Using the definition of the scalar product, find the angles between (b) →A = -2i^ + 4j^ and →B = 3i^ - 4j^ + 2k^ ,

The speed of the cars immediately after the collision will be the same as their speed before the collision, which is 14.6 m/s. In a perfectly inelastic collision, the objects involved in the collision will move together with the same speed after the collision as they had before the collision. This is because the total kinetic energy of the system is conserved in a perfectly inelastic collision.

Answer:

it is less than the trucks initial acceleration because a truck going downhill  has a enough speed and power to turn a car into a pancake so in this case (trucks always win)

Explanation:

Given parameters:

Displacement = 8km

Velocity  = 3.8km/h

Unknown:

time  = ?

Solution:

Velocity is displacement divided by time.

  Velocity  = \(\frac{displacement}{time}\)  

      Displacement  = velocity x time

Input the parameters:

              8  = 3.8  x time

 Time  = \(\frac{8}{3.8}\)   = 2.1s

The time taken is 2.1s

Answer:

for students to do nothing

Explanation:

because doing nothing is not a course goal

The number of people who watch the State of the Union speech varies annually but usually amounts to millions. The State of the Union speech is an annual address delivered by the President of the United States to a joint session of the United States Congress.

Given that this speech is a major national event, it is expected that a significant number of people tune in to watch it. The exact number of people who watch the State of the Union speech varies each year depending on various factors such as the popularity of the president, the issues discussed, and the media coverage.

However, according to Nielsen, a media research firm, approximately 37.2 million people watched the 2019 State of the Union speech delivered by President Donald Trump. This was a decline from the 45.6 million viewers who watched the speech in 2018. Nonetheless, the viewership was still high, indicating that the speech remains an important event in the US political calendar.

In conclusion, the number of people who watch the State of the Union speech varies annually but usually amounts to millions.

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If there are on average 55 grains of sand per mm³, then there would be a total of 5500000000 grains of sand if the sandbox is full.

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis.

As given in the problem, a child's sandbox is 1.0 meter wide, 1.0 meter long, and 10.0 cm deep,

The volume of the sandbox = length ×width ×depth

                                              = 1000×1000×100

                                              = 100000000 mm³

The average number of sand grains  in 1 mm³ = 55

The average number of sand in 100000000 mm³ = 5500000000

Thus, there would be  5500000000 sand grain particles in the sandbox.

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If we rearrange the circuit so that the inductor and capacitor were connected in series,the impedance would be  Decreased and the resonant frequency would be unchanged.

What is frequency?

Frequency is the rate at which something occurs over a particular period of time or in a given sample.

Sol-An LC circuit is made up of an inductor (L) and a capacitor (C). At the resonance condition of the LC circuit, the inductive reactance XL. becomes equal to the capacitive reactance Xc.

It is defined as-

XL= 2πfL

Xc= 1/2πfC

So when reactance are equal we have-

XL=Xc

2πfL= 1/2πfC

f^2=1/4π^2LC

f=1/2π√LC

The resonance condition is the same for both the parallel and series LC circuit, so the resonance frequency will not change.

The impedance of a parallel LC circuit is:

Z(w)= jL w^2-w^2•/w

In a series LC circuit, when w

, the impedance becomes equal to 0.

Therefore the impedance of a series LC circuit will decrease and the resonant frequency will remain the same.

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The equivalent resistance between points A and B in the diagram is 22 Ω

We shall begin by obtaining the equivalent resistance in parallel (i,e the three 6 Ω resistor). Details below:

1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃

1/Rₜ = 1/6 + 1/6 + 1/6

1/Rₜ = 3/6

1/Rₜ = 1/2

Rₜ = 2 Ω

Finally, we shall determine the equivalent resistance between A and B (i.e series arrangement). Details below:

R = R₁ + R₂ + R₃ + R₄ + R₅ + R₆ + R₇ + R₈ + R₉ + R₁₀ + R₁₁

R = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2

R = 22Ω

Thus, we can conclude that the equivalent resistance is 22 Ω

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When a beam of light travels from air into water, it bends due to the difference in the speed of light in the two mediums. The angle at which the beam of light enters the water, known as the incident angle, is denoted by θa. In this case, the incident angle is 32 degrees.

The index of refraction of water is n w 1.3, which means that light travels 1.3 times slower in water than in air. The index of refraction of air is na 1, which means that light travels at its fastest speed in air. When light enters a medium with a different refractive index, it bends according to Snell's law, which states that the ratio of the sines of the incident and refracted angles is equal to the ratio of the indices of refraction of the two mediums. Mathematically, this can be written as Using this formula, we can find the refracted angle θ at which the beam of light travels in the water. Plugging in the values given, we get Solving for -22 degrees. This means that the beam of light bends towards the normal (the line perpendicular to the surface of the water) and travels at an angle of -22 degrees in the water. In conclusion, when a beam of light enters water at an incident angle of 32 degrees, it refracts towards the normal and travels at an angle of -22 degrees in the water. The index of refraction of water, which is 1.3, is responsible for this bending of the light.

