(A) With 268.94 N tension must she stretch it.
26% increase in tension is needed to increase the frequency from 65.4 Hz to 73.4 Hz, corresponding to a rise in pitch from C to D.
Part (A)
Fundamental frequency =f0= 65.4 Hz.
The length of the vibrating portion of the string = l = 0.615 m
Mass= m = 14.8 g
We know, \(f_0 = \frac{v}{2l}\)
So, the value of v will be 65.4*2*0.615 = 80.442 m/s
As, We know,
\(T=\frac{v^2}{\frac{m}{l}}\)
So, the value of tension will be: \(\frac{80.442^2}{\frac{14.8}{0.615}}=\frac{6470.91}{24.06}=268.94\:N\)
Part (B)
Fundamental frequency =f0= 73.4 Hz.
The length of the vibrating portion of the string = l = 0.615 m
Mass= m = 14.8 g
We know, \(f_0 = \frac{v}{2l}\)
So, the value of v will be 73.4*2*0.615 = 90.282 m/s
As, We know,
\(T=\frac{v^2}{\frac{m}{l}}\)
So, the value of tension will be: \(\frac{90.282^2}{\frac{14.8}{0.615}}=\frac{8150.8395}{24.06}=338.77\:N\)
So, the percentage increase in tension will be \(\frac{338.77-268.94}{268.94}\times 100\%=25.96\% \approx 26\%\)
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The complete question should be:
a cellist tunes the c-string of her instrument to a fundamental frequency of 65.4 hz. the vibrating portion of the string is 0.615 m long and has a mass of 14.8 g .
Part A: With what tension must she stretch it?
Part B
What percent increase in tension is needed to increase the frequency from 65.4 Hz to 73.4 Hz, corresponding to a rise in pitch from C to D?
Pls explain ........................
Option A that is 8.6 x 10^4 volt is the potential difference between a point 0.79 mm from a charge of 7.6nC and a point of infinity.
What is potential difference how it is calculated out to be so?Potential difference can be stated as the difference of electrical potential between two points stated.Here in this question is given the charge 7.6 nC that is 7.6 x 10^-9 and the radius 0.79 mm that is 0.79 x 10^-3 m.Here the potential difference can be calculated out to be by the equation V = k x Q /R , where k is proportionality constant given in equation.V= 8.99 x 10^9 x 7.6x 10^-9 / 0.79 x 10^-3 , putting all the values in the equation.Finally the potential difference is calculate out to be 8.65 x 10^4 volts.To know more about potential difference visit:
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What is the relevant similarity in the following argument?
"If a single cell, under appropriate conditions, becomes a person in the space of a few years, there can surely be no difficulty in understanding how, under appropriate conditions, a cell may, in the course of untold millions of years, give origin to the human race"
a.
The human race is composed of many humans in the same way a human is composed of many cells
b.
understanding human biology is difficult and understanding the existence of the human race is difficult
c.
both involve biological processes of great complexity taking place under “appropriate conditions” and commencing with a single cell
d.
a person starts from a single cell and an animal life starts from a single cell
A driver of a car going 40 m/s (approx. 90 mph) suddenly sees the lights of a barrier 40.0 m ahead. It takes the driver 0.75 s before he applies the brakes (this is known as reaction time). Once he does begin to break the decelerates at a rate of 10.0 m/s^2 (Be careful of signs). Does he hit the barrier?
Answer:
Explanation:
Distance of barrier = 40 m
Distance covered during reaction time = .75 x 40 = 30 m .
distance covered during deceleration can be calculated as follows .
v² = u² - 2 a s
0 = 40² - 2 x 10 x s
s = 80 m
Total distance covered before coming to rest = 30 + 80 = 110 m
Distance of barrier = 40 m , so it will hit the barrier .
PLS HELP!! Our eyes perceive colors because of differences in which of the following properties of light?
Amplitude
Brightness
Wavelength
Source
Answer:
Your answer is wavelength
. How many meters away is a cliff if an echo is heard 0.5 s after the original sound? ( Assume that sound travels at 343 m/s on that day
Answer:
171.5 m
Explanation:
To find the distance, speed x time
342 x 0.5
171.5 m
Hope this helped!
