Answer:
d. 3
Explanation:
x = cos(4377π) + 8 sin(750°)
A full circle is 2π radians or 360°.
x = cos(4377π − 4376π) + 8 sin(750° − 720°)
x = cos(π) + 8 sin(30°)
x = -1 + 8 (1/2)
x = 3
The path of an object projected at a 45 degree angle with initial velocity of 80 feet per second is given by the −32 2 function h(x) = (80)2 x + x where x is the horizontal distance traveled and h(x) is the height in feet. Use the TRACE feature of your calculator to determine the height of the object when it has traveled 100 feet away horizontally.
Answer:
The height of the object is 50 feet
Explanation:
Given that:
The path of an object projected at a 45 degree angle with initial velocity of 80 feet per second is given by the function [tex]h (x) =\dfrac{-32}{(80)^2}x^2+x[/tex]
where;
x is the horizontal distance traveled and h(x) is the height in feet.
The objective is to use the TRACE feature of your calculator to determine the height of the object when it has traveled 100 feet away horizontally.
Before then;
If the function [tex]h (x) =\dfrac{-32}{(80)^2}x^2+x[/tex]
and x = 100
then :
[tex]h (x) =\dfrac{-32}{(80)^2}(100)^2+100[/tex]
[tex]h (x) =\dfrac{-32}{6400} \times 10000+100[/tex]
[tex]h (x) =- 0.005 \times 10000+100[/tex]
[tex]h (x) =- 50+100[/tex]
h(x) = 50 feet
Using the TRACE CALCULATOR,
In your Trace calculator;
input Y = X - 32 X^2/(80) this because in the calculator Y denotes h(x)
Now over to the WINDOW
set the window as follows:
Xmin = 0
Xmax = 200
Xsc1 =1
Ymin = 0
Ymax = 50
Ysc = 1
Xres = 1
After that, click on the graph key and an output will display as seen in the image below.
Therefore, the show the value of Y which we earlier said it denotes the h(x) = 50 feet
When submerged in water, the brick appears to have an additional force pushing it ___upward ___downward. This additional force is the buoyant force (B).
Answer:
Therefore, the brick appears to have an additional force pushing it upward.
Explanation:
When a brick is submerged in the water, it has two forces acting upon it. One force is the gravitational force or the weight of the brick, that acts downward. The weight force also acts on the brick when it is not in water. But, in water an additional force acts on the brick. This additional force is named as Buoyant Force. This force is equal to the weight of the water displaced by the brick. And this Buoyant Force acts on the brick in the upward direction. The formula for this force is given as follows:
Buoyant Force = (Density of Water)(Volume of Water Displaced)(g)
Therefore, the brick appears to have an additional force pushing it upward.
Select the correct answer.
Based on the law of conservation of energy, which statement is false?
O A. Energy is lost when machines don't work right.
OB.
We can't add more energy to the universe.
Ос.
We can't destroy energy that exists in the universe.
OD. Energy changes from one form to another.
Answer:A is the correct answer
Explanation:
How does the energy stored in an isolated capacitor change if the potential difference is increased by a factor of six
Answer:
Energy will be reduced by 0.3
Explanation:
Given that E = 1/2 QV
So if V is increased by 6
=> V = E/ 3Q
So the energy will be divided by a factor 1/3 of be reduced by 0.3
A positron and an electron annihilate each other upon colliding, thereby producing energy in the form of two gamma rays. Assuming that both gamma rays have the same energy (since both particles have the same mass), calculate the wavelength of the electromagnetic radiation used in pm. (1 pm = 10⁻¹² m; mass of electron (amu) = 0.000549)
Answer:
2.42631E-13m
Explanation:
First we find the mass defect
Which is m= 0-2(9.10939E-33kg)
= - 1.82188E-30kg
Now find the energy
S
E= mc²=( -18.82188E-30)(2.999792E8)²
= 1.63742E-13J
Thus energy per photon will be
1.63742E-13J/2= 8.18710E-14J
So wavelength is given as
Lambda= hc/E
= (6.62608E-34)(2.997E8)/8.18710J
= 2.42631E-13m
The wavelength of radiation used to annihilate a positron and an electron is required.