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The best method for monitoring the effects of heat would be B. infrared scanners. The effects of heat can be effectively monitored using infrared scanners, making option B the most suitable choice.

Infrared scanners detect and measure the infrared radiation emitted by objects based on their temperature. This allows them to visualize and analyze the distribution of heat in various systems and materials. By using infrared scanners, it becomes possible to identify hotspots, temperature variations, and potential issues caused by excessive heat.

While lasers can be used for certain applications such as temperature measurements, they are not the most suitable choice for monitoring the effects of heat in general. Laser thermometers, for instance, can measure the temperature of a specific spot but may not provide a comprehensive overview of the entire system or material.

Vibration analysis, on the other hand, is primarily used for monitoring mechanical vibrations and diagnosing issues related to machinery, rather than specifically assessing the effects of heat.

Similarly, ultrasonics primarily involve the use of sound waves for imaging and detecting objects, and although they can be useful in certain contexts, they are not specifically designed for monitoring the effects of heat.

Therefore, infrared scanners, with their ability to detect and analyze thermal radiation, offer the most effective and comprehensive means of monitoring the effects of heat.

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The magnitude of the total friction force exerted by the road on the tires at B will be 919.46 lb.

It is a type of opposition force acting on the surface of the body that tries to oppose the motion of the body. Its unit is Newton (N).

Mathematically, it is defined as the product of the coefficient of friction and normal reaction.

The given data in the problem is;

The weight is,W= 3,220 lb

The speed is,u= 60 mi/hr

The reducing speed is,v= 45 mi/hr

The distance traveled is,d= 300 ft

The radius of curvature of the path of the car at B is,R= 600 ft.

1 mile = 5280 ft

From the Newtons' equation of motion;

\(\rm v^2 = u^2 +2ad \\\\ \rm (45 \times \frac{5280}{3600} )^2 = (60 \times \frac{5280}{3600} )^2 +2a\times 300 \\\\\)

The tangential accelerations are;

\(\rm a_t = \frac{66^2 -88^2}{600} \\\\ \rm a_t = -5.65 ft/sec^2 \\\\\)

The force is found as;

\(\rm \sum F = ma \\\\ \frac{3220}{32.2} \times -5.65 \\\\ F_T= 565 \ lb\)

The normal force  is;

\(\rm F_n = \frac{3220}{32.2} \times \frac{66^2}{600} \\\\ F_N =726 \ lb\)

The net or the total friction force exerted by the road on the tires at B. is found as;

\(\rm F = \sqrt{(565)^2+(726)^2} \\\ F = 919.946 \ lb\)

Hence, the magnitude of the total friction force exerted by the road on the tires at B will be 919.46 lb.

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To increase the torque applied to a stubborn bolt, you would need more applied force and/or more lever-arm.

Option B is correct. By using a longer wrench or adding a cheater bar to the wrench, you can increase the lever-arm and therefore the torque applied. Additionally, using a breaker bar or impact wrench can increase the applied force and help to loosen the stubborn bolt.

Option A is not correct as only increasing the applied force may not be enough to break the bolt loose.

Option C is not correct as the applied torque can indeed be increased. Option D is not correct as reducing the applied force and lever-arm would decrease the torque applied.
To increase the torque applied to a stubborn bolt, you need both more applied force and more lever-arm. This is because torque is the product of force and lever-arm, and increasing both of these factors will result in a higher torque, making it easier to loosen the stubborn bolt.

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Miranda, one of Uranus's moons, displays the widest range of surface terrains, suggesting some catastrophic disruption.

Miranda is the smallest and innermost of the five major moons of Uranus. It is known for its highly varied and fragmented surface, which indicates a history of intense geological activity.

The range of surface terrains observed on Miranda suggests that it has undergone significant cataclysmic disruptions in its past.

One prominent feature on Miranda is the "Coronae," which are large and distinct regions of tectonic activity. These coronae are characterized by parallel ridges and valleys that have been folded and deformed, indicating intense geological forces.

The presence of these coronae suggests that Miranda experienced extreme tectonic activity, likely as a result of past catastrophic disruptions.

Another noteworthy feature on Miranda is the "Verona Rupes," a massive cliff that reaches heights of up to 20 kilometers (12 miles). This cliff is one of the tallest known in the solar system, suggesting significant tectonic forces that may have caused the crust to crack and shift, resulting in such a dramatic geological feature.