You pull horizontally on a 40-kg crate with a force of 650 N and the friction force on the crate is 250 N. The acceleration of the crate is
a. 2 m/s2
b. 4 m/s2
c. 10 m/s2
d. 14 m/s2
Answer:
Below
Explanation:
Net force causing the crate to accelerate will be 650 - friction = 400 N
F = ma
400 = 40 a shows a = 10 m/s^2
A contractor is pushing a stove across a kitchen floor with a constant velocity of 18 cm/s [fwd]. The contractor is exerting a constant horizontal force of 85 N [fwd]. The force of gravity on the stove is 447 N [down].
Determine the normal force (FN ) and the force of friction (Ff ) acting on the stove.
Determine the total force applied by the floor (Ffloor) on the stove.
Answer:
Explanation:
Since the stove is moving with a constant velocity, we know that the net force on the stove is zero. Therefore, the force of friction acting on the stove must be equal in magnitude and opposite in direction to the horizontal force being applied by the contractor. We can use Newton's second law to solve for the normal force and force of friction:
ΣF = ma
where ΣF is the net force, m is the mass of the stove, and a is the acceleration of the stove (which is zero in this case).
First, we need to convert the velocity to m/s and the forces to Newtons (N):
18 cm/s = 0.18 m/s
85 N [fwd] - force applied by contractor
447 N [down] - force of gravity on the stove
Now we can solve for the normal force:
ΣFy = 0 (since the stove is not accelerating in the y-direction)
FN - 447 N = 0
FN = 447 N
Therefore, the normal force acting on the stove is 447 N.
Next, we can solve for the force of friction:
ΣFx = 0 (since the stove is moving at a constant velocity)
Ff - 85 N = 0
Ff = 85 N [bkwd]
Therefore, the force of friction acting on the stove is 85 N [bkwd].
Finally, we can solve for the total force applied by the floor:
ΣF = ma = 0 (since the stove is not accelerating)
Ffloor - 85 N - 447 N = 0
Ffloor = 532 N [up]
Therefore, the total force applied by the floor on the stove is 532 N [up].
You skip north for 12 minutes to your best friend's house that is 1.5 kilometers away. What is your average velocity?
Answer:
The average velocity is 7.5 km/h
Explanation:
Let's convert minutes to hours so our answer can be given in a common units of km/hour:
12 minutes = 12/60 hours = 0.2 hours
Now we estimate the average velocity calculating the distance travelled over the time it took:
1.5 / 0.2 km/h = 7.5 km/h
Which of the following describes an electric insulator?
O A. A material that has a low resistance and prevents charges from
moving freely
B. A material that has a low resistance and allows charges to move
freely
C. A material that has a high resistance and prevents charges from
moving freely
D. A material that has a high resistance and allows charges to move
freely
The following that describes an electric insulator are :
C. A material that has a high resistance and prevents charges from moving freely.
The following that describes an electric insulator is a material that has a high resistance and prevents charges from moving freely. The conductors exhibit low resistance, which allows for the flow of current through it freely.Thus, the correct answer is C.
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OBJECT A 24 lb. turkey on Saturn UNIVERSAL GRAVITATION CONSTANT-G 6.673x10 M₁ = mass of planet (in kg) -11 Nm² 5.683x10²6 kg kg 26 M₂= object (in kg) = mass of d = distance between the center of 2 objects (in m) (sometimes we use "r" for radius) 58,232 km SHOW WORK F, gray = force due to gravity (in N)
The force due to gravity acting on a 24 lb. turkey on Saturn is approximately 1.253 N.
What is the gravitational force?
