The space probe Deep Space 1 was launched on October 24, 1998. Its mass was 474 kg. The goal of the mission was to test a new kind of engine called an ion propulsion drive. This engine generated only a weak thrust, but it could do so over long periods of time with the consumption of only small amounts of fuel. The mission was spectacularly successful. At a thrust of 56 mN how many days were required for the probe to attain a velocity of 790 m/s (1770 mi/h), assuming that the probe started from rest and that the mass remained nearly constant

The expression \(X^{N} + Y^{N}\)is not divisible by X - Y (where Y is not equal to 0).

To determine whether the expression \(X^{N} + Y^{N}\) is divisible by X - Y (where Y is not equal to 0), we can use the factor theorem and the property of binomial expansion.

The factor theorem states that if a polynomial P(x) is divisible by (x - a), then P(a) equals zero. In our case, if \(X^{N} + Y^{N}\) is divisible by (X - Y), then when we substitute X = Y into the expression, the result should be zero.

Let's substitute X = Y into the expression:

\(Y^{N} + Y^{N}\)

Since \(Y^{N}\) is equivalent to \(Y^{N}\) , the expression becomes:

2(\(Y^{N}\))

We can see that the expression 2(\(Y^{N}\)) is not equal to zero unless Y is equal to zero. Therefore, if Y is not equal to zero, \(X^{N} + Y^{N}\) is not divisible by X - Y.

In summary, unless Y is equal to zero, the expression \(X^{N} + Y^{N}\) is not divisible by X - Y according to the factor theorem and the given condition.

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Answer:

M g = M a = a (9 - 7) kg      with the two masses going in different directions

(7 + 9) kg * g = a * 2 kg       2 kg effective in prducing acceleration

a = 16 / 2 * g = 9.8 m/s^2 / 8 = 1.23 m/s^2

M1 a = T - M1 * g        T producing upward acceleration of 1.23 m/s^2

T = 7 (a + g) = 7 * 11 = 77 N

Check:

M2 a =  M2 * g - T          M2 producing downward acceleration

T = M2 (g - a) = 9 * (9.8 - 1.23) = 77 N

First option is correct.Larry the Rock is going through Static Equilibrium.

In this situation, Larry is at rest and remains stationary despite the forces acting on him. While David and Pancho are exerting equal forces from opposite sides, their forces cancel each other out, resulting in a net force of zero. As a result, Larry does not move or experience any acceleration.

Static equilibrium occurs when an object's forces and torques balance each other, leading to a stable, balanced state. In this case, the forces exerted by David and Pancho are equal in magnitude and opposite in direction, creating a condition where the resultant force is zero. As a result, Larry remains in a state of rest, unable to experience any movement or acceleration.Therefore, the type of equilibrium that Larry the Rock is going through is Static Equilibrium.

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To calculate the final temperature of an air-metal mixture, we need to use the principle of heat transfer.

The heat transfer equation states that the heat gained by the metal is equal to the heat lost by the air. This equation can be written as:

mcΔT = mairCpΔT

To make a prediction of the final temperature, we need to consider factors such as the thermal conductivity of the metal and air, the specific heat capacities of the materials, and the heat transfer coefficients at the metal-air interface. Additionally, the shape and size of the metal object and the surrounding environment can affect the final temperature.

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The given scenario involves calculating the acceleration of an object propelled by a force of 10 N with a mass of 30 kg. The object will accelerate at a rate of 0.333 m/s².

The equation for calculating acceleration is:

acceleration = force / mass

where acceleration is measured in meters per second squared (m/s²), force is measured in Newtons (N), and mass is measured in kilograms (kg).

Given:

mass = 30 kg

force = 10 N

To find the acceleration, we can substitute these values into the equation:

acceleration = force / mass

acceleration = 10 N / 30 kg

acceleration = 0.333 m/s²

Therefore, the object will accelerate at a rate of 0.333 meters per second squared. This means that for every second that passes, the object's velocity will increase by 0.333 meters per second.

It's worth noting that the direction of the force is also important in determining the direction of the acceleration. If the force is applied in the same direction as the motion of the object, it will speed up, but if the force is applied in the opposite direction, it will slow down.

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Answer:

Let's start by calculating how much of a head start Car A has in distance before Car B starts.

In 3 minutes, Car A will have travelled:

d = r * t = (60 km/h) * (3/60) h = 3 km

So when Car B starts, Car A is 3 km ahead.

Now let's consider the time it takes for both cars to meet. Let's call the time it takes for both cars to meet t.

During that time, Car A will travel at a speed of 60 km/h, and Car B will travel at a speed of 70 km/h.

