentage error is calculated by comparing the assumed value to the actual value and expressing the difference as a percentage of the actual value. In this case, since the assumed speed of sound is infinite, and the actual speed is finite, the difference is significant. Thus, the percentage error is 100%.
Assuming an infinite speed of sound can lead to inaccurate predictions and interpretations in various scientific fields, such as acoustics, engineering, and physics. It is important to recognize and account for the actual finite speed of sound when making calculations, designing systems, or analyzing phenomena involving sound propagation.
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What happens to potential energy as the car goes up the hill?
Name a type of food in which convection helps the cooking process. Explain your answer.
Answer: vegetable’s
Explanation: because they have nutrients
Meats and vegetables
Convection is a process by which heat is transferred by movement of a heated fluid such as air or water. Convection is a way in which heat travels.The other methods of heat transfer are conduction and radiation.Convection creates a dry atmosphere that caramelizes the sugars faster when roasting, so foods like meats and vegetables get browner, but the interiors stay moistConvection helps in cooking Meats and vegetables.For more information:
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a 23 g string is under 18 n of tension. a pulse travels the length of the string in 60 ms . part a how long is the string?
The length of the 23 g string is 9.69 m.
Part a : Given values are,Tension = 18 N, Mass of the string = 23 g = 0.023 kg, Time taken = 60 ms = 0.06 s
The formula to calculate the velocity of a wave is as follows:
Velocity of the wave = Tension / Linear mass density
As we know that,
Linear mass density = Mass / Length= 0.023 kg / Length
Where, Length = L
Putting the values of tension and linear mass density in the velocity formula,
18 N = (0.023 kg / L) x V
V = (18 N x L) / 0.023 kg
The formula to calculate the velocity of a wave in terms of length and time is as follows:
Velocity of the wave = Length / Time= L / 0.06 s
Putting the above formula in the previous equation we get,
18 N = (0.023 kg / L) x (L / 0.06 s)
Solving this equation further, we get,
L = (18 N x 0.06 s x L) / 0.023 kg
L² = (18 N x 0.06 s) / (0.023 kg)
L² = 93.913L = 9.69 m
Therefore, the length of the 23 g string is 9.69 m.
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20 BRAILY POINTS Which of the following actions will keep the gravitational force between two objects unchanged? Decreasing the mass of the objects Increasing the temperature of the objects Increasing the distance between the objects Decreasing the distance between the objects
Answer:
Explanation:
See attachment.
Decreasing the mass of the objects No. Force will change.
Increasing the temperature of the objects Yes, No change in force (at most a very small change if the heat causes excessive expansion, reducing the distance, although 1/2 will be further apart)
Increasing the distance between the objects No. Force will change.
Decreasing the distance between the objects No. Force will change.
REAL ANSWERS ONLY HELP
A ball is kicked at 25.0 degrees with respect to the ground with an initial velocity of 15.0 m/s. Calculate the horizontal and vertical components of the velocity.
Answer:
h = v 0 y 2 2 g . This equation defines the maximum height of a projectile above its launch position and it depends only on the vertical component of the initial velocity.
Explanation:
Starting from rest, you pushed a 10.0 kg lawnmower a distance of 25 meters by applying a force of 75 N at an angle 35 degrees below horizontal, as shown below. Use work and energy principles to calculate how fast the lawn mower is moving (in m/s) at the end of the 25 meters.
The lawn mower is moving with a velocity of 17.53 m/s
Energy is the ability to do work while Work is defined as the product of force and distance moved in the direction of the force. Both work and energy are measured in Joule (J)
Work = Force (F) × distance (d) = FdCosθ
With the above formula, we can obtain the energy used in pushing the lawn mower as illustrated below
From the question given above, the following data were obtained:
•Force (F) = 75 N
•Distance (d) = 25 m
•Angle (θ) = 35°
•Energy (E) =?
E = FdCosθ
E = 75 × 25 × Cos 35
E = 1535.91 J
Definition and Determination of the velocityVelocity is the rate of change of displacement with time.
Velocity and energy are related according to the following equation:
E = ½ × mass (m) × square velocity (v²)
E = ½mv²
With the above formula, we can obtain the velocity of the lawn mower as follow
•Mass (m) = 10 Kg
•Energy (E) = 1535.91 J
•Velocity (v) =?
E = ½mv²
1535.91 = ½ × 10 × v²
1535.91 = 5 × v²
Divide both side by 5
v² = 1535.91 / 5
Take the square root of both side
v = √(1535.91 / 5)
v = 17.53 m/s
Thus, the lawn mower is moving with a velocity of 17.53 m/s
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For a rigid body to be in equilibrium, the sum of the forces must equal zero and the sum of the torques must equal zero.a. Trueb. False
The total of the forces and the sum of the torques must both equal zero for a rigid body to be in equilibrium. This statement is true.
Equilibrium refers to a state in which an object is either at rest or moving with constant velocity in a straight line. A rigid body can be in equilibrium only if both the translational and rotational motions are balanced, i.e., the net force acting on the object is zero, and the net torque acting on it is also zero.
The sum of forces acting on a rigid body is known as the net force or the resultant force. According to Newton's second law of motion, the net force acting on a body is equal to the product of its mass and acceleration. If the net force acting on a rigid body is zero, then the acceleration of the body is also zero, and the body is either at rest or moving with constant velocity in a straight line.
Similarly, the sum of torques acting on a rigid body is known as the net torque or the resultant torque. Torque is the rotational equivalent of force and is the product of the force applied and the perpendicular distance from the axis of rotation to the point of application of the force. If the net torque acting on a rigid body is zero, then the body is not rotating, or it is rotating with constant angular velocity.
