Consider vectors u and v, where u = ⟨1, –1⟩ and v = ⟨1, 1⟩. what is the measure of the angle between the vectors?

Answer:

80J

Explanation:

K.E = ½ mv²

k.e = ½ * 80*

100²

ke= 4*20

ke= 80 J

The resultant magnitude and direction of the vectors are as follows:

The resultant magnitude and direction of the vectors are as follows:

A. A = √(5.7² + 3.4²)

A = 6.6

θ = tan⁻¹(3.4/5.7)

θ = 30.8° from the x-axis

B. B = √{(-10)² + (-3²)}

B 10.4

θ = tan⁻¹(3/10) + 180

θ = 16.7° + 180°

θ = 196.7° from the x-axis

C. C = √{(12)² + (-20²)}

C = 23.3

θ = 360° - tan⁻¹(20/12)

θ = 300° from the x-axis

D. D = √{(-30)² + (27²)}

D = 40.4

θ = 180 - tan⁻¹(27/30)

θ = 138° from the x-axis

E. E = √{(48)² + (12²)}

E = 49.5

θ = 360° - tan⁻¹(12/48)

θ = 346° from the x-axis

In conclusion, the resultant of the vectors and direction are obtained using the resultant vector formula.

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \:E = \dfrac{hc}{\lambda} [/tex]

here,

____________________________________

[tex]\qquad \sf  \dashrightarrow \: E = \cfrac{1.99 \times 10 {}^{ - 25} }{7 \times 10 {}^{ - 12} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: E= \cfrac{1.99}{7} \times 10 {}^{ (- 25 + 12)} { } [/tex]

[tex]\qquad \sf  \dashrightarrow \:E= 0.284 \times 10 { }^{ - 13} [/tex]

[tex]\qquad \sf  \dashrightarrow \: E= 2.84 \times 10 { }^{ - 14\:\; } J\: \: [/tex]

so, correct choice is A

Answer: A

Explanation:

The substance, if eliminated, that would completely prevent the greenhouse effect from occurring on earth is fossil fuels (option C).

Greenhouse effect is the process by which a planet is warmed by its atmosphere.

Greenhouse effect is caused by greenhouse gases that deplete the ozone layer.

Fossil fuels, when burned, will release greenhouse gases such as carbon etc. to the atmosphere.

Therefore, the substance, if eliminated, that would completely prevent the greenhouse effect from occurring on earth is fossil fuels.

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The way to perform the experiment is illustrated below.

Place each straw tightly without deforming the roundness of the straw into the corner of the set square.

Measure the distance from the corner of the set square to where the straw touches the set square using the 30 cm ruler. This will be the radius of each straw.

Multiply this radius by 2 in order to obtain the diameter of each straw.

Sum the diameter of each of the 10 straws.

Divide this sum by 10 to obtain the average value for the diameter of a straw.

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The smallest perimeter of the rectangle is of value 150 cm.

Given:

The area of the rectangle, A = 1350 cm²

Calculation:

Let the length of the rectangle be 'x'

      the breadth of the rectangle be 'y'

We know that the area of a rectangle is given as:

A = (x) × (y)  

Applying values in the above equation we get:

xy = 1350 cm²

Factorizing the value of 1350, the possible values of length and breadth of the rectangle is as listed below:

x (cm)         y (cm)

1350      ×       1

675       ×       2

450       ×       3

270       ×       5

225       ×       6

150        ×       9

135        ×       10

90         ×       15

75         ×        18

54         ×        25

50         ×        27

45         ×        30         (least possible value)

Thus, the smallest perimeter of the rectangle can be calculated as:

P = 2 (x + y)

  = 2 (45 + 30)

  = 150 cm

Therefore, the smallest perimeter that the rectangle will have is 150 cm.

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Answer: An object at rest has no kinetic energy, but it may have potential energy resulting from its location or structure.

Explanation: To find the answer, we need to know more about the kinetic and potential energies.

                           [tex]KE=\frac{1}{2}mv^2[/tex]

Thus, we can conclude that, an object at rest has no kinetic energy, but it may have potential energy resulting from its location or structure.

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The rate of change of the current in the larger inductor is 0.3mA/s.

To find the answer, we need to know about the relation between the emf and inductance.

Thus, we can conclude that the rate of change of the current in the larger inductor is 0.3mA/s.

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The magnetic flux through the circular cross-sectional area of the solenoid is 0.00066 Weber or (Tm²).

A wire tightly twisted in a lengthy, thin coil is a solenoid. Due to its design, the solenoid will have an electromagnet inside of it and a weak magnetic field surrounding it if we pass a current through it.