The wavelength of the electromagnetic radiation used is 2.42 pm.
The mass of positron and electron are equal
m = Mass = [tex]\dfrac{0.000549}{6.022\times 10^{26}}=9.11\times 10^{-31}\ \text{kg}[/tex]
c = Speed of light = [tex]3\times 10^{8}\ \text{m/s}[/tex]
h = Planck's constant = [tex]6.626\times 10^{-34}\ \text{Js}[/tex]
Total energy in the collision is
[tex]E_T=mc^2+mc_2\\\Rightarrow E_T=2mc^2\\\Rightarrow E_T=2\times 9.11\times 10^{-31}\times (3\times 10^{8})^2\ \text{J}[/tex]
Energy released per photon is
[tex]E=\dfrac{E_T}{2}\\\Rightarrow E=\dfrac{2\times 9.11\times 10^{-31}\times (3\times 10^{8})^2}{2}\\\Rightarrow E=9.11\times 10^{-31}\times (3\times 10^{8})^2\ \text{J}[/tex]
Energy is given by
[tex]E=\dfrac{hc}{\lambda}\\\Rightarrow \lambda=\dfrac{hc}{E}\\\Rightarrow \lambda=\dfrac{6.626\times 10^{-34}\times 3\times 10^8}{9.11\times 10^{-31}\times (3\times 10^{8})^2}\\\Rightarrow \lambda=2.42\times 10^{-12}\ \text{m}=2.42\ \text{pm}[/tex]
The wavelength of the electromagnetic radiation used is 2.42 pm.
Learn more:
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An organ pipe open at both ends has two successive harmonics with frequencies of 220 Hz and 240 Hz. What is the length of the pipe? The speed of sound is 343 m/s in air.
Answer:
The value is [tex]l = 8.58 \ m[/tex]
Explanation:
From the question we are told that
The frequencies of two successive harmonics is [tex]f_ a = 220 \ Hz[/tex] , [tex]f_b = 240 \ Hz[/tex]
The speed of sound in the air is [tex]v = 343 \ m/s[/tex]
Generally a harmonic frequency is mathematically represented as
[tex]f_n = \frac{n * v }{2l}[/tex]
here l is the length of the pipe
n is the order of position of the harmonics
Now since we do not know the order of the given harmonic frequencies but we are told that they are successive then the frequencies can be mathematically represented as
[tex]220 = \frac{n * v}{ 2 l }[/tex]
and
[tex]240 = \frac{ (n+1 ) v }{2l}[/tex]
So
[tex]240 - 220 = \frac{ (n+1 ) v }{2l} - \frac{n * v}{ 2 l }[/tex]
[tex]20 = \frac{v}{2l}[/tex]
=> [tex]l = 8.58 \ m[/tex]
A student attaches a length of nylon fishing line to a fence post. She stretches it out and shakes the end of the rope in her hand back and forth to produce waves on the line. The most efficient way for her to increase the wavelength is to
Answer:
increase the tension on the hose and shake the end fewer times per second.
Explanation:
This is because Tension of the rope is directly proportional to wavelength and inversely proportional to the frequency ( shakes per second) so increasing tension increases wavelength and vice versa
Wavelength= Tension/ frequency
The most efficient way for her to increase the wavelength is to increase the rate of shaking the rope per second.
What is wavelength?Wavelength measures the distance of wave that occur between one crest and another crest.
To increase the wavelength the rope end should be shaked in a number of time per second this will help build up tension in the rope.
Therefore, she should increase the rate of shaking the rope per second.
