A river current has a velocity of 5 km/h relative to the shore, and a boat moves in the same direction as the current at 5 km/h relative to the river. How can the velocity of the boat relative to the shore be calculated?
A. by subtracting the river current vector from the boat’s velocity vector
B. by dividing the river current vector by the boat’s velocity vector
C. by multiplying the vectors
D.by adding the vectors

Answer:

2.54 seconds

Explanation:

The period of a swing on a playground swing set can be calculated using the formula:

T = 2π√(L/g)

where T is the period, L is the length of the swing's chain, and g is the acceleration due to gravity, which is approximately 9.81 m/s².

Substituting the given values, we get:

T = 2π√(4.0 m/9.81 m/s²)

T = 2π√0.407

T = 2.54 s (rounded to two significant figures)

Therefore, the period of the swing is 2.54 seconds.

Hope this helps!

The acceleration due to gravity near the surface of the hypothetical planet is 3.02 m/s².

The formula for acceleration due to gravity is:

g = GM/r² Where, g = acceleration due to gravity G = universal gravitational constant M = mass of the planet r = radius of the planet

In this case, since the mass of the hypothetical planet is the same as that of Earth, we can use the mass of Earth instead of M.

Therefore, g is proportional to 1/r².

So, using the ratio of radii given (1.8), we can write:

r = 1.8 x r Earth, where r Earth is the radius of Earth.

Substituting this value of r in the formula for acceleration due to gravity, we get:

g = GM/(1.8 x r Earth)² = GM/(3.24 x rEarth²) = (1/3.24)GM/rEarth²

We know that the acceleration due to gravity on Earth (g Earth) is 9.8 m/s².

Therefore, we can calculate the acceleration due to gravity on the hypothetical planet (gh) as follows:

gh = (1/3.24) x g Earth = 3.02 m/s²

Thus, the acceleration due to gravity near the surface of the hypothetical planet is 3.02 m/s².

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Answer:

There are 13 a

Explanation:

That's the answer how many a r there

Answer:

the convex mirror will produce image 3. the image is virtual and is now behind the mirror and it becomes smaller but remains upright.

Explanation:

The equivalent resistance of the circuit shown  is 23 ohms.

Option A is correct.

Resistance is  described as the opposition that a substance offers to the flow of electric current.

In a series circuit, all components are connected end-to-end to form a single path for current flow.

In a parallel circuit, all components are connected across each other with exactly two electrically common nodes with the same volt.

We then 1/R = 1/100 + 1/100 + 1 /(50+ 50) +  1 /(50+ 50)

I/R = 0.04

R = 25 ohms.

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Since the car is accelerating at a constant rate, the distance it travels during each second of its motion will be directly proportional to the time it has been accelerating.

In the first second, the car moved a distance of 2 meters, and in the second second, it will move twice the distance of the first second, so the car will move additional distance of 2*2 = 4 meters during the second second of its motion.

The distance traveled during the second second of its motion is 1/2 * 2 = 1 meters.

A car that accelerates at a constant rate will move a distance equal to the initial velocity multiplied by time plus 1/2 the acceleration multiplied by the square of time. Since the car starts from rest, the initial velocity is zero.

Therefore, the distance traveled during the second second is 1/2 * acceleration \(* (time)^2 = 1/2 * a * t^2 = 1/2 * a * 1^2 = 1/2 * a\) Since the car moved 2.0 meters in the first second, it means the acceleration is\(2m/s^2\), and the distance traveled during the second second is 1/2 * 2 = 1 meters.

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Answer:

C. 4.3 seconds

Explanation:

B 0.56 s is the time period of a twirlers baton.

Centripetal acceleration is defined as the property of the motion of an object which traversing a circular path.

Any object that is moving in a circle and has an acceleration vector pointed towards the center of that circle is known as Centripetal acceleration.