The wide range of surface terrains observed on Miranda, including the presence of coronae and the massive Verona Rupes cliff, strongly indicates that this moon has experienced catastrophic disruptions in its past.

These disruptions likely involved intense tectonic activity, resulting in the deformation and fragmentation of Miranda's surface. The unique geological features on Miranda provide valuable insights into the complex history and dynamics of the Uranian moon system.

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The work done is 320 J and the distance covered is 2.5 m.

To calculate the work done in physics, you can use the formula:

Work (W) = Force (F) × Distance (d) × cosθ

However, since the question doesn't provide information about the force or the angle, we'll assume that the force is applied in the direction of motion, which means θ = 0° and cosθ = 1.

Given:

W = 320 J (work done)

d = 2.5 m (distance covered)

θ = 0° (angle between force and displacement)

Using the formula, we have:

320 J = F × 2.5 m × cos0°

Since cos0° = 1, the equation simplifies to:

320 J = F × 2.5 m

To find the force (F), we rearrange the equation:

F = 320 J / 2.5 m

F = 128 N

Therefore, the force applied is 128 N.

It's important to note that this calculation assumes that the force is constant over the entire distance and that there are no other factors influencing the work done.

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The acceleration of the airboat  is 2.2m/s^2 and starting from rest, it take the airboat to reach a speed of 12.0 m/s is 5.45s

Given mass of airboat (m) = 3.50 x 10^2kg

horizontal force of engine (F) = 7.70 x 10^2N

We know that from newtons laws of motion Force = mass x acceleration such that F = ma

(a) Now a = F/m = 7.70 x 10^2 / 3.50 x 10^2 = 2.2m/s^2

(b) Initial speed of airboat (u) = 0m/s

final speed (v) = 12m/s

We have acceleration a = 2.2m/s

Then we have another newtons law as: v = u+ at where t is the time taken

So t = v/a = 12/2.2 = 5.45s

Hence it takes to reach 5.45s a speed of 12m/s

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Answer:

True...................

..

.....................

Therefore, the diameter of the wire is approximately 2.2 μm. The answer is option D.

The resistance (R) of the wire can be calculated using Ohm's law:

V = IR

where V is the voltage of the battery, I is the current flowing through the wire, and R is the resistance of the wire. Therefore:

R = V / I = 1.5 V / 8.0 mA = 187.5 Ω

The resistance of a wire is given by the equation:

R = (ρL) / A

where ρ is the resistivity of the metal, L is the length of the wire, and A is the cross-sectional area of the wire.

Rearranging the equation to solve for A, we get:

A = ρL / R

Substituting the given values, we get:

A = \((2.24 x 10^{-8} m)(1.0 m) / 187.5 = 1.2 x 10^{-11} m^2\)

The cross-sectional area of a wire is given by the equation:

A = π\(d^2\) / 4

where d is the diameter of the wire.

Rearranging the equation to solve for d, we get:

d = 2 √(A / π) = \(2 \sqrt{[(1.2 x 10^{-11} m^2) / pi]}\)

d = 2.2 μm

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Answer:

Explanation:

a. From the information provided in the question, the blue liquid is a solution. This is because a solution is a type of homogeneous mixture (that has an evenly distributed solute in a solvent) which is the reason the liquid was said to be blue (and not immiscible blue solid in a liquid) but after been exposed to heat became just a blue solid. Typically, a solution has a solute and a solvent (combined), the solute here is the blue solid while the solvent is the liquid that made the combination a liquid.

b. Since the dish containing the liquid was placed on a windowsill, it can be assumed that the dish was subjected to heat from the sun which caused the liquid (in the solution) to evaporate after exposure to the heat from the sun (over the weekend) leaving the blue solid solute (of the solution) to remain in the dish. This can be referred to as evaporation to dryness in separation techniques (if the goal was to intentionally separate the solid solute from the liquid solvent).

The energy required is approximately twice the initial energy of the original droplet due to increased surface area.

To determine the amount of energy required to change a spherical droplet with a diameter of 2.20 mm into two smaller spherical drops of equal size, consider the principle of surface energy minimization.

When a droplet is divided into smaller droplets, the total surface area increases, leading to an increase in surface energy.

The surface energy can be calculated using the formula:

E = γ * A,

where E represents the energy, γ is the surface energy per unit area, and A is the total surface area.

Assuming the droplets are in a vacuum or surrounded by a medium with negligible interactions, the surface energy per unit area remains constant throughout the process.

Therefore, the change in energy is directly proportional to the change in surface area.

When a droplet is divided into two equal-sized droplets, the total surface area doubles.

