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^
Determine the unit vector normal to the planeThe 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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1) How many joules of heat are required to raise the temperature of 550 g of water from
12.7 °C to 28.8°C ? Specific heat of liquid water is 4.184 J/g °C.
Answer:
Explanation:
You can use [tex]Q = mc\Delta T=(550)(4.184)(28.8-12.7)=37049.32[/tex] joule.
6. A spring is originally 1.5 m long. It is stretched so that it is 1.8 m long. The spring constant is 50 N/m.
Find the potential energy stored in the spring.
Answer:
PE = 1/2 K X^2
K = 50 N/m
X = .3 m
PE = 1/2 * 50 * .3^2 = 2.25 Joules
Loosing weight without diet require moving to the top of a mountain explain using weight and gravitational force
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:
1. Discuss the two ways by which volcanoes are formed.
2. Does the theory of plate tectonics answer the question on why volcanoes erupt? Support your answer.
3. What are mantle plumes and where are they usually found?
4. What are the gases released by volcanoes in smaller amounts?
5. Extinct volcanoes may be classified as inactive volcanoes but this doest not mean they will not erupt again. Explain this statement.
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:)
A car travel from A to B at a speed of 30km per hour the average speed of the car the whole journey is?
If a lever was a meter long and the fulcrum was placed at 50mm, what would the mechanical advantage be?
Please show work if possible
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
a cup of coffee has a mass of .297 kg if you place this cup of coffee on a desk and let it sit there undisturbed how much force is the desk exerting on it
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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Consider the two-slit interference experiment. Electromagnetic radiation passes through the two slits that are a distance of 0.0170 nm apart. A fourth-order bright fringe forms at an angle of 8.0 degrees relative to the incident beam. What is the wavelength of the light? (1 point)
O 581 nm
O 420 nm
O 789 nm
O 591 nm
Answer:
The answer is 581
Explanation:
I just took the Quick Check and got it right.
An object with a mass of 70.5 kg is placed on a 2-meter strand of metal (with a 2-millimeter radius) hanging from the ceiling. It stretches 1 millimeter. What is this strand made of?
Based on the value of the Young's modulus, the strand of the metal is made of copper.
Young's modulus of the metalThe Young's modulus of the metal is calculated as follows;
E = stress/strain
Stress of the metalThe 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
Strain of the metalThe 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
Young's modulus of the metal
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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list down the general of the office of guardian and tutor
Answer:
legal guardians, the four types: personal guardians, financial guardians, conservators, and pet “guardians”
Which statement about the observed results of the double-slit experiment is true?
O Waves that are out of phase constructively interfere to create bright bands.
O Waves that are in phase destructively interfere to create bright bands.
O Waves that are in phase constructively interfere to create bright bands.
O Waves that are out of phase constructively interfere to create bright bands.
Waves that are in phase constructively interfere to create bright bands was observed in the double-slit experiment.
What is Interference?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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Can someone help with this
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]
theshold frequency ???
Answer:
The threshold frequency is defined as the minimum frequency of the incident radiation below which photoelectric emission or emission of electrons is not possible. The threshold frequency refers to the frequency of light that will cause an electron to dislodge emit from the surface of the metal.
Microphones are used to convert sound vibrations to electrical signals. In one kind of microphone, sound waves move a coil of wire up and down in a magnetic field, as shown in (Figure 1). The coil shown has a diameter of 1.4 cm and has 100 turns; the 0.010 T magnetic field points radially out from the north pole to the south.
If the microphone's emf at some instant is 10 mV , what is the speed of the coil?
The speed of coil of the microphone is 0.227 m/s
What is a Microphones?
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
An electron of mass 9.11 x 10 -31 kg moves with a speed of 0.8725 c. What is its momentum?
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
what are the four things that affect the resistance of a wire? A. length, diameter, material, and temperature B. weight, diameter, material, and temperature C. length, height, material, temperature D. length, weight, material, and temperature
Answer:
A. length, diameter, material, temperature
Objects change their speed and/or direction only when
Answer:
When an external force acts upon them
The maximum kinetic energy of electrons ejected from a sheet of uranium exposed to 250 nm ultraviolet light is 1.33 EV.
What is the work function of the uranium metal? (Planck's constant (h) is 6.626 × 10-34 J∙s, c is 3.0 × 108 m/s, 1 eV = 1.6 × 10-19 J)
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
What is work function?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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The two basic properties of all matter are ______ and ______.
options for first blank
a. length B. volume
options for second blank
a. density B. mass
Answer:
volume , mass
Explanation:
the 3 basic properties of a matter is volume, mass and shape.
Match the missions with their objectives.