To calculate the force due to gravity (F) acting on the 24 lb. turkey on Saturn, we need to use the formula for the gravitational force:
F = G * M₁ * M₂ / d²
where;
G is the universal gravitational constant, M₁ is the mass of Saturn, M₂ is the mass of the turkey, and d is the distance between the center of Saturn and the turkey.First, we need to convert the mass of the turkey from pounds to kilograms:
24 lb = 10.89 kg
Next, we need to convert the distance between Saturn and the turkey from kilometers to meters:
58,232 km = 5.8232 x 10⁷ m
Now we can substitute the values into the formula:
F = 6.673 x 10^-11 Nm²/kg² * 5.683 x 10²⁴ kg * 10.89 kg / (5.8232 x 10⁷ m)²
Simplifying this expression, we get:
F = 1.253 N
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For the arm shown in the picture below, calculate the torque, and the find the “torque load” assuming a current limit of 2 amps. Use the motor specification given in the table and the formulas to solve the problem. Video how your solved the problem (using a smart phone) and submit it to this assignment.
Explanation
the torque load is given by:
\(\begin{gathered} Torque\text{ load=}\frac{(\text{current limit-fre}e\text{current)}\cdot\text{stall torque}}{(\text{stall current-}fre\text{ current)}} \\ \end{gathered}\)hence
Step 1
Torque load
a)Let
\(\begin{gathered} free\text{ sp}eed=100\text{ RPM} \\ Stalltorque=1.67\text{ N}\cdot m \\ Stall\text{ current=}4.8\text{ Amps} \\ fre\text{ current=}0.37\text{ Amps} \\ \text{Current limit= 2 Amps} \end{gathered}\)b)now, replace in the formula
\(\begin{gathered} Torque\text{ load=}\frac{(\text{current limit-fre}e\text{ current)}\cdot\text{stall torque}}{(\text{stall current-}fre\text{ current)}} \\ Torque\text{ load=}\frac{(2\text{ Amps-}0.37\text{ amps)}\cdot1.67\text{ N}\cdot m}{(4.8\text{ Amps-}0.37\text{ Amps)}} \\ Torque\text{ load=}\frac{(1.63\text{amps)}\cdot1.67\text{ N}\cdot m}{(4.43\text{ Amps)}} \\ Torque\text{ load=0.61 N}\cdot m \end{gathered}\)therefore, the answer is
torque load: 0.61 N*m
Step 2
Torque:
the torque is given by the expression
\(\text{Torque}=\text{ force}\cdot\text{ distance}\)so , after checking the imagen
let
distance=0.5 m
force=30 N
now,replace and calculate
\(\begin{gathered} \text{Torque}=\text{ force}\cdot\text{ distance} \\ \text{Torque = 30 N}\cdot0.5\text{ m} \\ \text{Torque =}15\text{ N}\cdot m \end{gathered}\)so
torque: 15 N*m
I hope this helps you
Which statement about RNA polymerase is NOT true?
RNA polymerase reads a template strand of DNA 5' to 3'
RNA polymerase binds to a promoter region to initiate transcription
RNA polymerase adds a ribonucleotide to the 3' end of a growing RNA molecule
During transcription of a gene, RNA polymerase reads only one strand of DNA
Please explain!
Answer:
RNA polymerase reads a template strand of DNA 5' to 3'
Explanation:
RNA polymerase is the enzyme accountable for the transcription of the DNA. It shows one coast of the DNA and transcribed within the RNA. It combines the nucleotide to the 3' conclusion of the expanding series of the RNA. It commences the method by connecting to the promoter area of the gene. The enzyme increases nucleotide, not ribonucleotide.
Therefore, A. RNA polymerase reads a template strand of DNA 5' to 3' is false.
Answer:
RNA polymerase reads a template strand of DNA 5' to 3'.
Explanation:
RNA synthesis is less processive during elongation than during initiation. Synthesis begins with the polymerase binding two rNTP molecules. The polymerase frequently releases the nascent transcript before it reaches 8-10 nucleotides in length.
The half-life of a radioactive isotope is 210 d. How many days would it take for the decay rate of a sample of this isotope to fall to 0.58 of its initial rate?
It would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.
1. The decay rate of a radioactive isotope is proportional to the number of radioactive atoms present in the sample at any given time.
2. The decay rate can be expressed as a function of time using the formula: R(t) = R₀ * \(e^{(-\lambda t\)), where R(t) is the decay rate at time t, R₀ is the initial decay rate, λ is the decay constant, and e is the base of the natural logarithm.