Learn more on wavelength here,
https://brainly.com/question/10750459
Friction: During a hockey game, a puck is given an initial speed of 10 m/s. It slides 50 m on the horizontal ice before it stops due to friction. What is the coefficient of kinetic friction between the puck and the ice
Answer:
The value is [tex]\mu_k = 0.102 0[/tex]
Explanation:
From the question we are told that
The initial speed is [tex]u = 10 \ m/s[/tex]
The distance traveled is [tex]d = 50 \ m[/tex]
Generally we can obtain the acceleration using the kinetic equation as follows
[tex]v^2 = u^2 + 2as[/tex]
=> [tex]a = \frac{v^2 - u^2 }{ 2s}[/tex]
=> [tex]a = \frac{0^2 - 10^2 }{ 2 * 50 }[/tex]
=> [tex]a = -1 m/s^2[/tex]
The negative sign shows that the pluck is decelerating
The force driving the pluck is mathematically evaluated as
[tex]F = ma[/tex]
This force is also equivalent to the frictional force acting on the pluck
So
[tex]ma = m * g* \mu_k[/tex]
=> [tex]\mu_k = \frac{a}{g}[/tex]
=> [tex]\mu_k = \frac{1}{9.8 }[/tex]
=> [tex]\mu_k = 0.102 0[/tex]
which of the following graphs shows the motion of an object that starts to travel forward, stops for several seconds, and then returns to its original position
Answer:
B
Explanation:
in graph B, you can see that the position increases and remains constant for a while before returning to 0
In a double slit experiment, the intensity of light at the center of the central bright fringe is measured to be 6.2 µW/m2. What is the intensity half
Answer:
I_FWHW = 3.2 μW / m²
Explanation:
In the analysis of optics and electricity a very useful magnitude is the width at half height (FWHW) and the intensity at this height, which is given by
I_FWHW = I₀ / 2
corresponds to the width of the line for this intensity.
In this case they give the maximum intensity for which
I_FWHW = 6.2 / 2
I_FWHW = 3.2 μW / m²
You do not give more data in your exercise, but the most interesting calculation is to find the angle values for which you have this intensity since it is this range is 50% of the energy of the system, have I write the equation for this calculation
I = Io cos² x₁ (sin x / x)²
x₁ = π d sin θ /λ
x = π b sin θ /λ
where d is the separation of the slits and b the width of each slit
A medicine ball has a mass of 6 kg and is thrown with a speed of 4 m/s. What is its kinetic energy?
(24 j ) (48 J )(96 j )( 12j )
none of these
Answer:
[tex] \boxed{\sf Kinetic \ energy \ (KE) = 48 \ J} [/tex]
Given:
Mass (m) = 6 kg
Speed (v) = 4 m/s
To Find:
Kinetic energy (KE)
Explanation:
Formula:
[tex] \boxed{ \bold{\sf KE = \frac{1}{2} m {v}^{2} }}[/tex]
Substituting values of m & v in the equation:
[tex] \sf \implies KE = \frac{1}{2} \times 6 \times {4}^{2} [/tex]
[tex] \sf \implies KE = \frac{1}{ \cancel{2}} \times \cancel{2} \times 3 \times 16[/tex]
[tex] \sf \implies KE =3 \times 16[/tex]
[tex] \sf \implies KE = 48 \: J[/tex]
The wave function for a particle must be normalizable because:________ a. the particle's angular momentum must be conserved. b. the particle cannot be in two places at the same time. c. the particle must be somewhere. d. the particle's momentum must be conserved. e. the particle's charge must be conserved
Answer:
C the particle must be somewhere.
Explanation:
This is because normalization of wave function means the maximum probability of finding a particle in a region is 1. And a Wave function describes the probability of finding a particle in region. Also Since it is a probability distribution, its integral over all space must be 1, explaining that the probability that the particle is somewhere and thus it must integrate to 1, meaning it must be it must be normalizable
A horizontal rope is tied to a 55.0 kg box on frictionless ice. What is the tension in the rope if: The box is at rest
Answer:
T = 0
Explanation:
Given that,
Mass of the box, m = 55 kg
We need to find the tension in the rope if the box is at rest. When the object is at rest, its acceleration is equal to 0. It would mean that the net force equals 0. So, the tension in the rope is equal to 0.
When asked how to create an electromagnet, the best answer would be:
"You can create an electromagnet by applying a direct current to a non–magnetic material in order to create an electromagnetic field."
