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The unit vector normal to the plane is ; n = [tex]\frac{i}{\sqrt[3]{6} } - \frac{2j}{\sqrt[3]{6} } + \frac{7k}{\sqrt[3]{6} }[/tex]

Given data :

The unit vectors

a→=3i^-2j^-k^  and  b→=i^+4j^+k^

The unit vector normal to the plane is calculated as

n = [tex]\frac{a*b}{|b*b|}[/tex]  ---- ( 1 )

where ; a→ * b→ =  2i - 4j + 14k  and  |b * b| = [tex]\sqrt{216}[/tex]  

back to equation ( 1 )

n = ( 2i - 4j + 14k ) / [tex]\sqrt{216}[/tex]

  = [tex]\frac{i}{\sqrt[3]{6} } - \frac{2j}{\sqrt[3]{6} } + \frac{7k}{\sqrt[3]{6} }[/tex]

Hence we can conclude that The unit vector normal to the plane is ; n = [tex]\frac{i}{\sqrt[3]{6} } - \frac{2j}{\sqrt[3]{6} } + \frac{7k}{\sqrt[3]{6} }[/tex]

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Answer:

A. length, diameter, material, temperature

Matching the missions with their objectives

The NEAR ( Near Earth Asteroid Rendezvous ) is a mission whose objective is to study origin and nature of objects near the earth such as asteroids and comets.

Lunar prospector was a mission designed to perform an orbit investigation of the moon.

The deep impact mission created by NASA was to probe beneath the comet and discover the structure and composition. The deep impact projected lasted for 9 years in space.

Hence we can conclude that the missions and their objectives are as listed above.

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[tex]\bold{Heya!}[/tex]

Yup. your answer is correct!

        [tex]23,24.[/tex]

        [tex]23 \: + 24 = 47.[/tex]

        [tex]\frac{47}{2} = 23.5[/tex]

Hopefully This Helps ! ~

#LearnWithBrainly

[tex]\underline{Answer :}[/tex]

Jaceysan ~

Answer:

GIVE HIM BRAINLEST

Answer:

PE = 1/2 K X^2

K = 50 N/m

X = .3 m

PE = 1/2 * 50 * .3^2 = 2.25 Joules

Waves that are in phase constructively interfere to create bright bands was observed in the double-slit experiment.

This is defined as the phenomenon which occurs when two waves meet while traveling along the same medium.

A wave when in phase undergoes constructive interference while out of phase undergoes destructive interference which is why option C was chosen as the most appropriate choice.

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Answer:

legal guardians, the four types: personal guardians, financial guardians, conservators, and pet “guardians”

Answer:

You would weigh very slightly more at sea level than at the top of a mountain, not enough for you to notice, but a measurable amount. Weight, which really means gravitational force, is proportional to the product of the masses of two objects acting on each other, in this case the giant earth and the minuscule you.

Explanation:

Explanation:

momentum = mass × velocity

mass = 9.11 × 10^-31

velocity = 0.8725 multiplied by c ( which is the speed of light )

therefore velocity = 0.8725 × 3 × 10^8 = 2.6175 × 10^8 m/s

[tex]m = 9.11 \times 10 {}^{ - 31} \times 2.6175 \times 10 {}^{8} [/tex]

[tex]m = 9.11 \times 2.6175 \times 10 {}^{ - 31 + 8} [/tex]

[tex]m = 23.85 \times 10 {}^{ - 23} kgms {}^{ - 1} [/tex]

if this helped pls give brainliest

Answer:

Explanation:

You can use [tex]Q = mc\Delta T=(550)(4.184)(28.8-12.7)=37049.32[/tex] joule.

Answer:

very fast

Explanation:

Answer:

The mechanical advantage would depend on where the load force and the balancing force were placed on the stick

MA = (50 - F) / (L - 50)

Supoose the balancing force was placed at zero and the load at 75 cm

then MA = (50 - 0) / (75 - 50) = 50 / 25 = 2

or the balancing force was applied at 10 cm and the load force was applied at 60 cm then

MA =  (50 - 10) / (60 - 50) = 40 / 10 = 4

Seamus can add batteries to increase the voltage, and he can decrease the space between the wire coils to accomplish this goal.

This is defined as any type of force that causes objects to come together and is possessed by objects such as a magnet.

In order to increase the power of the magnet it is best to increase the voltage and decrease the space of the coils so as to ensure it attracts at least four paper clips which makes option C the most appropriate choice.

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Answer:

The answer is 581

Explanation:

I just took the Quick Check and got it right.

Answer:

100 kg

Explanation:

Net force = 350 - 50 = 300 N

F= ma

300 N  = m * 3 m/s^2

100 kg = mass

Given the measured value of mass M in the experiment the error in 2M is  ; dM

Given data :

Measured value of mass M = ( 0.743 ± 0.005 ) kg

The error in 2M in the measured value M = 0.743 ± 0.005 kg is dM while the error in M² will be 2dM

Hence we can conclude that the measured value of mass M in the experiment the error in 2M is  ; dM.