3. The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 210 days.
4. Using the half-life, we can find the decay constant (λ) using the formula: λ = ln(2) / T₁/₂, where ln(2) is the natural logarithm of 2 and T₁/₂ is the half-life.
5. Substituting the given half-life into the formula, we have: λ = ln(2) / 210.
6. Now, we need to find the time it takes for the decay rate to fall to 0.58 of its initial rate. Let's call this time "t".
7. Using the formula for the decay rate, we can write: 0.58 * R₀ = R₀ * e^(-λt).
8. Simplifying the equation, we get: 0.58 = \(e^{(-\lambda t\)).
9. Taking the natural logarithm of both sides, we have: ln(0.58) = -λt.
10. Substituting the value of λ from step 5, we get: ln(0.58) = -(ln(2) / 210) * t.
11. Solving for t, we have: t = (ln(0.58) * 210) / ln(2).
12. Evaluating the expression, we find: t ≈ 546.
13. Therefore, it would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.
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a piano dropped from a plane in the air. As it falls, upward force of air resistance gets greater as the piano picks up speed eventually, the resistance forces equal to the downward force of gravity. the piano now
Answer:
When the piano is dropped, the first force acting on it will be the gravitational force, that accelerates the piano at 9.8m/s^2 downwards.
As the piano accelerates, the velocity increases, now appears other force, the air resistance, that opposes to the motion of the piano.
As the velocity of the piano increases, also does the force that the air applies on the piano.
There is a point where the velocity of the piano is such that the air resistance is equal in magnitude, but in the opposite direction, to the force of gravity.
Then the net force on the piano is zero, which means that there is no acceleration, so the piano will keep falling down at constant velocity after this point.
What are some guidelines for preventing quackery and fraud when shopping? Select
all that appy.
Select 4 correct answer(s)
Be suspicious of a sales pitch that promises results too good to be true.
Be wary of advisors who sell products.What are some guidelines for preventing quackery and fraud when shopping? Select
all that appy.
Select 4 correct answer(s)
-Be suspicious of a sales pitch that promises results too good to be true.
-Be wary of advisors who sell products. -Don’t do any research before shopping. -Be cautious of mail-order and internet sales. -Be wary of product claims. -If a celebrity or athlete promotes it-it must be good
The steps/guidelines for preventing quackery and fraud when shopping are :
Be suspicious of a sales pitch that promises results too good to be trueBe cautious of mail-order and internet sales Be wary of product claims Be wary of advisors who sell products What is Quackery and FraudQuackery involves the claim of knowledge and provision of a fake and dishonest service to unsuspecting customers or clients and this is very common in medicine.
Fraud is the false representation of a material or service in order to cause loss of money or pain to an unsuspecting client or customer. some steps to prevent fraud are as follows :
If a sales pitch is too good to be true one should keep off from such product/service.when making internet sales and mail-order customers should be careful as there are a lot of imposters on the internet.Hence we can conclude that The steps/guidelines for preventing quackery and fraud when shopping are as listed above
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A dog and a sledge are on the frictionless ice of a frozen lake, 12.2 m apart but connected
by a rope of negligible mass. The dog exerts a certain horizontal force (N) on the rope. If
magnitudes of the sledge and the dog accelerations are 0.5 m/s2 and 0.2 m/s2,
respectively. How far from the dog's initial position (m) do they meet?
Answer:
x₁ = 3.481 m
Explanation:
In this exercise the acceleration of the dog and the sled are given, for which we can use the kinematic relations.
Let's start by fixing a reference system located on the sled and suppose that it moves to the right, the sled acceleration a₁ = 0.2 m / s, the dog is on the other side of the rope, so if the acceleration is a₂ = -0.5 m / s2, the negative sign indicates that it is moving to the left.