The centripetal acceleration is given by:

a = 4π²R/T²

Given values are:

a = 47.8 m/s²

D = 0.76 m  so , R = 0.76/2 = 0.38m

Using this formula,

47.8*T² = 4π² x0.38

T² = \(\frac{4*3.14^2*0.38}{47.8}\)

T = 0.56 s

Therefore,

A twirlers baton is 0.76 m long and spins around its center. The end of the baton has a centripetal acceleration of 47.8 m/s2 which have  time period of 0.56 s.

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.

Explanation:

option b is the correct one

If A 5kg objects is sliding across a floor at 10m/s.then the work done by friction to bring the 5 kg object to a stop is -250 Joules.

To calculate the work done by friction to bring the object to a stop, we need to determine the change in kinetic energy.

Given:

Mass of the object, m = 5 kg

Initial velocity, u = 10 m/s

Final velocity, v = 0 m/s (object comes to a stop)

The work done by friction can be calculated using the equation:

Work = Change in Kinetic Energy

The change in kinetic energy (ΔKE) can be calculated as:

ΔKE = (1/2) * m * (v^2 - u^2)

Plugging in the values:

ΔKE = (1/2) * 5 kg * (0 m/s)^2 - (10 m/s)^2

= (1/2) * 5 kg * (0 - 100 m^2/s^2)

= (1/2) * 5 kg * (-100 m^2/s^2)

= -250 J

The negative sign indicates that the work done by friction is in the opposite direction of the displacement of the object.

Therefore, the work done by friction to bring the 5 kg object to a stop is -250 Joules.

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Answer:

uuuugggghhhhhhhhggggffffffffffffff

Answer:

The geocentric model could not fully explain these changes in the appearance of the inferior planets (the planets between the Earth and the Sun). Furthermore, Galileo's observations of Jupiter's moons made it clear that celestial bodies do move about centers other than the Earth.

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Answer:Newton's first law of motion indicates that an objects motion or lack of motion will stay the same unless acted upon by an unbalanced force.

Explanation:

The gap the boat travels earlier than slowing down is 2.303m/\(αe^2\) v0 ln(10)

The equation of movement for the boat is given through:

m dv/dt = -\(αe^2v\)

in which m is the mass of the boat, v is the rate of the boat, and α is a steady that relies upon at the residences of the water.

To resolve for the rate of the boat as a feature of time, we are able to separate the variables and combine each facets of the equation:

\(m \int\limits v0^v dv / (v*√(1/v)) = -αe^2 ∫ zero^t dt\)

Simplifying the left-hand aspect the usage of the substitution u = 1/v and \(du = -dv/v^2\), we get:

\(-m ∫ 1/v0^1/v du = -αe^2 t\\-m ln(v/v0) = -αe^2 t\\ln(v/v0) = αe^2 t / m\\v(t) = v0 * e^(-αe^2 t / m)\)

To discover the time at which the boat stops, we are able to set v(t) identical to 0 and resolve for t:

\(v(t) = v0 * e^(-αe^2 t / m) = zero\\e^(-αe^2 t / m) = zero\\-αe^2 t / m = -∞\\t = ∞\)

v = zero.1v0 We can resolve for t in this example through putting v(t) = zero.1v0:

\(v(t) = v0 * e^(-αe^2 t / m) = zero.1v0\\e^(-αe^2 t / m) = zero.1\\-αe^2 t / m = ln(zero.1)\\t = -m/αe^2 ln(zero.1)\)

Finally, to discover the gap the boat travels earlier than it slows down, we are able to combine the rate equation from v0 to zero.1v0:

∫ \(x0^x dt = ∫ zero^t v(t) dt\)

in which x0 is the preliminary function of the boat. Substituting for v(t), we get: ∫\(x0^x dx / v(x) = -m/αe^2 ln(zero.1)\)

Using the substitution u = v/v0, we get: ∫ \(1^zero.1 du / u = -m/αe^2\)ln(zero.1)

\(ln(10) = -m/αe^2 ln(zero.1)\\x - x0 = -m/αe^2 ln(zero.1) * ln(10) / v0\\x - x0 = 2.303m/αe^2 v0 ln(10)\)

Therefore, the gap the boat travels earlier than slowing down is 2.303m/\(αe^2\) v0 ln(10). 