Equation of solenoid's magnetic field:

By utilizing the convolution operation as well as right hand rule, the magnetic field within a large solenoid is appropriately computed, but all of that can be condensed into:

B = (µ₀ × N × I )/ L

where

B = magnetic field (Tesla)

µ₀ = [tex]\pi[/tex]× 10^-7 (Tm/A ) is the vacuum permeability,

N = number of turns on solenoid,

I = electric current (Ampere)

L = length of the solenoid (m)

According to the question;

A diameter of solenoid 6.00 cm.

A radius of solenoid is 3 cm = 0.03m

Number of turns = 750

The length of solenoid is 10cm = 0.1m

Substitute all the values in equation to fine mangetic filed.

B = ([tex]\pi[/tex]×[tex]10^{-7}[/tex] × 750× 15 )/ 0.1

B = 0.035 Tesla

The formula for magnetic flux is

Ф = B×A

   = B×([tex]\pi[/tex][tex]r^{2}[/tex])

   = 0.035×[tex]\pi[/tex]×[tex].03^{2}[/tex]

Ф = 0.000099

Ф = 99×[tex]10^{-6}[/tex] Weber

Therefore, the magnetic flux through the circular cross-sectional area of the solenoid. is 99×[tex]10^{-6}[/tex] Weber.

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X and Y are two things that travel in the same direction. The mass of the things is the same. 5.0 m/s is the velocity of object x as it moves to the right. The velocity of object y to the left is 3.0 m/s. Objects x and y collide and adhere to one another. Following their collision, they both move at a speed of 1.0 m/s to the right.

Their velocity after colliding is 1.0 m / s to the right.

What is the velocity during the collision?

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The work done by the pushing force is 200 J; option B.

The work done in an inclined plane is given by the formula below:

Force, F = mgsinθ + ma

where a = 0

Work done = 80 * 5 * sin 30°

Work done = 200 J

In conclusion, work done is the product of force and distance.

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When a man pushes a box across a floor, as he increases the force he applies horizontally to the box, then the kinetic friction remains the same.

To find the answer, we need to know about friction.

Thus, we can conclude that, kinetic friction remains the same when we increase the applied force.

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As a guy pushes a box across a floor, the kinetic friction stays constant no matter how much force is applied on the box horizontally.

We must understand friction if we are to find the solution.

We can therefore draw the conclusion that kinetic friction does not change as the applied force is increased.

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The lion has a kinetic energy of 5000 j, the speed of the lion is  v = 100 / [tex]\sqrt{M1}[/tex]  m/s

Kinetic energy is a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy or Kinetic energy is the energy that an object possesses due to its motion. It is basically the energy of mass in motion. Kinetic energy can never be negative and it is a scalar quantity i.e. it provides only the magnitude and not the direction.

given

kinetic energy = 5000 J

speed = ?

since , mass is not given in the question

Let mass of lion will be = M1

kinetic energy = 1/2 * M1 * [tex]v^{2}[/tex]

             5000 J = 1/2 * M1 *  [tex]v^{2}[/tex]

             [tex]v^{2}[/tex] = [tex]\sqrt{10,000 / M1}[/tex]  m/s

              v = 100 / [tex]\sqrt{M1}[/tex]  m/s

The speed of the lion =  v = 100 / [tex]\sqrt{M1}[/tex]  m/s

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The amount of work done during the lifting process is 4465.125 J and our average power will be 42.525 W.

Given:

Depth of the well, h = 22.5m

Mass of heavy-duty steel chain, M = 17.9 kg

The combined mass of the water and bucket, m = 11.3 kg

time taken to raise the bucket out of the water, T = 1.75 min = 105 s

Calculation:

Consider that the center of mass of the steel chain is at the midpoint of the depth of the well.

Now, the work done during the lifting process can be calculated as:

W.D = (Work done in lifting bucket filled with water) + (work done to lift    

                                                                                              the steel chain)

W.D = mgh + Mg (h/2)      -( 1 )

where g is the acceleration due to gravity

Applying values in the above equation we get:

W.D = mgh + Mg (h/2)

       = (11.3 kg)(9.8 m/s²)(22.5 m) + (17.9 kg)(9.8 m/s²)(22.5 m / 2)

       = 2491.65 + 1973.475

       = 4465.125 J

We know that the average power is given as:

P_avg = W.D / T     - ( 2 )

where W.D is the work done during the lifting process

            T is the time taken to raise the bucket out of the well

Applying values in the above equation, we get:

P_avg = W.D / T

           = (4465.125 J)/(105 s)

           = 42.525 W

Therefore, the amount of work done during the lifting process is 4465.125 J and our average power will be 42.525 W.  