The initial position of the sled is x₁₀ = 0 and the initial position of the dog is x₂₀ = 12.2 m, let's write the expressions for the position
x₁ = x₁₀ + v₁₀ t + ½ a₁ t²
x₂ = x₂₀ + v₂₀ t + ½ a₂ t²
in this case the two bodies start from rest so their initial velocities are zero
we substitute the values
x₁ = 0 + 0 + ½ (0.2) t²
x₂ = 12.2 + 0 + ½ (-0.5) t²
at the point where the two meet, the position is the same
x₁ = x₂
½ 0.2 t² = 12.2 - ½ 0.5 t²
(0.1 + 0.25) t² = 12.2
t = \(\sqrt{ \frac{12.2}{0.35} }\)
t = 5.9 s
we look for the position of the sled (subscript 1)
x₁ = ½ 0.2 5.9²
x₁ = 3.481 m
How much is 813 in grams
I Math
To convert 813 into grams if it is already in grams, then the value remains as 813 grams. If it is in pounds, 813 pounds would be approximately 368,646.696 grams. If it is in kilograms, 813 kilograms would be equal to 813,000 grams.
To convert 813 into grams, we need to know the unit of measurement you're referring to. Grams are typically used to measure the weight of objects, but without additional context, it's difficult to provide an accurate answer.
If you are referring to 813 grams, then the conversion is straightforward, as it is already in grams.
If you are referring to another unit, such as pounds or kilograms, we can convert it to grams:
If you meant 813 pounds, one pound is approximately equal to 453.592 grams. Therefore, 813 pounds would be approximately 368,646.696 grams.
If you meant 813 kilograms, one kilogram is equal to 1,000 grams. Therefore, 813 kilograms would be equal to 813,000 grams.
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drawing shows a force vector that has a magnitude of 475 newtons.
Find the
(a) X,
(b) y, and
(c) z components of the vector.
X, Y, and Z components of the vector are 398, 384 and 279 resp.
Vector is a physical quantity which has both magnitude and direction. Vector A can be written as A = a₁i + a₂j + a₃k where a₁, a₂, a₃ are components along X, Y, Z axis resp. and i,j,k, are the unit vectors along X,Y,Z axis resp.
In this figure
vector F is at angle 36° from y axis, hence
x = Fcos33 = 475cos33 = 398 N
y = Fcos36 = 475cos36 = 384 N
z = Fsin36 = 475sin36 = 279 N
The vector can be written as
F = 398i + 384j + 279k
Hence x, y and z components of this force is 398, 384 and 279 resp.
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(6) Consider water flowing through a nozzle as shown in the figure below. Determine the height h (cm) if the gauge pressure at A is 34.5 kPa. A 61 cm ma B -Water rhol 1000 kg/m³ Flow Open to atmosphere Mercury rho2- 13600 kg/m
The height h is 25.91 cm. Pressure can be exerted by liquids, gases, or solids and can be influenced by factors such as temperature, volume, and altitude.
What is Pressure?
Pressure is defined as the force per unit area applied in a direction perpendicular to the surface of an object. It is usually expressed in units such as pascals (Pa), pounds per square inch (psi), or atmospheres (atm).
To solve for the height h, we need to use Bernoulli's equation, which states that the sum of pressure, kinetic energy, and potential energy is constant along a streamline of fluid flow.
At point A, the gauge pressure is 34.5 kPa. Since the flow is open to the atmosphere, we can assume that the absolute pressure at point A is:
P_A = P_atm + P_gauge
= 101.3 kPa + 34.5 kPa
= 135.8 kPa
At point B, the fluid is at rest, so the velocity is zero. Therefore, the kinetic energy term in Bernoulli's equation is zero.
Using the density of water and the density of mercury, we can convert the heights of the water column and the mercury column into pressure terms.
Let h1 be the height of the water column, and h2 be the height of the mercury column. Then, the pressure difference between points A and B is:
ΔP = ρ_water * g * h1 - ρ_mercury * g * h2
where g is the acceleration due to gravity.
Setting the pressures at A and B equal to each other, we have:
P_A + ΔP = P_B
Solving for h1, we get:
h1 = (P_B - P_A + ρ_mercury * g * h2) / (ρ_water * g)
The pressure at point B is atmospheric pressure, which is 101.3 kPa.