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(a) At a corresponding hill on Earth and a lesser gravity on planet Epslion, the height of the hill will cause a reduction in the initial speed of the snowboarder from 4 m/s to a value greater than zero (0).

(b) If the initial speed at the bottom of the hill is 5 m/s, the final speed at the top of the hill be greater than 3 m/s.

The effect of height  and gravity on speed on the given planet Epislon is determined by applying the principle of conservation of mechanical energy as shown below;

ΔK.E = ΔP.E

¹/₂m(v²- u²) = mg(hi - hf)

¹/₂(v²- u²) = g(0 - hf)

v² - u² = -2ghf

v² = u² - 2ghf

where;

when u² = 2gh, then v² = 0,

when gravity reduces, u² > 2gh, and v² > 0

Thus, at a corresponding hill on Earth and a lesser gravity on planet Epslion, the height of the hill will cause a reduction in the initial speed of the snowboarder from 4 m/s to a value greater than zero (0).

v² = u² - 2ghf

where;

Since g on Epislon is less than 9.8 m/s² of Earth;

5² - 2ghf > 3 m/s

Thus, if the initial speed at the bottom of the hill is 5 m/s, the final speed at the top of the hill be greater than 3 m/s.

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Answer:

1.Divergent boundaries (crust moves apart, magma fills in) Convergent boundaries (magma fills when one plate goes beneath another) Hot spots (a large magma plume rises from mantle)

2.Some mountains are made of solid rock, like the Rocky Mountains or the Swiss Alps. But, some mountains are actually volcanoes.

3.an area under the rocky outer layer of Earth, called the crust, where magma is hotter than surrounding magma.

4.hydrogen sulfide, carbon monoxide, hydrogen chloride, hydrogen fluoride, and other minor gas species.

5.Extinct volcanoes are not expected to erupt in the future. Inside an active volcano is a chamber in which molten rock, called magma, collects. Pressure builds up inside the magma chamber, causing the magma to move through channels in the rock and escape onto the planet's surface.

Explanation:

hope its help:)

Hi there!

A.

We can use the work-energy theorem to solve.

Initially, both blocks have gravitational potential energy, which is then converted to kinetic energy.

Recall:
[tex]U = mgh \\[/tex]

U = Potential Energy (J)
m = mass (kg)
g = acceleration due to gravity (m/s²)

h = height (m)

And at the end, block 2 has both kinetic and potential energy. Kinetic is defined as:
[tex]KE = \frac{1}{2}mv^2[/tex]

v = velocity (m/s)

We can do a summation of initial and final forces.

Initial:
[tex]E_i = m_2g\frac{h}{2} + m_1gh[/tex]

Final:
[tex]E_f = \frac{1}{2}m_2 v^2 + m_2g\frac{3h}{2} + \frac{1}{2}m_1 v^2[/tex]

Set the two equal (no energy loss in this situation) and solve for velocity.

[tex]m_2g\frac{h}{2} + m_1gh = \frac{1}{2}m_2 v^2 + m_2g\frac{3h}{2} + \frac{1}{2}m_1 v^2\\\\m_2g\frac{h}{2} + m_1gh - m_2g\frac{3h}{2} = \frac{1}{2}m_2 v^2 + \frac{1}{2}m_1 v^2\\\\v^2 = \frac{gh(\frac{m_2}{2} + m_1 - \frac{3m_2}{2})}{\frac{1}{2}m_2 + \frac{1}{2}m_1}\\\\v = \sqrt{\frac{gh(\frac{m_2}{2} + m_1 - \frac{3m_2}{2})}{\frac{1}{2}m_2 + \frac{1}{2}m_1}}\\\\v = \boxed{3.704 \frac{m}{s}}[/tex]

**This can be solved in a simpler way using a summation of forces.

B.

Now, we can do a summation of forces to solve. First, we must solve for the acceleration of the system now that we have found the velocity. Use the kinematic equation:
[tex]v_f^2 = v_i^2 + 2ad[/tex]

Initial velocity is 0 m/s, so:
[tex]v_f^2 = 2ad\\\\a = \frac{v_f^2}{2d} = \frac{(3.704^2)}{2(2.10)} = 3.267 \frac{m}{s^2}[/tex]

Now, we can use a summation of forces for any block. We can do block 1:
[tex]\Sigma F = m_1g - T[/tex]

Using Newton's Second Law:
[tex]m_1a = m_1g - T\\\\T = m_1g - m_1a \\T = m_1 (g - a) = 4.10(9.8 - 3.267) = \boxed{26.828 N}[/tex]

Answer:

Theres a diagram missing for Q

Explanation:

What is all this?