The distance that Car A will travel during that time is:

dA = 60 km/h * t

The distance that Car B will travel during that time is:

dB = 70 km/h * t

The total distance between the two cars when they meet is:

d = dA + dB

We want to find the value of t that makes dA + dB = 3 km (the distance that Car A is ahead of Car B when Car B starts).

Substituting the expressions for dA and dB, we get:

60 km/h * t + 70 km/h * t = 3 km

Simplifying, we get:

130 km/h * t = 3 km

t = 3 km / 130 km/h

t = 0.0231 h

Now we can calculate the distance that both cars will have travelled when they meet:

dA = 60 km/h * 0.0231 h = 1.38 km

dB = 70 km/h * 0.0231 h = 1.61 km

d = dA + dB = 1.38 km + 1.61 km = 2.99 km

Therefore, the two cars will draw level after travelling approximately 2.99 km from the starting point.

Answer:

10 Newtons.

Explanation:

F=MA

F=(5kg)(2 m/s^2)

10 N

Answer:

control

Explanation:

you always need a control in experiment

The quantity of heat energy that must be transferred to 2.25 kg of brass to raise its temperature from 20 °C to 240 °C is 195030 J

First, we shall list out the given parameters from the question. This is shown below:

The quantity of heat energy that must be transferred can be obtained as follow:

Q = MCΔT

= 2.25 × 394 × 220

= 195030 J

Thus, we can conclude quantity of heat energy that must be transferred is 195030 J

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The moment M applied to the disc to hold the system in equilibrium is 0.09 Nm.

To calculate the moment M applied to the disc that holds the system in equilibrium, we can use the principle of moments. The principle of moments states that the sum of the clockwise moments about a point is equal to the sum of the counterclockwise moments about the same point.

Let's consider point C as the pivot point. The clockwise moments are produced by the weight of BC and the unknown moment M, while the counterclockwise moments are produced by the weight of AB.

The weight of BC can be calculated as W_BC = linear density * length = 1 kg/m * 0.3 m = 0.3 kg.

The clockwise moment is given by M_clockwise = W_BC * BC = 0.3 kg * 0.3 m = 0.09 Nm.

Since the system is in equilibrium, the clockwise moments must balance the counterclockwise moments. Therefore, the counterclockwise moment produced by the weight of AB is also 0.09 Nm.

Hence, the moment M applied to the disc to hold the system in equilibrium is 0.09 Nm.

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Answer: The correct option is D ( stopping time is longer on the carpet).

Explanation:

When an object is involved in a collision, for a given amount of TIME, it experiences a FORCE that will result in its MASS undergoing a change in VELOCITY. The relationship between the fours physical quantities in the sentence above are found in impulse and momentum.

Momentum is defined as the product of the mass of the body and it's velocity while impulse is the product of force and time. The impulse experienced by an object is always equal to the change in its momentum. This is known as IMPULSE-MOMENTUM CHANGE THEOREM and it can be represented in the equation below :

Impulse= Force× time(t)

Change in Momentum = Mass(M) × velocity change ( v - u).

Therefore: F×t = M ( v - u).

In the application of impulse-momentum change in real life situations, force exerted on an object is affected by the collision time because force is inversely proportional to time. That is, the greater the time over which a collision occurs, the smaller the force acting upon the object. Thus, to minimize the effect of force on an object involved in a collision, the time must be increased.

From the example given, the wine glass may not break when it falls on a carpeted floor because the carpet minimize the effect of force on the glass by increasing its stopping time.

Regarding memory, conscious is to explicit memory as unconscious is to implicit memory.

The voltage across the inductor will be 98.361 volts.

Inductor is a passive component used in most power electronic circuits to store energy in the form of magnetic energy when electricity is applied to it.

In inductive reactance (RL), the current through the inductor changes when a potential difference is developed across it.

The potential difference and the rate of change of the current are proportional to each other.

Mathematically, V = \(\sqrt{Vr^{2} + Vl^{2} }\)

Vr = 85 v

V = 130 v

Vl can be calculated as

Vl² = V² - Vr²

Vl² = 130² - 85²

Vl² = 16900 - 7225

Vl² = 9675 v

Vl = 98.361 v

The voltage across the inductor is 98.361 v.

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The diameter of the smaller end of the pipe is approximately 0.78 meters.

To determine the diameter of the smaller end of the pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate of water should remain constant throughout the pipe.