Plugging in the given values, we get:
h1 = (101.3 kPa - 135.8 kPa + 13600 kg/m³ * 9.81 m/s² * h2) / (1000 kg/m³ * 9.81 m/s²)
h1 = (-34.5 kPa + 133137.6 Pa * h2) / 9810 Pa/m
Multiplying both sides by 100 cm/m to convert units, we get:
h1 = (-0.345 m + 13.31376 cm * h2)
Setting h1 = 0 (since we want the height at which the water column stops), we get:
0 = -0.345 m + 13.31376 cm * h2
Solving for h2, we get:
h2 = 0.345 m / (13.31376 cm)
= 25.91 cm
Therefore, the height h at which the water column stops is:
h = h1 + h2
= 0 + 25.91 cm
= 25.91 cm
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The ability of the medium to refract light rays?
Light Density
\(\frak{\fcolorbox{black}{pink}{Black Pink in your area}} \) ~←(>▽<)ノ
1. Which of the following does not affect the resistance of a wire?
a) Length
b) Temperature
c) Usage time
d) Cross-sectional area
2. If a 12V battery is passing current through a resistor with a current of 2A, what is the value of the resistor?
a 24resistance
b) 14resistance
c) 10resistance
d) 6resistance
3. Describe the differences between series and parallel circuits.
4. A circuit contains resistors of 8resistance and 4resistance,what is combined resistance if the resistors are combined:
a) In series
b) In parallel
5. A 0.5A current is passing across three resistors of 8resistance, 4resistance and 12resistance that are linked in series.
What is the potential difference of the circuit?
6. Wire A has a resistance of 24resistance. If wire B is double the length and has a diameter four times as large as wire A, what is the resistance of wire B?
What the answers due in 2 min
Hello ┬┴┬┴┤◕3◕)づ├┬┴┬┴
The answer is 3 m
the gap in between 4s and 6s is 5s
you follow your finger up to the purple like, and follow the purple line in a straight line to the left. It ends at 3m and that is your answer.
Question 2 of 10
Which of the following represents a beta particle?
O A. e
OB. Y
O C. a
O D. He
A taxi hurries with a constant speed of 60 miles per hour. How long will it take to travel a distance of 130 miles
Answer:
2.17 hrs
Explanation:
time = distance / velocity
We know that distance = 130 miles and velocity = 60 miles/h.
t = d / v
t = 130 miles / 60 miles/h
t = 2.17 hrs
It takes about 2.17 hours to travel a distance of 130 miles. Hope this helps, thank you !!
Please help I’m kinda in a rush to get these done
What three forces are always in effect?
Answer:The gravitational force is defined in Uniform Circular Motion and Gravitation, electric force in Electric Charge and Electric Field, magnetic force in Magnetism, and nuclear forces in Radioactivity and Nuclear Physics. On a macroscopic scale, electromagnetism and gravity are the basis for all forces.
Explanation:
Answer:
The gravitational force is defined in Uniform Circular Motion and Gravitation, electric force in Electric Charge and Electric Field, magnetic force in Magnetism, and nuclear forces in Radioactivity and Nuclear Physics. On a macroscopic scale, electromagnetism and gravity are the basis for all forces.
which of the following is an example of a physical change of matter
An example of a physical change of matter is (c) Melting ice.
Explanation: Melting ice is an example of a physical change of matter. When ice melts, it undergoes a change in state from a solid to a liquid, but its chemical composition remains the same. The water molecules in ice rearrange themselves to form liquid water, but no new substances are formed. This change can be reversed by cooling the liquid water to below its freezing point, causing it to solidify back into ice. Physical changes do not involve a change in the chemical identity of the substance, only a change in its physical properties, such as shape, size, or state.
In contrast, options a) Burning wood, b) Digesting food, and d) Rusting iron involve chemical changes. Burning wood involves a chemical reaction where wood reacts with oxygen to produce carbon dioxide, water vapor, and ash. Digesting food involves the breakdown of complex molecules into simpler ones through chemical reactions in the body. Rusting iron is a chemical reaction where iron reacts with oxygen and moisture in the air to form iron oxide.