NEAR
Lunar Prospector
Deep Impact
SETI
mapping the Moon's surface composition,
looking for possible deposits of polar ice,
and examining the Moon's resources,
structure, and origins
first space probe to orbit and perform
an in-depth Investigation of an asteroid
searching for extraterrestrial life in the universe
probing beneath the surface of a comet to
obtain clues about its internal composition
and structure
Matching the missions with their objectives
NEAR -------> First space probe to orbit and perform an in-depth Investigation of an asteroid. Lunar prospector ----- > mapping the Moon's surface composition,looking for possible deposits of polar ice,and examining the Moon's resources,structure, and origins.Deep Impact -------> probing beneath the surface of a comet to obtain clues about its internal composition and structureSETI -----> searching for extraterrestrial life in the universeThe Mission OverviewThe 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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If a snowboarder’s initial speed is 4 m/s and comes to rest when making it to the upper level. With a slightly greater initial speed of 5 m/s, the snowboarder is moving to the right on the upper level. His final speed in this case is 3 m/s. Suppose this situation is repeated on planet Epsilon, where gravity is less than gravity on earth.
A. Would the height of the hill on Epsilon cause a reduction in speed from 4 m/s to 0 greater than, less than, or equal to the height of the corresponding hill on earth? Explain.
B. Consider the hill on Epsilon discussed in part A. If the initial speed at the bottom of the hill is 5 m/s, will the final speed at the top of the hill be greater than, less than, or equal to 3 m/s? Explain.
(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.
Conservation of mechanical energy
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;
v is the final velocity at upper levelu is the initial velocityhf is final heightg is acceleration due to gravitywhen 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).
Final speedv² = u² - 2ghf
where;
u is the initial speed = 5 m/sg is acceleration due to gravity and its less than 9.8 m/s²v is final speedhf is equal heightSince 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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A dragster's top acceleration is 60 m/s.
If it accelerates for 3 seconds from the
starting line, how fast will it be going?
Answer:
very fast
Explanation:
If you go into a store to buy a digital thermometer and there are 8 instruments of the same brand and model, at the same price, but they indicate different temperature values, explain which one you choose and why.
Answer: I would buy the thermometer with the most features because they all cost the same price so why not you getting more than what you are paying for than buying something the same but with less feature and things it can do for the same price.
Hope this helps :) If so brainliest would mean alot thanks!
Explanation:
A atom in its ground state contains 18 electrons. how many of these electrons are in orbital l=0 values?
What is the centripetal acceleration of 30 kg child standing 5 meters from the center of a
rotating carousel? The carousel is rotating at a linear velocity of 20 m/s.
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
Year
Carbon Dioxide (CO2) in Atmosphere (ppm*)
2010
2011
Copyright © Enginuity Inc.
Copyright © Enginuity Inc.
Global Temperature Change – Student Guide
2012
2013
2014
2015
2016
2017
Answer:
Theres a diagram missing for Q
Explanation:
What is all this?
Could you add a question so I can answer it :)
1. A person walks 20 meters toward the east and then walks 30 meters toward the west. What is the total distance covered? What is the displacement? with explaination
2. What is the average speed of a car that travels 2000 meters in 5 minutes in meters/second? with explaination
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:
Seamus made an electromagnet from an iron nail, a piece of copper wire with three coils spread out across the nail, and a AAA-
sized battery. His magnet attracts only one paper clip, and he wants to boost the power of his magnet to attract at least four paper
clips. What two things can Seamus do to accomplish his goal?
A)
B
Seamus can add batteries to decrease the voltage, and he can decrease the
space between the wire coils.
Seamus can add batteries to increase the voltage, and he can increase the
space between the wire coils,
Seamus can add batteries to increase the voltage, and he can decrease the
space between the wire coils.
Seamus can add batteries to decrease the voltage, and he can increase the
space between the wire coils
D
Seamus can add batteries to increase the voltage, and he can decrease the space between the wire coils to accomplish this goal.
What is Attraction?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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is this right lol i think it is but im not so sure XD
[tex]\bold{Heya!}[/tex]
Yup. your answer is correct!
→ EXPLANATION :-1. just put the numbers in order [tex]^1^6^, ^1^8^,^2^3^,^2^4^,^2^9^,^3^0[/tex]2. Cross off high/low pairs, we left with the numbers :-[tex]23,24.[/tex]
3. Add the leftover numbers.[tex]23 \: + 24 = 47.[/tex]
Divide the sum of 2.[tex]\frac{47}{2} = 23.5[/tex]
Hopefully This Helps ! ~
#LearnWithBrainly
[tex]\underline{Answer :}[/tex]
Jaceysan ~
Answer:
GIVE HIM BRAINLEST
The Empire State Building is about 381m high. If you threw a baseball downward at 25 m/s from the top of the building how fast would it be traveling just before it landed?
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.