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Near the critical point of a pure fluid, the Gibbs energy obeys the scaling function λG(t,p)=G(λ a
⋅t,λ a
p) where the reduced temperature, pressure, and volume displacements are t= T c
T c
−T
p= P c
P c
−P
v= V
ˉ
c
V
ˉ
− V
ˉ
c
(a) Differentiation of G with respect to pressure gives the volume displacement, v=( ∂p
∂G
) Use Eqs.(1) and (3) to derive the scaling law for v(t,p) in terms of a t
and a p
. (b) The coefficient of thermal expansion, α p
, is given by α p
=( ∂t
∂v
) Use your result from part (a) to derive the scaling law for α p
(t,p) in terms of a t
and a p
. (c) Use your result from part (b) with p=0 and λ a
⋅t=1 to get the behavior of α p
(t,0) along the critical isobar. (d) The Gibbs energy scaling exponents, a t
and a p
, are related to the experimental coexistence curve exponent, β, and the experimental compressibility exponent, δ, by β= a t
1−a p
and δ= 1−a p
a p
Use Eqs.(5), to express your power law representation for α p
(t,0) in part (c) in terms of the experimental exponent(s). Hint: You will find that the exponent that governs the temperature dependence of α p
(t,0) is independent of δ.
The scaling law for volume displacement, v(t, p), in terms of scaling exponents aₜ and aₚ is given by v(t, p) = aᵥ / (∂G/∂(λₐ⋅t)).
The scaling law for v(t, p) in terms of aₜ and aₚ, we can start with the given expression for the Gibbs energy scaling function:
λG(t, p) = G(λₐ⋅t, λₐ⋅p) ---(1)
We differentiate this equation with respect to pressure (p) while treating t as a constant:
∂(λG)/∂p = (∂G/∂p)⋅(∂(λₐ⋅p)/∂p)
The derivative of λₐ⋅p with respect to p is λₐ. Now, using the relation v = (∂p/∂G), we can rewrite the above equation as:
v(t, p) = (∂p/∂G) = (∂(λG)/∂p) / (∂(λₐ⋅p)/∂p) = (∂G/∂p) / λₐ
Since G is a function of λₐ⋅t and λₐ⋅p, we can express ∂G/∂p as:
∂G/∂p = (∂G/∂(λₐ⋅p))⋅(∂(λₐ⋅p)/∂p)
Plugging this back into the equation for v(t, p), we get:
v(t, p) = (∂G/∂(λₐ⋅p)) / (λₐ⋅(∂(λₐ⋅p)/∂p))
Now, substitute the scaling function λG(t, p) from equation (1) into the above equation:
v(t, p) = (∂(λG)/∂(λₐ⋅p)) / (λₐ⋅(∂(λₐ⋅p)/∂p))
Simplifying further, we obtain:
v(t, p) = (∂(G(λₐ⋅t, λₐ⋅p))/∂(λₐ⋅p)) / (λₐ⋅(∂(λₐ⋅p)/∂p))
Using the chain rule of differentiation, we can rewrite the numerator as:
∂(G(λₐ⋅t, λₐ⋅p))/∂(λₐ⋅p) = (∂G/∂λₐ⋅t)⋅(∂(λₐ⋅t)/∂(λₐ⋅p))
Since (∂(λₐ⋅t)/∂(λₐ⋅p)) = (∂t/∂p), we can further simplify the expression:
v(t, p) = (∂G/∂λₐ⋅t) / (λₐ⋅(∂t/∂p))
Introduce the volume displacement scaling factor aᵥ as:
v(t, p) = aᵥ⋅(∂G/∂λₐ⋅t) / (λₐ⋅(∂t/∂p))
Comparing this equation with the desired form v(t, p) = aₜ⋅(∂t/∂p), we can conclude that:
aₜ = aᵥ / (∂G/
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Two 4 kg blocks hang from a rope that passes over two frictionless pulleys
The tension in the horizontal part of the rope is 39.24 N when the blocks are stationary and the rope has no mass.
What is tension force?The tension force is described as the force transferred through a rope, string, or wire as it is pulled by opposing forces.
The tension force is applied along the whole length of the wire, pulling energy equally on both ends.
The force in the rope is found as;
Tension = mass × acceleration due to gravity
T=mg
T = 4kg × 9.81 m/s²
T = 39.24 N
Hence,the tension in the horizontal part of the rope is 39.24 N
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Match these items.
1. Ca
electron
2. H 2O
fission
3. nuclear decay
atomic number
4. nuclear synthesis
neutron
5. η
proton
6. positive charge
fusion
7. e
element
8. number of protons in nucleus
compound
Answer:
ca is carbon dioxide h20 is water
Explanation:
How long does it take light to reach us from the sun, 1. 50 ×108km away?.
Answer:
8 minutes
Explanation:
It take 8 minutes for light to reach us from the sun.
A charge of 6.5 x 10-5 C is attracted by another charge with a force of 250 N when
they are separated by 0.15 m. Find the magnitude of the other charge.
8.65 X 105 C
9.62 × 10-2 C
6.15 x 10-6 C
O 9.62 x 10 c
Answer:
We can use Coulomb's law to solve this problem:
F = k * q1 * q2 / r^2
where F is the force between the two charges, k is Coulomb's constant (k = 9 x 10^9 N m^2 / C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between them.
We know the force F, the distance r, and the magnitude of one of the charges q1. We can rearrange the equation to solve for the magnitude of the other charge q2:
q2 = F * r^2 / (k * q1)
Substituting the values we have:
q2 = (250 N) * (0.15 m)^2 / (9 x 10^9 N m^2 / C^2 * 6.5 x 10^-5 C)
Simplifying:
q2 = 8.65 x 10^5 C
Therefore, the magnitude of the other charge is 8.65 x 10^5 C.