"You can create an electromagnet by covering a wire with insulation and applying a direct electrical current to the magnet."
"You can create an electromagnet by coiling a ferromagnetic material, wrapping in an insulator, and applying a current to the coil."
"You can create an electromagnet by wrapping an insulated wire around a metal with ferromagnetic properties and applying an electric current."
Answer:
"You can create an electromagnet by wrapping an insulated wire around a metal with ferromagnetic properties and applying an electric current."
Explanation:
An electromagnet is created by coiling a ferromagnetic material with the help of an insulated wire around it and applying a current . Insulated wire carrying current produces magnetic field around it . This field produces magnetic flux in the magnetic material and makes it magnet . When we switch of current , magnetic field ceases to exist and therefore , magnetic material ceases to be a magnet .
Explanation:
Ball A is dropped from the top of a building. At the same instant ball B is thrown vertically upwards from the ground. When the balls collide, they are moving in opposite direction and the speed of A is twice the speed of B. At what fraction of the height of the building did the collision occurs ?
Answer:
y/y₀ = 1/2 + v₀²/(2 g y₀)
Explanation:
This in a kinematics exercise in a mention
ball A.
Since the ball is dropped, its velocity starts at zero, at the meeting point the equation is
[tex]v_{A}^2[/tex]= - 2 g (y₀-y)
ball B
v_{B}^2 = v₀² - 2 g y
we substitute
2v_{B}^2 = -2 g (y₀ -y)
v_{B}^2 = - g y₀ + 2g y
v_{B}^2 = v₀² - 2gy
we have a system of two equations with two unknowns, therefore it can be solved. Let's multiply-by -1 and add
0 = g y₀ + v₀² -2gy
we clear the height
y = (g yo + v₀²) / 2g
y = yo / 2 + v₀² / 2g
In this exercise we assume that the height of the building is known and the initial velocity of ball B
The fraction is
y/yo = 1/2 + v₀²/(2gyo)
Which of the following is not a factor in whether a reaction will spontaneously occur? A. Entropy change of the system B. Enthalpy change of the system C. Temperature of the system D. Pressure change of the system
Answer:
D
Explanation:
pressure change have nothing to do with the spontaneity.
Entropy change , enthalpy change , temperature have roles in deciding spontaneity.
A toy of mass 0.190-kg is undergoing SHM on the end of a horizontal spring with force constant k = 350 N/m . When the toy is a distance 0.0140 m from its equilibrium position, it is observed to have a speed of 0.400 m/s .
A) What is the toy's total energy at any point of its motion?
B) What is the toy's amplitude of the motion?
C) What is the toy's maximum speed during its motion?
Answer
a)0.0495 J
b)0.01681 m
c)0.7218 m/s
Explanation:
Given
Mass of the.toy M = 0.190 kg
force constant k = 350 N/m
Displacement from equilibrium x = 0.0140 m
Speed v = 0.400 m/s
a)What is the toy's total energy at any point of its motion?
The total energy at any point of it's motion can be calculated by adding together both the potential and kinetic energy of the toy, since it's posses potential energy when at rest and kinetic energy at motion
Total energy E = kinetic energy + potential energy
E = ¹/₂mv² + ¹/₂kx²
E = ¹/₂ (0.190)(0.4)² + ¹/₂ (350)(0.0140)²
E = 0.0495 J
Hence,the total energy is 0.0495 J
b) the amplitude of the motion can be calculated using below formula
Let amplitude = A
E = ¹/₂KA²
if we make Amplitude A the subject of the formula we have
A=√(2E/k)
But we have calculated our E up there, our K was given in question then if we substitute we have
A= √(2×0.0495)/350
Ans: 0.01681 m
Hence, our Amplitude is 0.01681 m
c) the the toy's maximum speed during its motion can be calculated using the expression below
Let maximum speed = vmax
E = (1/2)M * vmax^2
If we make vmax the subject of the formula we have
vmax =√(2E/m)
vmax= √(2×0.0495)/0.190
vmax=0.7218 m/s
Hence our vmax is 0.7218 m/s
how far must he mirror mz of the michelson interferometer be moved so that 1600 fringes of laser light move across a line int he field of view
Answer:
The question is not complete. Let me explain Michelson interferometer and how to calculate a question like this.