So the energy needed to achieve this change is double the initial energy of the original droplet.

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1. W = 50J

2. W = 6.9J

3. Work done is same as force  = 30N

4. P = 480W

1. Here given:

F = 25N

D = 2m

We have to find  W = ?

Work done Formula : W= F x D

By substituting ,

W = 25 x 2

W = 50J

2. Here given,

F = 15N

Angle = 30°

distance = 3m

W = 15* 3 * cos 30

= 6.9 J

3. Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. When we apply a force of 30N to a wall, it responds with the same force.

4. The work done will be calculated using the formula:

W = mass*gravitational acceleration*height.

Furthermore,

power = work done / time.

500 + 100 = total weight

600 N = total weight

Maintain the values in the formula -

Work completed = 600*4

2400J

P = 2400/5

= 480W

Hence, the power is 480 Watt.

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Answer:

organ is larger cell..............

Answer:

organ

Explanation:

Answer:1.). -0.65

2.). 0.65

Explanation:

The required plate area is  1.78 x 10-3 m² if the parallel plate capacitor has a plate separation of 14.00 mm if it has a  capacitance of 9.00 pf.

To calculate the required plate area of a parallel plate capacitor to provide a capacitance of 9.00 pF with a plate separation of 14.00 mm and material between the plates being air,

the equation C = ε0A/d can be used.
Where C is the capacitance,

ε0 is the permittivity of free space,

A is the plate area, and

d is the plate separation.

Rearranging the formula in terms of Area,

Therefore A = (C x d) / ε0
Substituting the values
A = (9.00 pF x 14.00 mm) / 8.85 x 10-12 F/m
A = 1.78 x 10-3 m²

Therefore, the required plate area is 1.78 x 10-3 m² to provide a capacitance of 9.00 pF with a plate separation of 14.00 mm and material between the plates being air.

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26.676 × 10³ kg is the weight of the aluminum rod.

Given:

Length of cylindrical rod (h) = 45 cm

Diameter of a cylindrical rod = 4.53 cm

Radius of a cylindrical rod (r) = 2.3 cm

The density = 3.7*10^3kg/m^3

Volume of a cylindrical rod = πr²h

                                             = 3.14× (2.3)² × 45

                                             = 747.89 cm

                                             = 7.4789 m

To find weight ;

                         ρ = \(\frac{Mass}{Volume}\)                  ; ρ = Density

                        Mass = ρ × Volume

                                  = 3.7 × 7.48 × 10³

                                  =27.676 × 10³ kg

Therefore, the weight of the aluminum rod is 27.676 × 10³ kg.

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The vertical vector component of a ball kicked at an angle of 58 degrees with an initial velocity of 82 feet per second is 57.568 feet per second.

The vertical vector component is found by multiplying the initial velocity by the sine of the angle of inclination.

In this case, the sine of 58 degrees is 0.814155, so the vertical vector component is

82 * 0.814155 = 57.568 feet per second.

The vertical vector component represents the velocity of the ball in the vertical direction.

As the ball travels through the air, the vertical vector component will decrease due to the force of gravity.

However, the horizontal vector component will remain constant.

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Answer:

false

Explanation:

Answer:

New technology is developed that provides more information about the theory. (New technologies can lead to new results).

New experimental methods are designed to test a theory.

New information is discovered that does not support the theory.

Explanation:

A theory is an explanation of an aspect of the natural based on careful examination of facts. A theory by its definition can be repeatedly tested. A theory can be changed or replaced because of the following reasons:

To measure current using a digital multimeter, the probes of the meter would be placed in series with the component.  The correct answer is( b) in series with.

• Series combination is when two or more resistors are connected end to end consecutively, their combination

    is said to be the series combination. The total resistance of any number of resistances connected in series is

    equal to the sum of the individual resistance

•  The other options listed in the multiple choice question - in parallel, If resistors are connected in such

   a way that the potential difference gets applied to each of them, they are said to be connected in parallel.

• Therefore, the correct option is b.

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When an electron is moving due north in a region where the electric field points due west, then the electron curves away from due north towards the east. So, the option (D) is the correct answer.

The motion of the electron can be described by the Lorentz force equation:

F = qE + qv x B

Where,

F = force on a charged particle in newtons (N)

q = charge on a particle in coulombs (C)

E = electric field in volts per meter (V/m)

v = velocity of the charged particle in meters per second (m/s)

B = magnetic field in tesla (T)

The first term of the above equation, qE, is responsible for changing the direction of the charged particle (electron) due to the electric field. While the second term qv × B is responsible for the curve in the path of the charged particle due to the magnetic field.

Hence, the correct option is D.

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