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The TV's efficiency rating is 5.56%.

An isolated system has a constant total energy. Energy cannot be generated or destroyed; it can only be transformed from one form to another or transferred between systems. When all energy sources are considered, the overall energy of an isolated system is constant.

Efficiency is equal to (useful energy output/total energy intake) multiplied by 100%.

Useful energy output = light energy output + sound energy output

= 10 kJ + 30 kJ

= 40 kJ

Total energy input = electrical energy input

= 720 kJ

Substituting these values into the efficiency formula, we get:

Efficiency = (40 kJ / 720 kJ) x 100%

= 0.0556 x 100%

= 5.56%

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A fox getting its energy from a mouse and a mouse getting its energy from the grass  shows evidence of the carbon cycle

The carbon cycle is a necessary component within the global interchange between living species and the environment.

Through photosynthesis, plants absorb carbon dioxide from the atmosphere and convert it into vitalizing organic matter for consumption by animals; these organisms expend the energy obtained and consequently expel carbon dioxide back up into the air via respiration.

Moreover, when animals meet their demise and decompose, the carbon in their bodies is redeposited into Earth's soil only to eventually be delivered once again to the atmosphere through erosive activities or those generated from volcanoes.

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The total distance traveled by the object is 3h.

The total distance traveled by the object can be determined by applying the principle of conservation of energy as follows;

Since the object loses half its energy each time it hits the ground.

Hence it will rise half of the previous height each time, as potential energy at height h is given by;

P.E =  mgh

Thus, the object will rise h/2 after the first hit, then h/4 and so on.

Hence the total distance traveled by the object is calculated as follows;

s = h + (h/2 + h/2 + h/4 + h/4 + ---)

s = h + (h + h/2 + ---)

s = h + h(1 + 1/2 + 1/4 + ---)

s = h + h(1 +  (1/1 - 1/2) )

s = 3h

Thus, the total distance traveled by the object is 3h.

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The complete question is below:

An object is dropped from h height. graph v vs h? Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t→∞ is :

Answer:

5.03

Explanation:

trust me

In your business plan, the target market section should clearly identify both your primary and secondary market(s). The market analysis is basically the target market section of your business plan. It is a thorough examination of the ideal people to whom you intend to sell your products or services.

Answer:

EXAMPLE: If the California interstate went all the way to Jupiter and you could drive there going 65 mph, it would take you almost 850 years.

Answer:

E_Phase = 560V

Explanation:

The computation of the voltage i.e. dropped across each phase is shown below:

Given that

The delta connection line voltage is

E_line = 560 V

And, in the case of delta connection, the line voltage would be equivalent to the phase voltage

That means

E_Phase = E_Line

= 560 V

Hence, the voltage i.e. dropped across each phase is

E_Phase = 560V

The current (in amperes) the frying pan draws from the 500 volt circuit, given that it has a resistance of 25 ohms is 60 amperes

From the question given above, the following data were obtained:

The current drawn by the frying pan can be obtained as follow:

Voltage (V) = Current (I) × resistance (R)

Inputting the given parameters, we have:

1500 = Current × 25

Divide both sides by 25

Current = 1500 / 25

Current = 60 amperes

Thus, from the above calculation we can conclude that the current drawn by the frying pan is 60 amperes

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Differentiation

Derivative Rule [Basic Power Rule]:

\(\displaystyle\begin{aligned}f(x) & = cx^n \\f'(x) & = c \cdot nx^{n - 1} \\\end{aligned}\)

Derivative Rule [Chain Rule]:
\(\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)\)

Let's define what the problem gives us:

We know from our trigonometric derivatives that the derivative of \(\displaystyle \sin x\) is equal to \(\displaystyle \cos x\). However, since we have some arbitrary constant \(\displaystyle a\) multiplying \(\displaystyle x\) inside our \(\displaystyle \sin x\) function, we will have to apply the derivative rule of Chain Rule:

\(\displaystyle\begin{aligned}y & = \sin ax \\y' & = \boxed{ \cos (ax) (ax)' } \\\end{aligned}\)

To further simply the derivative, we now apply the derivative rule of Basic Power Rule and simplify:

\(\displaystyle\begin{aligned}y & = \sin ax \\y' & = \cos (ax) (ax)' \\& = (ax)' \cos ax \\& = 1 \cdot ax^{1-1} \cos ax \\& = ax^0 \cos ax \\& = \boxed{ a \cos ax } \\\end{aligned}\)

∴ the derivative of the function \(\displaystyle y = \sin ax\) is equal to \(\displaystyle \boxed{ y' = a \cos ax }\).

___

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Topic: Calculus

Unit: Differentiation

The diameter of the coins are:

The diamater of a shape is the line drawn through its center that divides the shape into equal segments

From the question, we have the following coins

2cedis coin, 20ps, 50ps

These coins are spent in Ghana (an African nation) and they have the following recorded measurements (diameter):

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Answer:

Explanation:

If we make a rather silly assumption that the runner does not leap upward somewhat as he leaves the edge of the first building, his initial vertical velocity is zero.

The time needed to drop 5 meters from vertical rest is

t = √(2s/g) = √(2(5)/9.8) = 1.01 s

so he needs a horizontal speed of at least

v = d/t = 8 / 1.01 = 7.91959...

v = 7.9 m/s. Better make it 8 m/s to be sure he clears the edge and lands on the roof.

Answer:

a. 273 K b. 90.1 K c. 5.26 atm d. 0.33 atm

Explanation:

For isothermal expansion PV = constant

So, P₁V₁ = P₂V₂ where P₁ = initial pressure of gas = 1 atm (standard pressure), V₁ = initial volume of gas, P₂ = final pressure of gas and V₂ = final volume of gas,

So, P₁V₁ = P₂V₂

P₂ = P₁V₁/V₂

Since V₂/V₁ = 0.19,

P₂ = P₁V₁/V₂

P₂ = 1 atm (1/0.19)  

P₂ = 5.26 atm

For an adiabatic expansion, PVⁿ = constant where n = ratio of molar heat capacities = 5/3 for monoatomic gas

So, P₂V₂ⁿ = P₃V₃ⁿ where P₂ = initial pressure of gas = 5.26 atm, V₂ = initial volume of gas, P₃ = final pressure of gas and V₃ = final volume of gas,

So, P₂V₂ⁿ = P₃V₃ⁿ

P₃ = P₂V₂ⁿ/V₃ⁿ

P₃ = P₂(V₂/V₃)ⁿ

Since V₃ = V₁ ,V₂/V₃ = V₂/V₁ = 0.19

1/0.19,

P₃ = P₂(V₂/V₃)ⁿ

P₃ = 5.26 atm (0.19)⁽⁵/³⁾

P₃ = 5.26 atm × 0.0628

P₃ = 0.33 atm

Using the ideal gas equation

P₃V₃/T₃ = P₄V₄/T₄ where P₃ = pressure after adiabatic expansion = 0.33 atm , V₃ = volume after adiabatic expansion, T₃ = temperature after adiabatic expansion  P₄ = initial pressure of gas = P₁ = 1 atm , V₄ = initial volume of gas = V₁ and T₄ = initial temperature of gas = T₁ = 273 K (standard temperature)

P₃V₃/T₃ = P₄V₄/T₄

T₃ = P₃V₃T₄/P₄V₄    

T₃ = (P₃/P₄)(V₃/V₄)T₂

Since V₃ = V₄ = V₁ and P₄ = P₁

V₃/V₄ = 1 and P₃/P₄ = P₃/P₁

T₃ = (P₃/P₁)(V₃/V₄)T₂

T₃ = (0.33 atm/1 atm)(1)273 K  

T₃ = 90.1 K

So,

a. The highest temperature attained by the gas is T₁ = 273 K

b. The lowest temperature attained by the gas = T₃ = 90.1 K

c. The highest pressure attained by the gas is P₂ = 5.26 atm

d. The lowest pressure attained by the gas is P₃ = 0.33 atm

This question involves the concepts of thickness and length.