Could you add a question so I can answer it :)

Answer: The maximum kinetic energy KEe of ejected electrons (photoelectrons) is given by KEe = hf − BE, where hf is the photon energy and BE is the binding energy (or work function) of the electron to the particular material.

Explanation:

The work function of the uranium metal will be given by the value 7.9*10^-19

The work function of a particle is defined as the product of the planks constant to the frequency of the particle.

[tex]\phi=h\times f[/tex]

Now the frequency will be given as

[tex]f=\dfrac{c}{\lambda}[/tex]

So the formula will become

[tex]\phi=\dfrac{hc}{\lambda}[/tex]

h=6.626 × 10-34 J∙s

c=3.0 × 108 m/s

[tex]\lambda[/tex] = 250 nm 250* 10^-9

[tex]\phi=\dfrac{6.626\times 10^{-26}\times3\times 10^{8}}{250\times 10^{-9}}[/tex]

[tex]\phi=7.9\times 10^{-19}[/tex]

Hence the work function of the uranium metal will be given by the value 7.9*10^-19

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Answer:

it builds muscle cells

Explanation:

took test

Answer:

1.) 30 m is the total distance covered 10m is the displacement you

2.)24,000m/h (24km/h or 6.67m/s) Average speed is calculated by dividing the total distance that something has traveled by the total amount of time it took it to travel that distance

Explanation:

Answer:

volume , mass

Explanation:

the 3 basic properties of a matter is volume, mass and shape.

Answer:

Explanation:

You can use that [tex]v = v_{o}+gt[/tex] or [tex]v^{2}=v_{o}^{2}+2gh=(25)^{2}+(2)(10)(381)=8245 \rightarrow v \approx 90.8[/tex] m/s.

Based on the value of the Young's modulus, the strand of the metal is made of copper.

The Young's modulus of the metal is calculated as follows;

E = stress/strain

The stress of the metal is calculated as follows;

σ = F/A = mg/A

where;

A is area of the metal

A = πr²

A = π( 2 x 10⁻³)²

A = 1.257 x 10⁻⁵ m²

σ = (70.5 x 9.8) / (1.257 x 10⁻⁵)

σ = 5.5 x 10⁷ N/m²

The strain is calculated as follows;

strain = x/L

where;

x is extension

L is original length

strain = (1 x 10⁻³ m) / 2 m

strain = 5 x 10⁻⁴

E = stress/strain

E = (5.5 x 10⁷ ) / (5 x 10⁻⁴)

E = 1.1 x 10¹¹ N/m²

E = 110 Gpa

The Young's modulus of copper metal is 110 Gpa

Thus, based on the value of the Young's modulus, the strand of the metal is made of copper.

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Answer:

80m/s2

Explanation:

m=30kg. r = 5meter v = 20m/s2 a= ? centripetal acceleration = v*v/r

20*20/5=80m/s2

centripetal acceleration=80 m/s2

The desk is exerting a normal force of approximately 2.913 Newtons on the cup of coffee, which is also equal to 2.913 N in magnitude.

The force that the desk exerts on the cup of coffee is known as the normal force. This force counteracts the weight of the coffee cup due to gravity. The normal force is equal in magnitude and opposite in direction to the force exerted by the cup's weight.

The weight of an object is given by the equation:

Weight = mass × acceleration due to gravity

Where:

Mass = 0.297 kg (mass of the coffee cup)

Acceleration due to gravity (on the surface of the Earth) ≈ 9.81 m/s²

Weight = 0.297 kg × 9.81 m/s² ≈ 2.913 kg m/s² (Newtons)

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The speed of coil of the microphone is 0.227 m/s

A microphone is a device used to transmit sound energy through electrical energy. it makes use of magnetic fields whose strength is measures in Tesla

Given data

D = 1.4cm = 0.014m

N = 100

B = 0.010T

emf = 10mV

speed = dx / dt = ?

solution

emf = N dΦ / dt

Φ = BA

A =  2 pi R x

R = D / 2 = 0.014 / 2 = 0.007

emf = N d ( B 2 pi R x ) / dt

emf = N B 2 pi R dx / dt

and dx / dt = speed

speed = emf / N B 2 pi R

speed = 10 * 10 ^ -3 / ( 100 * 0.010 * 2 * 3.142 * 0.007)

speed = 10 * 10 ^ -3 / ( 0.043988 )

speed = 0.227 m/s

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ε = vLB

v - velocity = ?

ε - emf = 10mV = 0.01V

B - magnetic field = 0.010 T

L - length of wire = find

Find L

N - turns of wire = 100

d = diameter = 1.4 cm = 0.014 m

L = circumference of 1 turn of wire * # of turns of wire

L = 2πr * N

L = πdN

L = π * 0.014 m * 100

L = 1.4π m

Return to main equation

ε = vLB

[tex]v = \frac{\epsilon}{LB}[/tex]

[tex]v = \frac{0.01}{(1.4\pi)*(0.010)}[/tex]

v = 0.227 m/s