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Note: The complete question is:
Which of the following is an example of a physical change of matter?
a) Burning wood
b) Digesting food
c) Melting ice
d) Rusting iron
the radiation that is least damaging to humans is
The radiation that is least damaging to humans is non-ionizing radiation.
What is non ionizing radiationNon-ionizing radiation refers to the type of radiation that does not have enough energy to remove tightly bound electrons from atoms or molecules, thus not causing significant damage to biological tissues.
Examples of non ionizing radiation include radio waves, microwaves, visible light and low energy ultraviolet (UV) radiation. while excessive exposure to any form of radiation can have adverse effects, non-ionizing radiation is generally considered to be less harmful compared to ionizing radiation, which includes X-rays and gamma rays.
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IBM has a fast computer that it calls the Blue Gene/L that can do '136.8
teracalculations per second. How many calculations can it do in a microsecond?
Answer:
138.6 megacalculations
Explanation:
This is a pretty straightforward one.
All it needs is to convert the degree of measurement.
Dimensions in physics are attributed names, which state the power to which they're are raised. Just as how
Kilo and Mega means the numbers are raised to the power of 3 and 6 respectively. There also exists the ones that indicates how small, such as milli and micro, which are to the powers of -3 & -6.
The question says the IBM computer calculates at an astonishing 136.8 teracalculations.
Tera in physics means it's raised to the power of 12. Thus, the IBM calculates at an astonishing rate of
136.8*10^12 calculations per second.
We're then asked how many calculations it does in 1 micro second. Like I had highlighted earlier, 1 micro second is 1 raised to the power of -6. Or succinctly put,
1 micro second = 1*10^-6.
If the IBM does
138.6*10^12 = 1 second,
Then it does
x = 1*10^-6 second.
When we cross multiply, we have
138.6*10^12 * 1*10^-6, and that is
138.6*10^6 calculations, or say, 138.6 megacalculations.
The IBM does 138.6 megacalculations in 1 micro second, which is still astonishing, by the way
Two traveling sinusoidal waves are described by the wave functions
Y1 : 4.95sin[π(3.80x-1180t)]
Y2 : 4.95sin[π(3.80x-1180t-0.250)]
Where x , y1 and y2 are in meters and t is in seconds
The wave function of the resultant wave, Y1 + Y2 is Y = 4.95sin[π(3.80x - 1180t - 0.206)].
The wave function Y1 describes a sinusoidal wave with an amplitude of 4.95 meters, a wavelength of λ = 2π/3.8 ≈ 1.65 meters, and a frequency of f = 1180/3.8 ≈ 310 Hz. The phase of the wave is such that the maximum displacement occurs at x = 0 and t = 0, and the wave is moving in the negative x direction.
The wave function Y2 also describes a sinusoidal wave with the same amplitude and wavelength as Y1, but with a phase difference of 0.25 seconds. This means that Y2 is shifted to the left (negative x direction) by a distance of Δx = λΔφ/2π = λ(0.25)/2π ≈ 0.206 meters. The frequency and speed of Y2 are the same as Y1.
To determine the resultant wave Y, we add the two wave functions: Y = Y1 + Y2. Using the trigonometric identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b), we can simplify the expression for Y:
Y = 4.95sin[π(3.80x - 1180t)] + 4.95sin[π(3.80x - 1180t)cos(0.25) + cos(π/2)sin(0.25)]
Y = 4.95sin[π(3.80x - 1180t)] + 4.95sin[π(3.80x - 1180t + 0.25)]
Y = 4.95sin[π(3.80x - 1180t - 0.206)]
The resultant wave Y is a sinusoidal wave with the same amplitude and wavelength as Y1 and Y2, but with a phase shift and a different waveform due to interference. The frequency and speed of Y are also the same as Y1 and Y2.
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-- The given question is incomplete, the complete question is
"Two traveling sinusoidal waves are described by the wave functions
Y1 : 4.95sin[π(3.80x-1180t)]
Y2 : 4.95sin[π(3.80x-1180t-0.250)]
Where x , y1 and y2 are in meters and t is in seconds. Find the wave function of the resultant wave (Y1 + Y2)." --