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The force require to keep grouper submerged is 8.207N.

According to Archimedes principle  buoyant force of any object must equal to weight of fluid it displaced.

The expression for the force exerted to stay submerged in salt water is

           F = F(b) - w(fish)

 where F(b) = buoyant force

              w(fish) = weight

      now substitute w(b) for F(b)

   →  F = Vρg - w(fish)

where  V = volume of sea water

             ρ = density of sea water

Now by Archimedes principle   V = m(fish)  / ρ(fish)

    →    F = (m(fish) / ρ (fish) ) ρg - m(fish)g

           F =   (85 kg/1015 kg-m^-3) (1.025× 10³ kg-m^-3) (9.8 m/s^2)

                                  -   (85kg)  × 9.8 m/s^2

           F = 841.207N - 833N

           F = 8.207 N

  Hence, the force require to keep grouper submerged is 8.207N.

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The tidal volume which typically maintains normal oxygenation and elimination of carbon dioxide is 8 to 10 ml/kg of body mass.

Tidal volume refers the amount of air that moves in and out of the lungs in one respiratory cycle.

During a respiratory cycle, oxygen moves into the lungs and the tissues during inhalation, while carbon dioxide moves out of the lungs during exhalation.

The continuous outward movement of carbon dioxide and inward movement of oxygen ensures that the body maintains homeostasis and internal or tissue respiration continues.

The normal tidal volume is about 500 ml per inspiration or 7 ml/kg of body mass.

However, for normal oxygenation and elimination of carbon dioxide, a tidal volume of about 8 to 10 ml/kg of body mass is required.

In conclusion, the tidal volume is a measure of the amount of air flow in the lungs for each respiratory cycle.

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If a star appears to move relative to other stars over a one-year period, this motion is due to the star's true space motion.

What is the proper motion of stars?

Proper motion is the angular change in position of a star across our line of sight, measured in arc seconds per year, and symbolized with the letter  μ.

Proper motion is generally measured by measuring the movement of the image of a star with respect to more distant background stars over that time period.

Here we are told that star appears to move relative to other stars over 1 year period.

So we know that,

True space motion is the annual apparent motion of a star across the sky.

True Space Motion is Combination of radial velocity, proper motion, and distance.

Hence,

If a star appears to move relative to other stars over a one-year period, this motion is due to the star's true space motion.

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Answer:

Virgo will be the highest zodiac constellations at night.

Answer:

the answer to your question will be D

Explanation:

5 N* 3S =3.25

The time taken for the athlete to finish the race is 20 s (Option A)

Power is simply defined as the rate at which work is done. It can be expressed mathematically as

Power (P) = work (W) / time (t)

But

Work = weight × distance

Therefore,

Power = (weight × distance ) / time

Power = (weight × distance ) / time

5400 = (539 × 200) / t

5400 = 107800 / t

Cross multiply

5400 × t = 107800

Divide both side by 5400

t = 107800 / 5400

t = 20 s

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Answer:

Need quiet to concentrate

Are reflective

Are self-aware

Take time making decisions

Feel comfortable being alone

Don’t like group work

Prefer to write rather than talk

And maybe even feel tired after being in a crowd

Explanation:

b) internal energy drives plate motion

Lithospheric plates are part of a planetary scale thermal convection system. The energy source for plate tectonics is Earth’s internal heat while the forces moving the plates are the “ridge push” and “slab pull” gravity forces.

A tectonic plate (also called lithospheric plate) is a massive, irregularly shaped slab of solid rock, generally composed of both continental and oceanic lithosphere.

The motion of tectonic plates is driven by convection in the mantle. Convection: The process of heat transfer from one part of a fluid to another part by the actual movement of the particles of the fluid is called convection. Liquid and gases are heated by the process of convection.

In simple terms, convection is the idea that dense, cold things sink, and buoyant, warm things rise. In the earth the cold sinking things are slabs (subducting plates) and the warm things are plumes, or just rising material from deeper in the mantle.

hence , correct option is b) internal

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A new CFD method for determination of translational is RANS simulations

Using numerical analysis and data structures, the field of computational fluid dynamics (CFD) studies and resolves issues involving fluid flows. The computations necessary to model the fluid's free-stream flow and its interactions with surfaces constrained by boundary conditions (both liquids and gases) are done on computers. Better answers can be found using high-speed supercomputers, which are frequently needed to address the most challenging issues.

Five prominent CFD methods -

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Answer:if youre looking for the weight of the thermas in genral it should be 500n

Explanation:using the formula w=mg

w=500x10

giving us 500 newtons which is the weight.