Answer 4.85 * [tex]10^{-4}[/tex]m
Explanation:
The Michelson Interferometer is an instrument which produces interference fringes by splitting a light beam into two parts, it then recombines them after they have travelled different optical paths.
The formula to measure the minute displacement is Δd=m * λ[tex]_{0}[/tex]/2
where m is the number of fringes passing a given point as the movable plane mirror is moved
and λ[tex]_{0}[/tex] is the monochromatic lamp of wavelength
In the question, m = 1600. Let us assume that the wavelength is 606 nm
Solution
Δd=m * λ[tex]_{0}[/tex]/2
Δd=1600 * 606nm/2 = 1600 * 303nm = 484800nm
We convert the nm to m (nm / [tex]10^{-9}[/tex])
4.85 * [tex]10^{-4}[/tex]m
What is the main reason why would a fan be expected to warm the air that passes through it? A or B?
A. The fan does work on the air in the room leading to an increase in its thermal energy and temperature.
B.The fan transfers heat to the air in the room leading to an increase in its thermal energy and temperature.
Answer:
A. The fan does work on the air in the room leading to an increase in its thermal energy and temperature.
Explanation:
Fans move fluid, typically a gas, such as air, through a room or an enclosure. A fan consists of a rotating arrangement of vanes or blades (impeller), which acts on the air. The action of the impeller does work on the fan by compressing and moving the air forward, doing work on it in the process. The work done on the fan leads to an increase in the thermal energy of the air.
Cassidy walks 1 mile then turns 90 degrees and walks 2 miles Distance:Displacement:
Explanation:
The total displacement is 3 miles
What is displacement?
Simply put it is the sum total of the changes in position of an object from it initial position to it final position, It is a vector quantity and has a direction and magnitude.
In our example the displacement the total points of movement can be annotated as
From A to B to C
From A to B= 1 mile
From B to C= 1 miles
Displacement is 1 + 2= 3 miles
What is the magnitude of the momentum of a 33 g sparrow flying with a speed of 8.7 m/s?
Answer:
0.2871 kg m/s
Explanation:
p = mv
convert 33g into kg (0.033)
mulitply byt 8.7 to get 0.2871
Silver has a work function of 4.5 eV . Part A What is the longest wavelength of light that will release an electron from a silver surface
Answer:
λ = 2.7608 x 10⁻⁷ m = 276.08 nm
Explanation:
The work function of a metallic surface is the minimum amount of photon energy required to release the photo-electrons from the surface of metal. The work function is given by the following formula:
Work Function = hc/λ
where,
Work Function = (4.5 eV)(1.6 x 10⁻¹⁹ J/1 eV) = 7.2 x 10⁻¹⁹ J
h = Plank's Constant = 6.626 x 10⁻³⁴ J.s
c = speed of light = 3 x 10⁸ m/s
λ = longest wavelength capable of releasing electron.
Therefore,
7.2 x 10⁻¹⁹ J = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/λ
λ = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(7.2 x 10⁻¹⁹ J)
λ = 2.7608 x 10⁻⁷ m = 276.08 nm
If a ball is accelerating down through the air with no horizontal motion, what must be true about the net forces acting on the ball? (a) The net force on the ball is directed upward. (b) The net force on the ball is zero. (c) The gravitational force is greater than the drag. (d) The drag is greater than the gravitational force.
Answer:
The net force on the ball is zero.
Explanation:
The net force and the acceleration on the falling skydiver is upward. An upward net force on a downward falling object would cause that object to slow down. The skydiver thus slows down. As the speed decreases, the amount of air resistance also decreases until once more the skydiver reaches a terminal velocity.A force can cause a resting object, or it can accelerate a moving object by changing the object's speed or direction. When the forces on an object are balanced, the net force is zero and there is no change in the object's motion. When an unbalanced force acts on an object, the object accelerates.