The mass flow rate is given by the equation:
Mass flow rate = density of water * cross-sectional area * velocity

Since the density of the water remains constant, we can write:
Cross-sectional area1 * velocity1 = Cross-sectional area2 * velocity2

Given that the velocity1 is 13 m/s, the diameter1 is 1.2 m, and the velocity2 is 30 m/s, we can solve for the diameter2 using the equation:
(pi * (diameter1/2)^2) * velocity1 = (pi * (diameter2/2)^2) * velocity2

Simplifying the equation:
(1.2/2)^2 * 13 = (diameter2/2)^2 * 30

Calculating the equation:
(0.6)^2 * 13 = (diameter2/2)^2 * 30

0.36 * 13 = (diameter2/2)^2 * 30

4.68 = (diameter2/2)^2 * 30

Dividing both sides by 30:
0.156 = (diameter2/2)^2

Taking the square root of both sides:
0.39 = diameter2/2

Multiplying both sides by 2:
0.78 = diameter2

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Answer:

Emotional and Social Development

During the preschool years, your little one is learning to read emotional cues and is getting better at relating to other people, according to the New York University Child Study Center 1⭐

⭐This is a verified and trusted source

New York University Child Study Center: The Preschool Years: (Ages Four and Five) Expectations and Challenges

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. He can empathize with others and make friends with other children his own age. By his fifth birthday, your preschooler often seeks friends of the same gender and shows a preference for playing with other children, rather than adults. Your preschooler also engages in pretend play and can probably tell the difference between reality and fantasy, according to the American Academy of Pediatrics.

Physical Development

There's a big difference between a 2-year-old and a 5-year-old. During the preschool years, your child develops in many physical ways. She goes from toddling around unsteadily to being able to jump, stand on one foot, walk up and down stairs and walk backward, according to the New York University Child Study Center 1⭐

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New York University Child Study Center: The Preschool Years: (Ages Four and Five) Expectations and Challenges

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. By the time she's 5, your little one should also be able to ride a tricycle, build a block tower, paint on paper, skip, throw a ball, dress and undress and begin drawing recognizable objects, adds the University of Illinois Extension.

The density of water is approximately 1 g/cm^3. Therefore, the volume of 2800 g of water would be 2800 cm^3 because density is mass/volume, and so volume is mass/density.

Since this volume is inside a cubic box, the length of each side of the cube (a, for instance) could be found by taking the cubic root of the volume. This is because the volume of a cube is calculated by a^3 (length of one side cubed). Hence, a = cube root of 2800 cm^3 ≈ 14.1 cm.

Converting centimeters to meters (as 1 meter is equal to 100 centimeters), we get approximately 0.141 meters.

So the filled cubic box has a side length of approximately 0.141 m.

Answer:    

2 : A large storm

Explanation: I hope this helps

Answer:

Data that we know:

Mass of the car = 950kg.

Gravitational acceleration = -9.8m/s^2.

Acceleration of the car = -1.2 m/s^2.

(the negative signs are because that accelerations point downwards)

Now, the total acceleration of the car is:

-1.2m/s^2 = -9.8m/s^2 + Ac.

Where Ac is the acceleration caused by the cable, that is opposite to the acceleration of the car:

Ac = 9.8m/s^2 - 1.2m/s^2 = 8.6m/s^2.

Now we have the accelerations, remember that by second's newton law we have:

F = m*a

Then the force of the cable is:

Fc = 8.6m/s^2*950kg = 8,170N.

The gravitational force is:

Fg = -9.8m/s^2*950kg = -9,310N

The net force is:

Ft = 8,170N - 9,310N = -1,140N.

Below is the free body-diagram.

Answer:

g = 0.0114 m/s²

Explanation:

The value of acceleration due to gravity on the surface of the moon can be given by the following formula:

\(g = \frac{Gm}{r^2}\)

where,

g = acceleration due to gravity on the surface of moon = ?

G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²

m = mass of moon = 4.2 x 10¹⁶ kg

r = radius of moon = 1.57 x 10⁴ m

Therefore,

\(g= \frac{(6.67\ x\ 10^{-11}\ N.m^2/kg^2)(4.2\ x\ 10^{16}\ kg)}{(1.57\ x\ 10^4\ m)^2}\)

g = 0.0114 m/s²

Answer:

\(35.0\; \rm m \cdot s^{-1}\).

Explanation:

The question states that the rocket gains speed steadily. In other words, the acceleration of this rocket in that four seconds would be constant.

Using information from the question:

Apply the SUVAT equation \(\displaystyle \frac{1}{2}\, a \cdot t^{2} + v_{0}\cdot t = x\) to find \(a\), the acceleration of this rocket.

\(\displaystyle \frac{1}{2}\, a \times (4.00\; {\rm s})^{2} + 0 = 70.0\; \rm m\).