Answer:

R = ρ L / A     where R is the resistance and ρ the resistivity:

R2 / R1 = (L2 / A2) / (L1 / A1) = L2 * A1 / (L1 * A2)

R2 / R1 =  (2 L * A) / (L * 2 A) = 1

Their resistances should be the same.

The thicker wire has one-fourth the resistance of the thinner wire.

The characteristic of a substance that prevents the flow of current is known as resistance. The free electrons begin to move in a specific direction when a voltage is applied across the conductor. These electrons collide with atoms or molecules as they move, creating heat in the process. These atoms or molecules prevent free electrons from moving through a substance. Resistance is represented by the symbol R.

Specific resistance is another name for resistivity. A substance with certain dimensions, such as one meter in length and a cross-sectional area of one square meter, has a resistance that is represented by its resistivity. Resistivity or specific resistance is represented by ρ.

The relation between resistance R and resistivity ρ is given as:

                                              R = ρL/A

where,

R = resistance of the conductor

ρ =  resistivity of the material

L = length of the conductor

A = cross-sectional area of the conductor

Given,

r₁ = 2r₂

L₁ = L₂

where

r₁ = radius of the first conductor

r₂ = radius of the second conductor

L₁ = length of the first conductor

L₂ = length of the second conductor

To find

R₁/R₂ =?  (the ratio of R₁ and R₂)

If the radius is twice the other then the area will become,

A₁ = π r₁²

A₂ = π r₂²

A₁ = π (2r₂)²

   = 4π r₂²

Therefore,

A₁ = 4 A₂

Now put the values in the formula,

R = ρL/A

R₁/R₂ = ρ L₁ A₂/  ρ L₂ A₁

R₁/R₂ = L A₂/ L (4A₂)

R₁/R₂ = 1/4

R₁ = R₂/4

Hence, the thicker wire with twice the radius of the thin wire has one-fourth the resistance of the thinner wire.

I understand the question you are looking for is this:

How do the resistances of two conducting wires compare if they have the same length, but one is twice the radius of the other?

(a) The thicker wire has half the resistance of the thinner wire

(b) The resistance is the same in both wires

(c) The thicker wire has one-fourth the resistance of the thinner wire

(d) The thicker wire has twice the resistance of the thinner wire.

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The threshold frequency for sodium metal is

5.49 x 10^14 s-1

Given:

photon with frequency = 6.66 × 10^14 s−1

kinetic energy = 7.74 × 10−20 j

To Find:

threshold frequency

Solution: The threshold frequency is defined as the minimum frequency of incident radiation below which the photoelectric emission is not possible completely. irrespective of the intensity of incident radiation

We know, relation between threshold frequency, kinetic energy and frequency s given by :

K.E = hv - hvo

Here h is plank's constant and vo, is threshold frequency.

Putting all these value in above equation we get:

7.74 x 10^-20 = (6.66 × 10^14-vo) x 6.626 x 10^-34

vo = 5.49 x 10^14 s^-1

Hence, the threshold frequency for sodium metal is 5.49 x 10^14 s-1

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(a) The diameter of the largest orbit just before the protons exit the cyclotron is 39 cm.

(b) The number of orbits completed by the proton during this 1.0 ms is 14000 revolutions.

What is  kinetic energy?

The kinetic energy of an object is the energy that it possesses due to its motion.

It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.

Formula of KE:

K.E = 1/2mv²

mv² = 2 K.E

v = sqrt( 2*KE / M)

Here,

(a)

The KE of the medical isotopes = 6.5 MeV

substituting the values,

v = sqrt( 2* 6.5* 1.6* 10^-13 / 1.67* 10^-27 )

v = 3.53 × 10⁷ m/s

Now the centripetal force:

mv² / R = qvB

r = q*v / mv²

r = ( 1.67* 10^-27 * 3.53 × 10⁷ ) / ( 1.9* 1.6* 10^-19 )

r = 0.19415 m

diameter d = 2r,

d= 2(0.19415  m)

d= 0.39 m ≅ 39 cm

(b)

The time period to complete a revolution around the spiral trajectory is:

T = 2πr / v

T = 2*3.14* 0.1941 / 3.53*10^7

T = 0.7 × 10⁻⁷ s

Thus, the number of orbits that the proton does to complete the revolution in 1 ms is:

n = t / T

n = 10^-3 / (0.7*10^-7)

n = 14285.71  ≅ 14000 revolutions

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Your question is incomplete, but most probably full question was:

A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV. The magnetic field in the cyclotron is 1.9 T.

(a) What is the diameter of the largest orbit, just before the protons exit the cyclotron? Express your answer with the appropriate units. d = 57 cm Previous

(b) A proton exits the cyclotron 1.0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1.0 ms?