"40" gold atoms could stack on top of one another in the gold foil.

We will use the unitary method here to find out the no. of gold atoms that could stack on top of each other in the gold foil of thickness 1 x 10⁻⁷ m, when the side length of each cubic atom is 2.5 x 10⁻⁹ m.

Therefore,

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Answer:4m/s2

Explanation:

It is because if we take the equation of force

F=ma so

a=F/m

Put the values

a=400/100

a=4

Unit of the accelaration is m/s2. So

a=4m/s2

The answer is 4 m/s²

The mass is 100 kg

The force is 400N

The acceleration can be calculated as follows

a= force/mass

= 400/100

= 4 m/s²

Hence the object will move quickly at 4 m/s²

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When displaying sections of data, bar charts is used. As long as the number of categories to compare, vertical bar charts can be useful for comparing several category discrete data, like ages, classes, schools.

Charts and graphs are useful visual aids because they make information accessible and quick to understand. So, it is not unexpected that both print and digital media frequently use graphs. When data is displayed as a graph rather than a table, it can often be easier to understand because the graph might show a pattern or comparison.

Visual representations of data, such as tables and graphs, are used to arrange information and reveal patterns and correlations. To present the results of their research, scientists and researchers frequently employ tables and graphs.

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Answer:

the magnitude of the electrostatic force between these two charged particles is 4.32 x 10^-28 N.

Explanation:

F = k * (q1 * q2) / r^2

where:

F is the electrostatic force

k is the Coulomb's constant (9 x 10^9 Nm^2/C^2)

q1 and q2 are the charges of the particles

r is the distance between the particles

Plugging in the given values:

q1 = 8 x 10^-19 C

q2 = 4.8 x 10^-19 C

r = 1.2 x 10^-4 m

k = 9 x 10^9 Nm^2/C^2

we can calculate the electrostatic force:

F = (9 x 10^9 Nm^2/C^2) * (8 x 10^-19 C) * (4.8 x 10^-19 C) / (1.2 x 10^-4 m)^2

F = 4.32 x 10^-28 N

The electrostatic force between these two particles is therefore calculated to be **1.44x10⁻¹⁴ N**1 using Coulomb's equation of electrostatic force.

With a force proportional to the product of the charges and inversely proportional to the square of the distance between them, Coulomb's law states that like charges repel and opposite charges attract. There is a formula that may be used to calculate the force between two point charges. Charles-Augustin de Coulomb created Coulomb's law in 1785

The electrostatic force between two charges is inversely proportional to the square of the distance between them and directly proportional to the product of their magnitudes1.

The centers of the two tiny charged particles in this example are separated by a distance of **1.2x10⁻⁴ meter**, with charges of **8x10⁻¹⁹** and **4.8*10⁻¹⁹**, respectively.

F is the electrostatic force

k is the Coulomb's constant (9 x 10⁹ Nm²C²)

q1 and q2 are the charges of the particles

r is the distance between the particles

Plugging in the given values:

q1 = 8 x 10⁻¹⁹ C

q2 = 4.8 x 10⁻¹⁹C

r = 1.2 x 10⁻⁴ m

k = 9 x 10₉ Nm²/C²

we can calculate the electrostatic force:

F = (9 x 10⁹Nm²/C²) * (8 x 10⁻¹⁹ C) * (4.8 x 10⁻¹⁹ C) / (1.2 x 10⁻⁴ m)²

The electrostatic force between these two particles is therefore calculated to be **1.44x10⁻¹⁴N**1 using Coulomb's equation of electrostatic force.