\(\begin{aligned}a &= \frac{70.0\; \rm m}{\displaystyle \frac{1}{2} \times (4.00\; {\rm s})^{2}} = 8.75\; \rm m \cdot s^{-2}\end{aligned}\).

In other words, this rocket accelerated from rest at a constant \(a = 8.75\; \rm m \cdot s^{-2}\) for \(t = 4.00\; \rm s\). The final velocity of this rocket would be:

\(\begin{aligned}& v_{0} + a\cdot t \\ =\; & 0 \; \rm m\cdot s^{-1} + 8.75\; \rm m\cdot s^{-2} \times 4.00\; \rm s \\ =\; & 35.0\; \rm m\cdot s^{-1}\end{aligned}\).

The inverse of the mass is referred to as acceleration. The acceleration will be slower the more mass there is.

Acceleration is the rate of change in an object's velocity over time in mechanics. One of the vector quantities is speed. The direction of the net force exerted on an object is what determines its acceleration. The change in velocity rate is referred to as acceleration. Usually, but not always, acceleration implies a change in velocity.

A circular object moving at a constant velocity is still accelerating because its velocity is changing in the opposite direction. In physics, acceleration is the rate of change in an object's velocity over time.  According to Newton's second law, the sum of all forces acting on an object determines its acceleration. Meters per second (ms²) is the SI unit for acceleration.

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Answer:

Fossil fuels are energy sources that come directly from nature. First, the sun's radiant energy is stored as chemical energy in plants by photosynthesis. When the plants die, they start decaying. After many years, the plants are turned into fossil fuels.

Explanation:

Fossil fuels rely on the Sun's energy because the energy in fossil fuels came from plants and algae as they performed photosynthesis, which requires sunlight.

When sunlight strikes a plant, some of the energy is trapped through photosynthesis and is stored in chemical bonds as the plant grows.

(u should paraphrase it)

Answer:

a)   P' = P_original, b)  P ’= P_original + ρ  g Δh

Explanation:

The expression for nanometric pressure is

          P = ρ g h

where ρ  is the density of the liquid and h is the height

a) we change the radius of the barrel, but keeping the same height

as the pressure does not depend on the radius it remains the same

        P' = P_original

b) We change the barrel height

         h ’≠ h

we substitute in the equation

      P ’= ρ  g h’

      h ’= h + Δh

      P ’= ρ  g (h + Δh)

      P ’= (ρ  g h) + ρ  g Δh

      P ’= P_original + ΔP

In this case, the pressure changes due to the new height,

*if it is higher than the initial one, the pressure increases

*if the height is less than the initial one, the pressure is less

The owl started out at a height of about 3.2 metres.

Gravity is the force that draws objects toward the center of a planet or other object.

Gravitational potential energy (GPE) is calculated as follows:

GPE = mass x gravity x height. Since we are aware of the owl's mass (4 kg) and the change in GPE (-800 J) in this case, we can rewrite the formula to account for the height: tallness = GPE / (mass x gravity).

On Earth, the acceleration caused by gravity is roughly 9.8 m/s2.

By entering the known numbers, we obtain the height change as follows: -800 J / (4 kg x 9.8 m/s2) = -0.408 metres.

By combining the ultimate height (which is believed to be 0 metres) with the height change, we may get the initial height as follows: 0 m + (-0.408 m) = -0.408 m = 0.408 m = 3.2m.

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The current I through the 4 kΩ resistor in the original circuit is 0.199 mA.

Thévenin's theorem states that any linear network of voltage and current sources and resistors can be replaced by an equivalent circuit consisting of a single voltage source and a single resistor. The equivalent circuit provides the same output voltage and current as the original circuit for any external load connected to it.

To find the current I in the circuit using Thévenin's theorem, we need to follow these steps:

Step 1: Find the Thévenin equivalent voltage (Vth) across the 4 kΩ resistor.

To find Vth, we need to first find the open circuit voltage (Voc) across the 4 kΩ resistor. We can do this by removing the 4 kΩ resistor and finding the voltage between its two terminals using a voltage divider:

Voc = 6 kΩ/(2 kΩ + 6 kΩ) x 2 mA = 1.2 V

Next, we need to find the Thévenin equivalent resistance (Rth) across the 4 kΩ resistor. To do this, we need to short-circuit all the independent voltage sources (in this case, there is only one) and find the equivalent resistance seen from the terminals of the 4 kΩ resistor. With the 2 mA current source shorted out, the 2 kΩ and 4 kΩ resistors are in parallel:

Rth = 2 kΩ || 4 kΩ = 1.33 kΩ

Step 2: Replace the original circuit with the Thévenin equivalent circuit.

We can now replace the original circuit with the Thévenin equivalent circuit, which consists of a voltage source Vth = 1.2 V in series with a resistor Rth = 1.33 kΩ.