What is the power in a circuit that has a current of 12 amps and a resistance of 100 ohms? a. 14,400 watts b. 8.3 watts c. 144 watts d. 1200 watts
Answer:
a. 14,400 Watts
Explanation:
Power is current times voltage.
P = IV
Voltage is current times resistance.
V = IR
Substitute:
P = I²R
P = (12 A)² (100 Ω)
P = 14,400 W
A train is travelling along a straight track at constant velocity from Western Station to Eastern station. The mile markers increase towards the east. A passenger notices that, at mile marker 25, the reading on this stopwatch is 15 minutes, and at mile marker 60, the reading on this stopwatch is 45 minutes. What is the velocity of the train in meters per second
Answer:
Explanation:
Displacement of train = 60 - 25 = 35 mile
= 35 x 1.6 = 56 km
duration of time = 45 - 15 = 30 minutes
= 30 x 60 = 1800 s
velocity of train = displacement / time
= 56 / 1800 = .03111 km /s
= 31.111 m / s
3.60×10^23 nitrogen molecules collide with a 16.0 cm^2 wall each second. Assume that the molecules all travel with a speed of 450 m/s and strike the wall head on. What is the pressure on the wall?
Answer:
The pressure on the wall is 9416.25 N/m²
Explanation:
Please see the attachments below
A diffraction-limited lens can focus light to a 10-μ m-diameter spot on a screen. Do the following actions make the spot diameter larger, smaller, or leave it unchanged? a. Decreasing the wavelength of light: b. Decreasing the lens diameter c. Decreasing the focal length: d. Decreasing the lens-to-screen distance:
Answer:
a) the size of the sport DECREASES , b)the spot size is increased
c) it has no effect and d) spot size DECREASES
Explanation:
The expression for constructive interference in diffraction is
a sin θ = m λ
the chaff of the spot is given by the minimum interference m = 1
a sin θ = λ
let's use trigonometry to find the angle
tan λ= y / L
tan θ = sin θ / cos t = sin θ
sin θ = y / L
a y / L = lam
in the case of materials with circular dome, the problem must result in polar coordinates, with which a numerical constant is introduced
y = 1.22 L / a lam
let's analyze each electrode action in this equation
a) Decrease lam
y ’= 1.22 L / a lm2
lam2 <lamo
y '<y
therefore the size of the sport DECREASES
b) decreases the lens diameter
a '<a
y ’= 1.22 L / a’ lam
y '> y
the spot size is increased
c) Decrease the focal length
The expression does not depend on the focal length, so it has no effect
d) decrease in L
y ’= 1.22 L’ / a lam
spot size DECREASES
A toy car travels at 5.3 m/s. The car travels a distance of 17.8 m. How long did it
take to travel that distance?
Explanation:
Assuming constant speed:
Distance = speed × time
17.8 m = (5.3 m/s) t
t = 3.36 s
According to the chart, one gram of copper and
gram(s) of gold
would change their temperatures by approximately the same amount by
adding heat to them.
A) one
B) two
C) three
D) four
Answer:
C) three
Explanation:
Let gram of gold required be m . Let temperature change in both be Δ t .
heat absorbed = mass x specific heat x change in temperature
for copper
heat absorbed = 1 x .385 x Δt
for gold
heat absorbed = m x .129 x Δt
So
m x .129 x Δt = 1 x .385 x Δt
m = 2.98
= 3 g approximately .
A gas is compressed by an isothermal process that decreases its volume by a factor of 2. In this process, the pressure:________
a. Does not change
b. Increases by a factor of less than 2.
c. Increases by a factor of 2.
d. Increases by a factor of more than 2.
Answer:
In this process, the pressure increases by a factor of 2.
Explanation:
For an isothermal process, the temperature remains constant throughout the process.
Also, PV = constant
It means that there is an inverse relationship between pressure and volume of the gas.
If the volume is decreased by a factor of 2, the pressure increases by a factor of 2. Hence, the correct option is (c).