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The unit of measure of work is (d) Newton meter, which is commonly abbreviated or acronym as Nm or Joule (J). Option D is correct.

The quantity of energy transferred by a force operating via a displacement is referred to as work. It is computed by dividing the amount of force applied in the displacement direction by the length of the force's application. The mathematical formula for work (W) is

W=f×d×cosФ

Theta is the angle between the force vector and the displacement vector. F is the force, d is the displacement, and d is the displacement.

The unit of work, also known as the Newton meter (Nm) or Joule (J), is created by multiplying the force, measured in Newtons, by the distance, measured in meters. In many branches of research and engineering, the Joule is the unit of labor and energy that is most frequently employed.

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The vector product of A=2.00i+3.00j+1.00k and B=1.00i-3.00j-2.00k is C=9.00i+4.00j-9.00k.

To find the vector product (also known as the cross product) of two vectors, A and B, we can use the following formula:

C = A × B

Where C is the resultant vector, A and B are the given vectors, and × denotes the cross product.

Given A = 2.00i + 3.00j + 1.00k and B = 1.00i - 3.00j - 2.00k, we can substitute these values into the formula to find the vector product:

C = (2.00i + 3.00j + 1.00k) × (1.00i - 3.00j - 2.00k)

Now, let's expand the cross product using the properties of vector products:

C = (2.00i × 1.00i) + (2.00i × -3.00j) + (2.00i × -2.00k) +

   (3.00j × 1.00i) + (3.00j × -3.00j) + (3.00j × -2.00k) +

   (1.00k × 1.00i) + (1.00k × -3.00j) + (1.00k × -2.00k)

Now, let's calculate each of these cross products:

C = (2.00 × 1.00) \(i^2\) + (2.00 × -3.00) i × j + (2.00 × -2.00) i × k +

   (3.00 × 1.00) j × i + (3.00 × -3.00) \(j^2\) + (3.00 × -2.00) j × k +

   (1.00 × 1.00) k × i + (1.00 × -3.00) k × j + (1.00 × -2.00) \(k^2\)

Since i × j = k, j × k = i, and k × i = j, we can simplify the expression further:

C = 2.00k - 6.00i + 4.00i - 9.00j + k - 3.00j - 2.00j - 2.00k

Combining like terms, we get:

C = (2.00i + 4.00i) + (-6.00i - 9.00j - 3.00j) + (2.00k + k - 2.00k)

Simplifying further:

C = 6.00i - 12.00j + k

Therefore, the vector product of A and B is C = 6.00i - 12.00j + k, which can be written as C = 9.00i + 4.00j - 9.00k in terms of i, j, and k.

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The vector product of A and B is -3i - 5j - 9k.

The vector product, also known as the cross product, of two vectors A and B is denoted as A x B. It is a vector that is perpendicular to both A and B. To calculate the vector product, you can use the formula A x B = (Ay * Bz - Az * By)i + (Az * Bx - Ax * Bz)j + (Ax * By - Ay * Bx)k.

In this case, we have A = 2.00i + 3.00j + 1.00k and B = 1.00i - 3.00j - 2.00k. Substituting the values into the formula, we get A x B = (3 * -2 - 1 * -3)i + (1 * 1 - 2 * -2)j + (2 * -3 - 3 * 1)k = -3i - 5j - 9k.

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The energy needed to heat the copper from 25 °C  to 45 °C if the specific heat capacity of copper is 380 J/kg °C is 9880 J

ΔT = T - To

ΔT = Change in temperature

T = Final temperature

To = Initial temperature

T = 45 °C

To = 25 °C

ΔT = 45 - 25

ΔT = 20 °C

q = m C ΔT

q = Heat Energy

m = Mass

C = Specific heat capacity

m = 1.3 kg

C = 380 J / kg °C

q = 1.3 - 380 * 20

q = 9880 J

Therefore, the energy needed to heat the copper to 45 °C is 9880 J

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