Step 3: Find the current I through the 4 kΩ resistor in the Thévenin equivalent circuit.

To find the current I, we can use Ohm's law:

I = Vth/(Rth + 4 kΩ) = 1.2 V/(1.33 kΩ + 4 kΩ) = 0.199 mA

Therefore, the current I through the 4 kΩ resistor in the original circuit is 0.199 mA.

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Answer:

Explanation is given

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After 0.100 s, the cat would be 0.049 m below its initial position, with a velocity of 0.98 m/s. After 0.200 s, the cat would be 0.196 m below its initial position, with a velocity of 1.96 m/s. Finally, after 0.300 s, the cat would be  0.441 m below its initial position, with a velocity of approximately 2.94 m/s.

To calculate the position and velocity of the sleeping cat after certain time intervals, we need to make some assumptions and use basic principles of physics.

Assuming the cat falls vertically downward due to gravity and ignoring air resistance, we can apply kinematic equations to solve the problem.

(a) Position:

Using the equation for the position of an object in free fall, h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is time, we can determine the position of the cat.

After 0.100 s: h = (1/2)(9.8 m/s^2)(0.100 s)^2 = 0.049 m (approximately)

After 0.200 s: h = (1/2)(9.8 m/s^2)(0.200 s)^2 = 0.196 m (approximately)

After 0.300 s: h = (1/2)(9.8 m/s^2)(0.300 s)^2 = 0.441 m (approximately)

(b) Velocity:

The velocity of the cat can be calculated using the equation v = gt, where v is the velocity and t is time.

After 0.100 s: v = (9.8 m/s^2)(0.100 s) = 0.98 m/s (approximately)

After 0.200 s: v = (9.8 m/s^2)(0.200 s) = 1.96 m/s (approximately)

After 0.300 s: v = (9.8 m/s^2)(0.300 s) = 2.94 m/s (approximately)

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The centripetal force acting on the small piece of dried cement is 0.01 N   when mass 50 g stuck to the inside wall of mixer.

Any force that alters velocity in the direction toward the center of a circular motion is referred to as a centripetal force. The centripetal force is produced by the portion of the force that is perpendicular to the velocity.

The period of the cement mixer can be calculated as:

                                T = 50 sec/rev

                                     = 2πr/v,

where r is the radius of the mixer and

v is the velocity of the piece of dried cement.

Solving for v, we get v = 2πr/T.

Substituting the given values, we get

                               v = 2π(2.5 m)/(50 sec/rev)

                                         = 0.314 m/s.

The centripetal force acting on the piece of dried cement can be calculated using the formula :

                                     F = m v² / r,

where m is the mass of the cement,

v is the velocity, and

r is the radius of the mixer.

Substituting the given values, we get

                                 F = (0.05 kg)(0.314 m/s)²/(2.5 m)

                                                      = 0.01 N.

Therefore, the centripetal force acting on the small piece of dried cement is 0.01 N.

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Answer:

Refractive index of the plastic = 1.46

Explanation:

By Snell's law,

\(\frac{\text{sin}\theta _{2} }{\text{sin}\theta _{1}}=\frac{n_1}{n_2}\)

Here, \(\theta _1\) = Angle of incidence in medium 1 (Plastic)

\(\theta_2\) = Angle of refraction in medium 2 (Water)

\(n_1\) = Refractive index of medium 1 (Plastic)

\(n_2\) = Refractive index of medium 2 (Water)

By substituting values in the formula,

\(\frac{\text{sin}(48.7)}{\text{sin}(55.5)}=\frac{1.33}{n_2}\)

\(n_2=\frac{1.33\times \text{sin}(55.5)}{\text{sin}(48.7)}\)

    = 1.46

Therefore, refractive index of the plastic = 1.46

The skater's final angular velocity is approximately 9.86 rad/s.

The skater's final angular velocity can be calculated using the principle of conservation of angular momentum. The equation for angular momentum is given by:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Initially, the skater has an angular momentum of:

L_initial = I_initial * ω_initial

Substituting the given values:

L_initial = 2.12 kg m² * 3.25 rad/s

The skater's final angular momentum remains the same, as angular momentum is conserved:

L_final = L_initial

The final moment of inertia is given as 0.699 kg m². Therefore, the final angular velocity can be calculated as:

L_final = I_final * ω_final

0.699 kg m² * ω_final = 2.12 kg m² * 3.25 rad/s

Solving for ω_final:

ω_final = (2.12 kg m² * 3.25 rad/s) / 0.699 kg m²

Hence, the skater's final angular velocity is approximately 9.86 rad/s.

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